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:heavy_check_mark: verify/LibraryChecker/graph/tree/PointSetTreePathCompositeSumFixed.test.cpp

Depends on

Code

#include "../../../../atcoder/modint.hpp"
#include "../../../../template/template.hpp"
using namespace atcoder;
using mint = modint998244353;
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root"
#include "../../../../graph/tree/TreeDPPointSet.hpp"

vector<mint> A, eb, ec;

struct Path {
  mint a, b, g, d;
  Path(mint a = 1, mint b = 0, mint g = 0, mint d = 0) : a(a), b(b), g(g), d(d) {}
};

Path compress(const Path& p, const Path& c) {
  return Path(p.a * c.a, c.a * p.b + c.b, c.a * p.g + c.b * p.d + c.g, c.d + p.d);
}

struct Point {
  mint sum;
  mint cnt;
  Point(mint sum = 0, mint cnt = 0) : sum(sum), cnt(cnt) {}
};

Point point_e() {
  return {0, 0};
}

Path path_e() {
  return Path();
}

Point rake(const Point& a, const Point& b) {
  return Point(a.sum + b.sum, a.cnt + b.cnt);
}

Path add_v(int v, Point p) {
  mint B = eb[v];
  mint C = ec[v];
  return Path(B, C, B * (p.sum + A[v]) + C * (p.cnt + 1), p.cnt + 1);
}

Path vertex(int v) {
  mint B = eb[v];
  mint C = ec[v];
  return Path(B, C, B * A[v] + C, 1);
}

Point add_e(Path p) {
  return Point(p.g, p.d);
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  int n, q;
  in(n, q);
  A.assign(n, 0);
  eb.assign(n, 1);
  ec.assign(n, 0);

  rep(i, n) {
    lint x;
    in(x);
    A[i] = x;
  }

  hld<Path, compress, path_e, Point, rake, point_e, add_v, add_e, vertex> t(n);

  vector<int> U(n - 1), V(n - 1);
  vector<mint> B(n - 1), C(n - 1);

  vector<vector<pair<int, int>>> g(n);

  rep(e, n - 1) {
    int u, v;
    lint b, c;
    in(u, v, b, c);
    U[e] = u;
    V[e] = v;
    B[e] = mint(b);
    C[e] = mint(c);
    t.add_edge(u, v);
    g[u].push_back({v, e});
    g[v].push_back({u, e});
  }

  vector<int> par(n, -1);
  vector<int> par_e(n, -1);
  vector<int> chi_e(n - 1, -1);

  queue<int> que;
  par[0] = -2;
  que.push(0);
  while (!que.empty()) {
    int v = que.front();
    que.pop();
    for (auto [to, e] : g[v]) {
      if (par[to] != -1) continue;
      par[to] = v;
      par_e[to] = e;
      chi_e[e] = to;
      que.push(to);
    }
  }
  eb[0] = 1;
  ec[0] = 0;
  rep(i, 1, n) {
    int e = par_e[i];
    eb[i] = B[e];
    ec[i] = C[e];
  }

  t.build(0);

  rep(i, q) {
    int com;
    in(com);
    if (com == 0) {
      int w;
      lint x;
      in(w, x);
      A[w] = x;
      t.set(w);
    } else {
      int e;
      lint y, z;
      in(e, y, z);
      int ch = chi_e[e];
      eb[ch] = y;
      ec[ch] = z;
      t.set(ch);
    }
    out(add_e(t.tree_dp()).sum.val());
  }
}
#line 1 "atcoder/modint.hpp"



#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

#line 1 "atcoder/internal_math.hpp"



#include <utility>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned long long y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder


#line 1 "atcoder/internal_type_traits.hpp"



#line 7 "atcoder/internal_type_traits.hpp"

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder


#line 14 "atcoder/modint.hpp"

