#pragma GCC target("avx2") #pragma GCC optimize("03") #pragma GCC optimize("unroll-loops") #include using namespace std; typedef long double ld; typedef long long ll; typedef unsigned long long ull; #define endl "\n" #define FOR(i,a,b) for(int i=(a);i<=(b);i++) #define rep(i,n) for(int i=0;i<(n);i++) #define PII pair #define PLL pair #define ALL(x) (x).begin(), (x).end() constexpr int INF=1<<30; constexpr ll LINF=1LL<<60; constexpr ll mod=1e9+7; constexpr int NIL = -1; templatevector vec(int len, T elem) { return vector(len, elem); } // auto dp = vec(52, vec(103, vec(103, INF))); templateinline bool chmax(T &a, const T &b) { if (ainline bool chmin(T &a, const T &b) { if (binline int popcount(T a) {return __builtin_popcount(a);} templateinline T emod(T a, T p) { return (a%p + p) % p;} template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) {os << '\n'; for (auto v : vec) os << v << ' '; os << '\n'; return os;} template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } //------------------- struct mint { ll x; mint(ll x=0):x(x%mod){} bool operator==(const mint a)const{return x==a.x;} bool operator!=(const mint a)const{return x!=a.x;} bool operator>=(const mint a){return (x >= a.x)? 1: 0;} bool operator<(const mint a){return !(*this>=a);} bool operator>(const mint a){return (x > a.x)? 1:0;} bool operator<=(const mint a){return !(*this>a);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this; } mint& operator/=(const mint a) { return (*this) *= a.inv(); } mint operator+(const mint a) const { mint res(*this); return res+=a; } mint operator-(const mint a) const { mint res(*this); return res-=a; } mint operator*(const mint a) const { mint res(*this); return res*=a; } mint operator/(const mint a) const { mint res(*this); return res/=a; } mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; //2 square if (t&1) a *= *this; return a; } // for prime mod mint inv() const { return pow(mod-2); } friend ostream& operator<<(ostream& os, const mint& m){ os << m.x; return os; } }; class UnionFind { private: unsigned size_; std::vector par, rank; //par = root? -size: par public: UnionFind() : size_(0), par(std::vector()), rank(std::vector()) {}; UnionFind(unsigned size__) : size_(size__) { par.resize(size_+1); rank.resize(size_+1); for (unsigned i = 0; i <= size_; i++) par[i] = -1, rank[i] = 0; } //unsigned size() { return size_; } unsigned root(unsigned x) {return par[x] < 0 ? x : par[x] = root(par[x]); } bool same(unsigned x, unsigned y) { return root(x) == root(y); } void unite(unsigned x, unsigned y) { x = root(x), y = root(y); if (x == y) return; if (rank[x] < rank[y])par[y] += par[x], par[x] = y; else if (rank[x] == rank[y])par[x] += par[y], par[y] = x, rank[x]++; else par[x] += par[y], par[y] = x; } int size(int x){ return -par[root(x)];} bool operator==(const UnionFind &u) { return par == u.par; } bool operator!=(const UnionFind &u) { return par != u.par; } }; constexpr int MX = 2e5+5; vector G[MX]; mint ans = 0; ll n,m,x; ll dfs(int c, int par) { ll res=0; for(auto [to, cost]: G[c]) { if(to==par) continue; ll cur = dfs(to, c); ans += mint(x).pow(cost) * (n - cur) * cur; // cout << cur << endl; res += cur; } return res+1; } int main() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cin >> n >> m >> x; UnionFind uf(n); rep(i, m) { int x1,y1; cin >> x1 >> y1; x1--; y1--; ll z; cin >> z; if(!uf.same(x1,y1)) { uf.unite(x1,y1); G[x1].emplace_back(y1, z); G[y1].emplace_back(x1, z); } } // rep(i, n) { // cout << G[i] << endl; // } dfs(0, -1); cout << ans << endl; return 0; }