#line 2 "/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp" #define _CRT_SECURE_NO_WARNINGS #pragma target("avx") #pragma optimize("O3") #pragma optimize("unroll-loops") #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 #define rep(i,n) for(int i=0;i<(lint)(n);i++) #define REP(i,n) for(int i=1;i<=(lint)(n);i++) #define all(V) V.begin(),V.end() typedef long long lint; typedef unsigned long long ulint; typedef std::pair P; typedef std::pair LP; constexpr int INF = INT_MAX/2; constexpr lint LINF = LLONG_MAX/2; constexpr double eps = DBL_EPSILON; constexpr double PI=3.141592653589793238462643383279; template class prique :public std::priority_queue, std::greater> {}; template inline bool chmax(T& lhs, const U& rhs) { if (lhs < rhs) { lhs = rhs; return 1; } return 0; } template inline bool chmin(T& lhs, const U& rhs) { if (lhs > rhs) { lhs = rhs; return 1; } return 0; } inline lint gcd(lint a, lint b) { while (b) { lint c = a; a = b; b = c % b; } return a; } inline lint lcm(lint a, lint b) { return a / gcd(a, b) * b; } bool isprime(lint n) { if (n == 1)return false; for (int i = 2; i * i <= n; i++) { if (n % i == 0)return false; } return true; } template T mypow(T a, lint b) { if (!b)return T(1); if (b & 1)return mypow(a, b - 1) * a; T memo = mypow(a, b >> 1); return memo * memo; } lint modpow(lint a, lint b, lint m) { if (!b)return 1; if (b & 1)return modpow(a, b - 1, m) * a % m; lint memo = modpow(a, b >> 1, m); return memo * memo % m; } template void printArray(std::vector& vec) { rep(i, vec.size() - 1)std::cout << vec[i] << " "; std::cout << vec.back() << std::endl; } template void printArray(T l, T r) { T rprev = r; rprev--; for (T i = l; i != rprev; i++) { std::cout << *i << " "; } std::cout << *rprev << std::endl; } #line 3 "/Users/kaage/Desktop/ProgrammingWorkspace/library/graph/UnionFind.hpp" class UnionFind { protected: std::vector par, rank, size; public: UnionFind(unsigned int size) { par.resize(size); rank.resize(size, 0); this->size.resize(size, 1); rep(i, size) { par[i] = i; } } int find(int n) { if (par[n] == n)return n; return par[n] = find(par[n]); } void unite(int n, int m) { n = find(n); m = find(m); if (n == m)return; if (rank[n] < rank[m]) { par[n] = m; size[m] += size[n]; } else { par[m] = n; size[n] += size[m]; if (rank[n] == rank[m])rank[n]++; } } bool same(int n, int m) { return find(n) == find(m); } int getsize(int n) { return size[find(n)]; } }; #line 3 "/Users/kaage/Desktop/ProgrammingWorkspace/library/algebraic/ModInt.hpp" class ModInt { lint value; public: static const unsigned int modulo; ModInt() : value(0) {} template ModInt(T value = 0) : value(value) { if (value < 0)value = -(lint)(-value % modulo) + modulo; this->value = value % modulo; } inline operator int()const { return value; } inline ModInt& operator+=(const ModInt& x) { value += x.value; if (value >= modulo)value -= modulo; return *this; } inline ModInt& operator++() { if (value == modulo - 1)value = 0; else value++; return *this; } inline ModInt operator-()const { return ModInt(0) -= *this; } inline ModInt& operator-=(const ModInt& x) { value -= x.value; if (value < 0)value += modulo; return *this; } inline ModInt& operator--() { if (value == 0)value = modulo - 1; else value--; return *this; } inline ModInt& operator*=(const ModInt& x) { value = value * x.value % modulo; return *this; } inline ModInt& operator/=(ModInt rhs) { int exp = modulo - 2; while (exp) { if (exp & 1)*this *= rhs; rhs *= rhs; exp >>= 1; } return *this; } template ModInt operator+(const T& rhs)const { return ModInt(*this) += rhs; } template ModInt& operator+=(const T& rhs) { return operator+=(ModInt(rhs)); } template ModInt operator-(const T& rhs)const { return ModInt(*this) -= rhs; } template ModInt& operator-=(const T& rhs) { return operator-=(ModInt(rhs)); } template ModInt operator*(const T& rhs)const { return ModInt(*this) *= rhs; } template ModInt& operator*=(const T& rhs) { return operator*=(ModInt(rhs)); } template ModInt operator/(const T& rhs)const { return ModInt(*this) /= rhs; } template ModInt& operator/=(const T& rhs) { return operator/=(ModInt(rhs)); } }; std::istream& operator>>(std::istream& ist, ModInt& x) { lint a; ist >> a; x = a; return ist; } #line 4 "main.cpp" const unsigned int ModInt::modulo=1000000007; int n,m,x; ModInt ans; std::vector> vec; std::vector

edges[200010]; bool used[200010]; int dfs(int node){ used[node]=true; int cnt=1; for(const P& i:edges[node]){ if(!used[i.first]){ int s=dfs(i.first); ans+=mypow(ModInt(x),i.second)*s*(n-s); cnt+=s; } } return cnt; } int main(){ std::cin>>n>>m>>x; rep(i,m){ int a,b,c; std::cin>>a>>b>>c; vec.push_back({c,{a,b}}); } UnionFind uf(n+1); for(const auto& i:vec){ if(!uf.same(i.second.first,i.second.second)){ uf.unite(i.second.first,i.second.second); edges[i.second.first].emplace_back(i.second.second,i.first); edges[i.second.second].emplace_back(i.second.first,i.first); } } dfs(1); std::cout<