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder


#line 2 "template/template.hpp"
#pragma region Macros
#include <bits/stdc++.h>
#include <tr2/dynamic_bitset>

using namespace std;
using namespace tr2;
using lint = long long;
using ull = unsigned long long;
using ld = long double;
using int128 = __int128_t;
#define all(x) (x).begin(), (x).end()
#define uniqv(v) v.erase(unique(all(v)), v.end())
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP1(i, n) for (auto i = std::decay_t<decltype(n)>{}; (i) != (n); ++(i))
#define REP2(i, l, r) for (auto i = (l); (i) != (r); ++(i))
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define logfixed(x) cout << fixed << setprecision(10) << x << endl;

ostream &operator<<(ostream &dest, __int128_t value) {
  ostream::sentry s(dest);
  if (s) {
    __uint128_t tmp = value < 0 ? -value : value;
    char buffer[128];
    char *d = end(buffer);
    do {
      --d;
      *d = "0123456789"[tmp % 10];
      tmp /= 10;
    } while (tmp != 0);
    if (value < 0) {
      --d;
      *d = '-';
    }
    int len = end(buffer) - d;
    if (dest.rdbuf()->sputn(d, len) != len) {
      dest.setstate(ios_base::badbit);
    }
  }
  return dest;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != (int)v.size() ? " " : "");
  }
  return os;
}

template <typename T>
ostream &operator<<(ostream &os, const set<T> &set_var) {
  for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
    os << *itr;
    ++itr;
    if (itr != set_var.end()) os << " ";
    itr--;
  }
  return os;
}

template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &set_var) {
  for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
    os << *itr;
    ++itr;
    if (itr != set_var.end()) os << " ";
    itr--;
  }
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
  for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
    os << itr->first << " -> " << itr->second << "\n";
  }
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const unordered_map<T, U> &map_var) {
  for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
    os << itr->first << " -> " << itr->second << "\n";
  }
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &pair_var) {
  os << pair_var.first << " " << pair_var.second;
  return os;
}

void out() { cout << '\n'; }
template <class T, class... Ts>
void out(const T &a, const Ts &...b) {
  cout << a;
  (cout << ... << (cout << ' ', b));
  cout << '\n';
}

void outf() { cout << '\n'; }
template <class T, class... Ts>
void outf(const T &a, const Ts &...b) {
  cout << fixed << setprecision(14) << a;
  (cout << ... << (cout << ' ', b));
  cout << '\n';
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

inline void in(void) { return; }
template <typename First, typename... Rest>
void in(First &first, Rest &...rest) {
  cin >> first;
  in(rest...);
  return;
}

template <typename T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

vector<lint> dx8 = {1, 1, 0, -1, -1, -1, 0, 1};
vector<lint> dy8 = {0, 1, 1, 1, 0, -1, -1, -1};
vector<lint> dx4 = {1, 0, -1, 0};
vector<lint> dy4 = {0, 1, 0, -1};

#pragma endregion
#line 3 "verify/LibraryChecker/graph/tree/PointSetTreePathCompositeSumFixed.test.cpp"
using namespace atcoder;
using mint = modint998244353;
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root"
#line 2 "data-structure/segment-tree/SegmentTree.hpp"
template <class S, auto op, auto e>
struct segtree {
 private:
  unsigned int seg_bit_ceil(unsigned int n) {
    unsigned int x = 1;
    while (x < (unsigned int)(n)) x *= 2;
    return x;
  }

 public:
  static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
                "op must work as S(S, S)");
  static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
                "e must work as S()");
  segtree() : segtree(0) {}
  explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
  explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
    size = (int)seg_bit_ceil((unsigned int)(_n));
    log = __builtin_ctz((unsigned int)size);
    d = std::vector<S>(2 * size, e());
    for (int i = 0; i < _n; i++) d[size + i] = v[i];
    for (int i = size - 1; i >= 1; i--) {
      update(i);
    }
  }

  void set(int p, S x) {
    assert(0 <= p && p < _n);
    p += size;
    d[p] = x;
    for (int i = 1; i <= log; i++) update(p >> i);
  }

  S get(int p) const {
    assert(0 <= p && p < _n);
    return d[p + size];
  }

  S prod(int l, int r) const {
    assert(0 <= l && l <= r && r <= _n);
    S sml = e(), smr = e();
    l += size;
    r += size;

    while (l < r) {
      if (l & 1) sml = op(sml, d[l++]);
      if (r & 1) smr = op(d[--r], smr);
      l >>= 1;
      r >>= 1;
    }
    return op(sml, smr);
  }

