#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using P = pair; constexpr int INF = 1001001001; constexpr int mod = 1000000007; // constexpr int mod = 998244353; template inline bool chmax(T& x, T y){ if(x < y){ x = y; return true; } return false; } template inline bool chmin(T& x, T y){ if(x > y){ x = y; return true; } return false; } struct mint { int x; mint() : x(0) {} mint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} mint& operator+=(const mint& p){ if((x += p.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint& p){ if((x -= p.x) < 0) x += mod; return *this; } mint& operator*=(const mint& p){ x = (int)(1LL * x * p.x % mod); return *this; } mint& operator/=(const mint& p){ *this *= p.inverse(); return *this; } mint operator-() const { return mint(-x); } mint operator+(const mint& p) const { return mint(*this) += p; } mint operator-(const mint& p) const { return mint(*this) -= p; } mint operator*(const mint& p) const { return mint(*this) *= p; } mint operator/(const mint& p) const { return mint(*this) /= p; } bool operator==(const mint& p) const { return x == p.x; } bool operator!=(const mint& p) const { return x != p.x; } mint pow(int64_t n) const { mint res = 1, mul = x; while(n > 0){ if(n & 1) res *= mul; mul *= mul; n >>= 1; } return res; } mint inverse() const { return pow(mod - 2); } friend ostream& operator<<(ostream& os, const mint& p){ return os << p.x; } friend istream& operator>>(istream& is, mint& p){ int64_t val; is >> val; p = mint(val); return is; } }; struct UnionFind{ int sz; // vertex number vector par; vector rank; UnionFind(int n) : sz(n) { par.resize(sz); rank.assign(sz, 0); for(int i = 0; i < sz; ++i){ par[i] = i; } } int find(int x){ if(par[x] == x) return x; else return par[x] = find(par[x]); } bool same(int x, int y){ return find(x) == find(y); } void unite(int x, int y){ x = find(x), y = find(y); if(x == y) return; if(rank[x] < rank[y]) par[x] = y; else{ par[y] = x; if(rank[x] == rank[y]) ++rank[x]; } } }; int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); int N, M, X; cin >> N >> M >> X; vector> es(M); for(auto& [z, x, y] : es){ cin >> x >> y >> z; --x, --y; } sort(es.begin(), es.end()); vector>> graph(N); UnionFind uf(N); for(auto& [z, x, y] : es){ if(uf.same(x, y)) continue; uf.unite(x, y); graph[x].emplace_back(y, mint(X).pow(z)); graph[y].emplace_back(x, mint(X).pow(z)); } vector dp(N, 1); mint ans = 0; auto dfs = [&](auto&& self, int from = 0, int par = -1) -> void { for(auto [to, cost] : graph[from]){ if(to == par) continue; self(self, to, from); dp[from] += dp[to]; ans += cost * dp[to] * (N - dp[to]); } }; dfs(dfs); cout << ans << endl; return 0; }