#719328 (C++17) No.1784 Not a star yet...

• 問題: No.1784 Not a star yet...
• ユーザー: NyaanNyaan
• 提出日時: 2021-11-23 23:05:03
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: WA
• 実行時間: -
• コード長: 21,372 bytes
• コンパイル時間: 3,773 ms
• コンパイル使用メモリ: 296,816 KB
• 最終ジャッジ日時: 2025-01-26 00:56:08
• ジャッジサーバーID （参考情報）: judge1 / judge5

ファイルパターン	結果
sample	WA * 3
other	WA * 23 TLE * 8 MLE * 30

ソースコード

/**
 *  date : 2021-11-23 23:04:51
 */

#define NDEBUG
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  T &x() { return first; }
  const T &x() const { return first; }
  U &y() { return second; }
  const U &y() const { return second; }

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

}  // namespace Nyaan

// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan

// inout
namespace Nyaan {

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

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

void in() {}
template <typename T, class... U>
void in(T &t, U &... u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &... u) {
  cout << t;
  outr(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//


template <typename T>
struct edge {
  int src, to;
  T cost;

  edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
  edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;

// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
                      bool is_1origin = true) {
  UnweightedGraph g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    if (is_1origin) x--, y--;
    g[x].push_back(y);
    if (!is_directed) g[y].push_back(x);
  }
  return g;
}

// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
                        bool is_1origin = true) {
  WeightedGraph<T> g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    cin >> c;
    if (is_1origin) x--, y--;
    g[x].emplace_back(x, y, c);
    if (!is_directed) g[y].emplace_back(y, x, c);
  }
  return g;
}

// Input of Edges
template <typename T>
Edges<T> esgraph(int N, int M, int is_weighted = true, bool is_1origin = true) {
  Edges<T> es;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    es.emplace_back(x, y, c);
  }
  return es;
}

// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
                           bool is_directed = false, bool is_1origin = true) {
  vector<vector<T>> d(N, vector<T>(N, INF));
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    d[x][y] = c;
    if (!is_directed) d[y][x] = c;
  }
  return d;
}
// 一般のグラフのstからの距離！！！！
// unvisited nodes : d = -1
vector<int> Depth(const UnweightedGraph &g, int start = 0) {
  int n = g.size();
  vector<int> ds(n, -1);
  ds[start] = 0;
  queue<int> q;
  q.push(start);
  while (!q.empty()) {
    int c = q.front();
    q.pop();
    int dc = ds[c];
    for (auto &d : g[c]) {
      if (ds[d] == -1) {
        ds[d] = dc + 1;
        q.push(d);
      }
    }
  }
  return ds;
}

// Depth of Rooted Weighted Tree
// unvisited nodes : d = -1
template <typename T>
vector<T> Depth(const WeightedGraph<T> &g, int start = 0) {
  vector<T> d(g.size(), -1);
  auto dfs = [&](auto rec, int cur, T val, int par = -1) -> void {
    d[cur] = val;
    for (auto &dst : g[cur]) {
      if (dst == par) continue;
      rec(rec, dst, val + dst.cost, cur);
    }
  };
  dfs(dfs, start, 0);
  return d;
}

// Diameter of Tree
// return value : { {u, v}, length }
pair<pair<int, int>, int> Diameter(const UnweightedGraph &g) {
  auto d = Depth(g, 0);
  int u = max_element(begin(d), end(d)) - begin(d);
  d = Depth(g, u);
  int v = max_element(begin(d), end(d)) - begin(d);
  return make_pair(make_pair(u, v), d[v]);
}

// Diameter of Weighted Tree
// return value : { {u, v}, length }
template <typename T>
pair<pair<int, int>, T> Diameter(const WeightedGraph<T> &g) {
  auto d = Depth(g, 0);
  int u = max_element(begin(d), end(d)) - begin(d);
  d = Depth(g, u);
  int v = max_element(begin(d), end(d)) - begin(d);
  return make_pair(make_pair(u, v), d[v]);
}

