#include #include #include #include #include #include #include using namespace std; typedef long long ll; struct UnionFind { vector data; UnionFind(int size) : data(size, -1) { } bool unionSet(int x, int y) { x = root(x); y = root(y); if (x != y) { if (data[y] < data[x]) swap(x, y); data[x] += data[y]; data[y] = x; } return x != y; } bool findSet(int x, int y) { return root(x) == root(y); } int root(int x) { return data[x] < 0 ? x : data[x] = root(data[x]); } int size(int x) { return -data[root(x)]; } }; const ll MOD = 1000000007; class ModInt{ public: ll v; ModInt(ll _v = 0){ v = _v; } ModInt operator+(ll n){ return ModInt((v+n)%MOD); } ModInt operator-(ll n){ return ModInt((v-n+MOD)%MOD); } ModInt operator*(ll n){ return ModInt((v*n)%MOD); } ModInt operator/(ll n){ return ModInt((ModInt(n).inv()*v).v%MOD); } void operator+=(ll n){ v = (v+n)%MOD; } void operator-=(ll n){ v = (v-n+MOD)%MOD; } void operator*=(ll n){ v = (v*n)%MOD; } ModInt operator+(ModInt n){ return ModInt((v+n.v)%MOD); } ModInt operator-(ModInt n){ return ModInt((v-n.v+MOD)%MOD); } ModInt operator*(ModInt n){ return ModInt((v*n.v)%MOD); } ModInt operator/(ModInt n){ return ModInt((n.inv()*v).v%MOD); } void operator+=(ModInt n){ v = (v+n.v)%MOD; } void operator-=(ModInt n){ v = (v-n.v+MOD)%MOD; } void operator*=(ModInt n){ v = (v*n.v)%MOD; } void operator=(ModInt n){ v = n.v; } void operator=(ll n){ v = n; } ModInt inv(){ if(v == 1) return ModInt(1); else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD); } }; ostream& operator<<(ostream& os, const ModInt& m){ os << m.v; return os; } istream & operator >> (istream &in, ModInt &m){ in >> m.v; return in; } ModInt pow(ModInt a, ll n) { ModInt ans = 1; ModInt tmp = a; for (int i = 0; i <= 60; i++) { ll m = (ll)1 << i; if (m & n) { ans *= tmp; } tmp *= tmp; } return ans; } ll N, M, X; ModInt ans = 0; int x[200000], y[200000], z[200000]; bool used[200000]; int depth[200000]; int ch[200000]; vector G[200000]; bool used_dfs[200000]; void dfs(int v){ used_dfs[v] = true; ch[v] = 1; for(int to: G[v]){ if(!used_dfs[to]) { dfs(to); ch[v] += ch[to]; } } } int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; cin >> N >> M >> X; UnionFind uf(N); for(int i = 0; i < M; i++){ cin >> x[i] >> y[i] >> z[i]; x[i]--; y[i]--; int rx = uf.root(x[i]), ry = uf.root(y[i]); if(rx != ry){ used[i] = true; G[x[i]].push_back(y[i]); G[y[i]].push_back(x[i]); uf.unionSet(x[i], y[i]); } } dfs(0); for(int i = 0; i < M; i++){ if(used[i]){ if(ch[x[i]] > ch[y[i]]) swap(x[i], y[i]); ans += pow(X, z[i])*ch[x[i]]*(N-ch[x[i]]); } } cout << ans << endl; }