  S all_prod() const { return d[1]; }

  template <bool (*f)(S)>
  int max_right(int l) const {
    return max_right(l, [](S x) { return f(x); });
  }
  template <class F>
  int max_right(int l, F f) const {
    assert(0 <= l && l <= _n);
    assert(f(e()));
    if (l == _n) return _n;
    l += size;
    S sm = e();
    do {
      while (l % 2 == 0) l >>= 1;
      if (!f(op(sm, d[l]))) {
        while (l < size) {
          l = (2 * l);
          if (f(op(sm, d[l]))) {
            sm = op(sm, d[l]);
            l++;
          }
        }
        return l - size;
      }
      sm = op(sm, d[l]);
      l++;
    } while ((l & -l) != l);
    return _n;
  }

  template <bool (*f)(S)>
  int min_left(int r) const {
    return min_left(r, [](S x) { return f(x); });
  }
  template <class F>
  int min_left(int r, F f) const {
    assert(0 <= r && r <= _n);
    assert(f(e()));
    if (r == 0) return 0;
    r += size;
    S sm = e();
    do {
      r--;
      while (r > 1 && (r % 2)) r >>= 1;
      if (!f(op(d[r], sm))) {
        while (r < size) {
          r = (2 * r + 1);
          if (f(op(d[r], sm))) {
            sm = op(d[r], sm);
            r--;
          }
        }
        return r + 1 - size;
      }
      sm = op(d[r], sm);
    } while ((r & -r) != r);
    return 0;
  }

 private:
  int _n, size, log;
  std::vector<S> d;

  void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};
#line 2 "graph/tree/TreeDPPointSet.hpp"

template <class Path, auto compress, auto Path_e, class Point, auto rake, auto Point_e, auto add_v, auto add_e, auto vertex>
struct hld {
 private:
  int n, root;
  vector<vector<int>> g;
  vector<int> heavy_p, heavy_l, light_p, idx, idx_c;
  segtree<Path, compress, Path_e> seg;
  segtree<Point, rake, Point_e> seg2;

  int dfs(int cur, int prev) {
    int sub = 1;
    for (int& nex : g[cur]) {
      if (nex == prev) {
        swap(g[cur].back(), nex);
        g[cur].pop_back();
        break;
      }
    }
    int best = 0;
    int idx = -1;
    for (int i = 0; i < int(g[cur].size()); i++) {
      int cnt = dfs(g[cur][i], cur);
      sub += cnt;
      if (best < cnt) {
        best = cnt;
        idx = i;
      }
    }
    if (!g[cur].empty()) swap(g[cur][idx], g[cur].front());
    for (int i = 1; i < int(g[cur].size()); i++) light_p[g[cur][i]] = cur;
    return sub;
  }

  void dfs2(int cur, int top, int& id, int& id2) {
    heavy_p[cur] = top;
    idx[cur] = --id;
    if (!g[cur].empty()) {
      dfs2(g[cur].front(), top, id, id2);
      heavy_l[cur] = heavy_l[g[cur].front()];
    } else {
      heavy_l[cur] = cur;
    }
    for (int i = 1; i < int(g[cur].size()); i++) dfs2(g[cur][i], g[cur][i], id, id2);
    for (int i = 1; i < int(g[cur].size()); i++) idx_c[g[cur][i]] = id2++;
  }

  Point init_segtree(int top, vector<Path>& init_path, vector<Point>& init_point) {
    vector<int> heavy_path;
    int v = top;
    while (1) {
      heavy_path.emplace_back(v);
      if (g[v].empty()) break;
      v = g[v].front();
    }
    for (int v : heavy_path) {
      Point light = Point_e();
      for (int i = 1; i < int(g[v].size()); i++) {
        int ch = g[v][i];
        Point child_point = init_segtree(ch, init_path, init_point);
        init_point[idx_c[ch]] = child_point;
        light = rake(light, child_point);
      }
      if (g[v].size() > 1) {
        init_path[idx[v]] = add_v(v, light);
      } else {
        init_path[idx[v]] = vertex(v);
      }
    }
    Path path = Path_e();
    for (int i = int(heavy_path.size()) - 1; i >= 0; i--) {
      int v = heavy_path[i];
      path = compress(path, init_path[idx[v]]);
    }
    return add_e(path);
  }

 public:
  hld(int n, int root = 0) : n(n), root(root), g(n), heavy_p(n, -1), heavy_l(n, -1), light_p(n, -1), idx(n), idx_c(n) {}

  void add_edge(int u, int v) {
    g[u].emplace_back(v);
    g[v].emplace_back(u);
  }

  void build(int root = 0) {
    int id = n;
    int id2 = 0;
    dfs(root, -1);
    dfs2(root, root, id, id2);
    vector<Path> init_path(n, Path_e());
    vector<Point> init_point(n, Point_e());
    init_segtree(root, init_path, init_point);
    seg = segtree<Path, compress, Path_e>(init_path);
    seg2 = segtree<Point, rake, Point_e>(init_point);
  }