// nodes on the path u-v ( O(N) )
template <typename G>
vector<int> Path(G &g, int u, int v) {
  vector<int> ret;
  int end = 0;
  auto dfs = [&](auto rec, int cur, int par = -1) -> void {
    ret.push_back(cur);
    if (cur == v) {
      end = 1;
      return;
    }
    for (int dst : g[cur]) {
      if (dst == par) continue;
      rec(rec, dst, cur);
      if (end) return;
    }
    if (end) return;
    ret.pop_back();
  };
  dfs(dfs, u);
  return ret;
}

ostream& operator<<(ostream& os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string res;
  while (x) res.push_back(x % 10 + '0'), x /= 10;
  reverse(begin(res), end(res));
  return os << res;
}

struct Rational {
  using R = Rational;
  using i128 = __int128_t;
  // using i64 = long long;
  // using u64 = unsigned long long;
  using i64 = __int128_t;
  using u64 = __uint128_t;
  i64 x, y;
  Rational() : x(0), y(1) {}
  Rational(i64 _x, i64 _y = 1) : x(_x), y(_y) {
    assert(y != 0);
    if (_y != 1) {
      i64 g = gcd(x, y);
      if (g != 0) x /= g, y /= g;
      if (y < 0) x = -x, y = -y;
    }
  }

  u64 gcd(i64 A, i64 B) {
    u64 a = A >= 0 ? A : -A;
    u64 b = B >= 0 ? B : -B;
    return __gcd(a, b);
    /*
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a);
    int m = __builtin_ctzll(b);
    a >>= n;
    b >>= m;
    while (a != b) {
      int d = __builtin_ctzll(a - b);
      bool f = a > b;
      u64 c = f ? a : b;
      b = f ? b : a;
      a = (c - b) >> d;
    }
    return a << min(n, m);
    */
  }

  friend R operator+(const R& l, const R& r) {
    return R(l.x * r.y + l.y * r.x, l.y * r.y);
  }
  friend R operator-(const R& l, const R& r) {
    return R(l.x * r.y - l.y * r.x, l.y * r.y);
  }
  friend R operator*(const R& l, const R& r) { return R(l.x * r.x, l.y * r.y); }
  friend R operator/(const R& l, const R& r) {
    assert(r.x != 0);
    return R(l.x * r.y, l.y * r.x);
  }
  R& operator+=(const R& r) { return (*this) = (*this) + r; }
  R& operator-=(const R& r) { return (*this) = (*this) - r; }
  R& operator*=(const R& r) { return (*this) = (*this) * r; }
  R& operator/=(const R& r) { return (*this) = (*this) / r; }
  R operator-() const {
    R r;
    r.x = -x, r.y = y;
    return r;
  }
  R inverse() const {
    assert(x != 0);
    R r;
    r.x = y, r.y = x;
    if (x < 0) r.x = -r.x, r.y = -r.y;
    return r;
  }
  R pow(long long p) const {
    R res(1), base(*this);
    while (p) {
      if (p & 1) res *= base;
      base *= base;
      p >>= 1;
    }
    return res;
  }

  friend bool operator==(const R& l, const R& r) {
    return l.x == r.x && l.y == r.y;
  };
  friend bool operator!=(const R& l, const R& r) {
    return l.x != r.x || l.y != r.y;
  };
  friend bool operator<(const R& l, const R& r) {
    return i128(l.x) * r.y < i128(l.y) * r.x;
  };
  friend bool operator<=(const R& l, const R& r) { return l < r || l == r; }
  friend bool operator>(const R& l, const R& r) {
    return i128(l.x) * r.y > i128(l.y) * r.x;
  };
  friend bool operator>=(const R& l, const R& r) { return l > r || l == r; }
  friend ostream& operator<<(ostream& os, const R& r) {
    os << r.x;
    if (r.x != 0 && r.y != 1) os << "/" << r.y;
    return os;
  }

  long long toMint(long long mod) {
    assert(mod != 0);
    i64 a = y, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return i128((u % mod + mod) % mod) * x % mod;
  }
};

template <typename R = Rational>
struct Binomial {
  vector<R> fc;
  Binomial(int = 0) { fc.emplace_back(1); }
  void extend() {
    int n = fc.size();
    R nxt = fc.back() * n;
    fc.push_back(nxt);
  }
  R fac(int n) {
    while ((int)fc.size() <= n) extend();
    return fc[n];
  }
  R finv(int n) { return fac(n).inverse(); }
  R inv(int n) { return R{1, max(n, 1)}; }
  R C(int n, int r) {
    if (n < 0 or r < 0 or n < r) return R{0};
    return fac(n) * finv(n - r) * finv(r);
  }
  R operator()(int n, int r) { return C(n, r); }
};



