#include using namespace std; #define REP(i,n) for(ll i=0;i<(ll)n;i++) #define dump(x) cerr << #x << " = " << (x) << endl; #define spa << " " << #define fi first #define se second #define ALL(a) (a).begin(),(a).end() #define ALLR(a) (a).rbegin(),(a).rend() using ld = long double; using ll = long long; using ull = unsigned long long; using pii = pair; using pll = pair; using pdd = pair; template struct V : vector { using vector::vector; }; V() -> V; V(size_t) -> V; template V(size_t, T) -> V; template vector make_vec(size_t n, T a) { return vector(n, a); } template auto make_vec(size_t n, Ts... ts) { return vector(n, make_vec(ts...)); } template ostream& operator << (ostream& os, const pair v){os << "(" << v.first << ", " << v.second << ")"; return os;} template ostream& operator<<(ostream &os, const vector &v) { for (auto &e : v) os << e << ' '; return os; } template ostream& operator<<(ostream& os, const vector> &v){ for(auto &e : v){os << e << "\n";} return os;} struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; template bool chmax(T &a, const T &b) { if (a bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; } void fail() { cout << -1 << '\n'; exit(0); } inline int popcount(const int x) { return __builtin_popcount(x); } inline int popcount(const ll x) { return __builtin_popcountll(x); } template void debug(vector>&v,ll h,ll w){for(ll i=0;i void debug(vector&v,ll n){if(n!=0)cerr< class modint { // long long から modint を作るときは必ず正の数にしてからコンストラクタに入れること! // そうしないとバグります using u64 = std::uint_fast64_t; public: u64 a; constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {} constexpr u64 &value() noexcept { return a; } constexpr const u64 &value() const noexcept { return a; } constexpr modint operator+(const modint rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint rhs) const noexcept { return modint(*this) /= rhs; } constexpr modint &operator+=(const modint rhs) noexcept { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr modint &operator-=(const modint rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr modint &operator*=(const modint rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr modint &operator/=(modint rhs) noexcept { u64 exp = Modulus - 2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } }; using mint = modint; using vm = vector; using vvm = vector; ostream& operator << (ostream& os, const mint v){ os << v.value(); return os; } template constexpr T power(T x, U exp) { T ret = static_cast(1); while (exp) { if (exp % static_cast(2) == static_cast(1)) ret *= x; exp /= static_cast(2); x *= x; } return ::std::move(ret); } // par[i]  は,iがrootなら-(連結成分のサイズ)を,iがrootではないならばrootを返す // root(x) は必ずroot を返す struct UnionFindSize { vector par; UnionFindSize(int n) : par(n, -1) { } void init(int n) { par.assign(n, -1); } int root(int x) { if (par[x] < 0) return x; else return par[x] = root(par[x]); } bool issame(int x, int y) { return root(x) == root(y); } bool merge(int x, int y) { x = root(x); y = root(y); if (x == y) return false; if (par[x] > par[y]) swap(x, y); // merge technique par[x] += par[y]; par[y] = x; return true; } int size(int x) { return -par[root(x)]; } void print(){ cout << "uf: "; for(int i=0;i<(int)par.size();i++) cout << root(i) << " "; cout << endl; } }; using Graph = V>; int main(){ ll N, M, X; cin >> N >> M >> X; V x(M), y(M), z(M); REP(i, M) cin >> x[i] >> y[i] >> z[i]; REP(i, M) x[i]--, y[i]--; V ids(M); iota(ALL(ids), 0); sort(ALL(ids), [&](ll x, ll y){ return z[x] < z[y]; }); UnionFindSize uf(N); Graph G(N); mint res = 0; for(auto idx: ids){ if(uf.merge(x[idx], y[idx])){ G[x[idx]].emplace_back(y[idx], z[idx]); G[y[idx]].emplace_back(x[idx], z[idx]); } } auto dfs = [&](auto self, ll now, ll par)->ll{ ll sz = 1; for(auto tup: G[now]){ ll next = tup.first; ll zz = tup.second; if(next == par) continue; ll tmp_sz = self(self, next, now); res += mint(tmp_sz) * (N-tmp_sz) * power(mint(X), zz); sz += tmp_sz; } return sz; }; dfs(dfs, 0, -1); cout << res << endl; return 0; }