  Path tree_dp() {
    return seg.prod(idx[heavy_l[root]], idx[root] + 1);
  }

  void set(int i) {
    while (1) {
      if (g[i].size() > 1) {
        int ch_num = int(g[i].size()) - 1;
        if (ch_num == 1) {
          seg.set(idx[i], add_v(i, seg2.get(idx_c[g[i][1]])));
        } else {
          seg.set(idx[i], add_v(i, seg2.prod(idx_c[g[i][1]], idx_c[g[i][1]] + ch_num)));
        }
      } else {
        seg.set(idx[i], vertex(i));
      }
      int nex = light_p[heavy_p[i]];
      if (nex == -1) break;
      int l = idx[heavy_l[heavy_p[i]]];
      int r = idx[heavy_p[i]] + 1;
      if (r - l == 1) {
        seg2.set(idx_c[heavy_p[i]], add_e(seg.get(l)));
      } else {
        seg2.set(idx_c[heavy_p[i]], add_e(seg.prod(l, r)));
      }
      i = nex;
    }
  }
};
#line 7 "verify/LibraryChecker/graph/tree/PointSetTreePathCompositeSumFixed.test.cpp"

vector<mint> A, eb, ec;

struct Path {
  mint a, b, g, d;
  Path(mint a = 1, mint b = 0, mint g = 0, mint d = 0) : a(a), b(b), g(g), d(d) {}
};

Path compress(const Path& p, const Path& c) {
  return Path(p.a * c.a, c.a * p.b + c.b, c.a * p.g + c.b * p.d + c.g, c.d + p.d);
}

struct Point {
  mint sum;
  mint cnt;
  Point(mint sum = 0, mint cnt = 0) : sum(sum), cnt(cnt) {}
};

Point point_e() {
  return {0, 0};
}

Path path_e() {
  return Path();
}

Point rake(const Point& a, const Point& b) {
  return Point(a.sum + b.sum, a.cnt + b.cnt);
}

Path add_v(int v, Point p) {
  mint B = eb[v];
  mint C = ec[v];
  return Path(B, C, B * (p.sum + A[v]) + C * (p.cnt + 1), p.cnt + 1);
}

Path vertex(int v) {
  mint B = eb[v];
  mint C = ec[v];
  return Path(B, C, B * A[v] + C, 1);
}

Point add_e(Path p) {
  return Point(p.g, p.d);
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  int n, q;
  in(n, q);
  A.assign(n, 0);
  eb.assign(n, 1);
  ec.assign(n, 0);

  rep(i, n) {
    lint x;
    in(x);
    A[i] = x;
  }

  hld<Path, compress, path_e, Point, rake, point_e, add_v, add_e, vertex> t(n);

  vector<int> U(n - 1), V(n - 1);
  vector<mint> B(n - 1), C(n - 1);

  vector<vector<pair<int, int>>> g(n);

  rep(e, n - 1) {
    int u, v;
    lint b, c;
    in(u, v, b, c);
    U[e] = u;
    V[e] = v;
    B[e] = mint(b);
    C[e] = mint(c);
    t.add_edge(u, v);
    g[u].push_back({v, e});
    g[v].push_back({u, e});
  }

  vector<int> par(n, -1);
  vector<int> par_e(n, -1);
  vector<int> chi_e(n - 1, -1);

  queue<int> que;
  par[0] = -2;
  que.push(0);
  while (!que.empty()) {
    int v = que.front();
    que.pop();
    for (auto [to, e] : g[v]) {
      if (par[to] != -1) continue;
      par[to] = v;
      par_e[to] = e;
      chi_e[e] = to;
      que.push(to);
    }
  }
  eb[0] = 1;
  ec[0] = 0;
  rep(i, 1, n) {
    int e = par_e[i];
    eb[i] = B[e];
    ec[i] = C[e];
  }

  t.build(0);

  rep(i, q) {
    int com;
    in(com);
    if (com == 0) {
      int w;
      lint x;
      in(w, x);
      A[w] = x;
      t.set(w);
    } else {
      int e;
      lint y, z;
      in(e, y, z);
      int ch = chi_e[e];
      eb[ch] = y;
      ec[ch] = z;
      t.set(ch);
    }
    out(add_e(t.tree_dp()).sum.val());
  }
}
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