template <typename mint>
std::pair<int, mint> GaussElimination(vector<vector<mint>> &a,
                                      int pivot_end = -1,
                                      bool diagonalize = false) {
  int H = a.size(), W = a[0].size();
  int rank = 0, je = pivot_end;
  if (je == -1) je = W;
  mint det = 1;
  for (int j = 0; j < je; j++) {
    int idx = -1;
    for (int i = rank; i < H; i++) {
      if (a[i][j] != mint(0)) {
        idx = i;
        break;
      }
    }
    if (idx == -1) {
      det = 0;
      continue;
    }
    if (rank != idx) {
      det = -det;
      swap(a[rank], a[idx]);
    }
    det *= a[rank][j];
    if (diagonalize && a[rank][j] != mint(1)) {
      mint coeff = a[rank][j].inverse();
      for (int k = j; k < W; k++) a[rank][k] *= coeff;
    }
    int is = diagonalize ? 0 : rank + 1;
    for (int i = is; i < H; i++) {
      if (i == rank) continue;
      if (a[i][j] != mint(0)) {
        mint coeff = a[i][j] / a[rank][j];
        for (int k = j; k < W; k++) a[i][k] -= a[rank][k] * coeff;
      }
    }
    rank++;
  }
  return make_pair(rank, det);
}


template <typename mint>
vector<vector<mint>> LinearEquation(vector<vector<mint>> a, vector<mint> b) {
  int H = a.size(), W = a[0].size();
  for (int i = 0; i < H; i++) a[i].push_back(b[i]);
  auto p = GaussElimination(a, W, true);
  int rank = p.first;

  for (int i = rank; i < H; ++i) {
    if (a[i][W] != 0) return vector<vector<mint>>{};
  }

  vector<vector<mint>> res(1, vector<mint>(W));
  vector<int> pivot(W, -1);
  for (int i = 0, j = 0; i < rank; ++i) {
    while (a[i][j] == 0) ++j;
    res[0][j] = a[i][W], pivot[j] = i;
  }
  for (int j = 0; j < W; ++j) {
    if (pivot[j] == -1) {
      vector<mint> x(W);
      x[j] = 1;
      for (int k = 0; k < j; ++k) {
        if (pivot[k] != -1) x[k] = -a[pivot[k]][j];
      }
      res.push_back(x);
    }
  }
  return res;
}

using mint = Rational;
using namespace Nyaan;

void Nyaan::solve() {
  inl(N);
  map<int, int> ws;
  Edges<ll> es;
  rep(i, N - 1) {
    inl(u, v, w);
    --u, --v;
    es.emplace_back(u, v, w);
    ws[w]++;
  }
  int X = 0, Y = 0;
  mint a = 0, b = 0;
  tie(a, X) = *begin(ws);
  if (sz(ws) == 2) tie(b, Y) = *next(begin(ws));

  vector<vector<mint>> A((X + 1) * (Y + 1) - 1,
                         vector((X + 1) * (Y + 1), mint{}));
  vector<mint> B((X + 1) * (Y + 1));

  auto id = [&](int i, int j) { return i * (Y + 1) + j; };

  rep(i, X + 1) rep(j, Y + 1) {
    if (i == X and j == Y) continue;

    mint p = N * (N - 1) / 2 - (X + Y - 1);
    mint q = N - i - j;

    if (i != 0) A[id(i, j)][id(i - 0, j)] += a * i * q;
    if (i != 0) A[id(i, j)][id(i - 1, j)] += a * i * (p - q);
    if (j != 0) A[id(i, j)][id(i, j - 0)] += b * j * q;
    if (j != 0) A[id(i, j)][id(i, j - 1)] += b * j * (p - q);
    if (i != X) A[id(i, j)][id(i + 0, j)] += a * (X - i) * (p - q + 1);
    if (i != X) A[id(i, j)][id(i + 1, j)] += a * (X - i) * (q - 1);
    if (j != Y) A[id(i, j)][id(i, j + 0)] += b * (Y - j) * (p - q + 1);
    if (j != Y) A[id(i, j)][id(i, j + 1)] += b * (Y - j) * (q - 1);

    mint all = (a * X + b * Y) * p;
    A[id(i, j)][id(i, j)] -= all;
    B[id(i, j)] = -all / N;
  }

  auto xs = LinearEquation(A, B)[0];
  trc(LinearEquation(A, B));
  rep(i, X + 1) rep(j, Y + 1) { trc(i, j, xs[id(i, j)]); }

  vi cx(N), cy(N);
  each(e, es) {
    (a == e.cost ? cx : cy)[e.src]++;
    (a == e.cost ? cx : cy)[e.to]++;
  }
  trc(cx, cy);
  mint ans = 0;
  rep(i, N) ans += xs[id(cx[i], cy[i])];
  ans -= xs[id(1, 0)] * X + xs[id(0, 1)] * Y + xs[id(X, Y)];
  //for(auto&r:xs)out(1.0*r.x/r.y);
  //out(ans);
  out(1.0 * ans.x / ans.y);
}