#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 #include #include #include #include #include #include #include #include #include using namespace std; #define SZ(x) (int)(x.size()) #define REP(i, n) for(int i=0;i=0;--i) #define RFOR(i, a, b) for(int i=b-1;i>=a;--i) #define all(x) begin(x),end(x) #define dump(x) cerr<<#x<<" = "<<(x)<; using vvi = vector; using vll = vector; using vvll = vector; using P = pair; const double eps = 1e-8; const ll MOD = 1000000007; const int INF = INT_MAX / 2; const ll LINF = LLONG_MAX / 2; template bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T &a, const T &b) { if (b < a) { a = b; return true; } return false; } template ostream &operator<<(ostream &os, const pair p) { os << p.first << ":" << p.second; return os; } template ostream &operator<<(ostream &os, const vector &v) { os << "["; REP(i, SZ(v)) { if (i) os << ", "; os << v[i]; } return os << "]"; } template ostream &operator<<(ostream &os, const map &mp) { os << "["; for (auto it = mp.begin(); it != mp.end(); ++it) { if (it != mp.begin()) { os << ", "; } os << *it; } return os << "]"; } // edit using Int = ll; class Mint { using u64 = std::uint_fast64_t; u64 Modulus = MOD; public: u64 a; constexpr Mint(const u64 x = 0) noexcept: a(x % Modulus) {} constexpr u64 &value() noexcept { return a; } constexpr const u64 &value() const noexcept { return a; } constexpr Mint operator+(const Mint rhs) const noexcept { return Mint(*this) += rhs; } constexpr Mint operator-(const Mint rhs) const noexcept { return Mint(*this) -= rhs; } constexpr Mint operator*(const Mint rhs) const noexcept { return Mint(*this) *= rhs; } constexpr Mint operator/(const Mint rhs) const noexcept { return Mint(*this) /= rhs; } constexpr Mint &operator+=(const Mint rhs) noexcept { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr Mint &operator-=(const Mint rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr Mint &operator*=(const Mint rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr Mint &operator/=(Mint rhs) noexcept { u64 exp = Modulus - 2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } constexpr Mint &pow(int rhs) noexcept { u64 exp = static_cast(rhs); Mint base(a); a = 1; while (exp) { if (exp % 2) { *this *= base; } base *= base; exp /= 2; } return *this; } }; struct UnionFind { vector par, sz; UnionFind(int n) : par(n), sz(n, 1) { for (int i = 0; i < n; ++i) par[i] = i; } int root(int x) { if (par[x] == x) return x; return par[x] = root(par[x]); } void merge(int x, int y) { x = root(x); y = root(y); if (x == y) return; if (sz[x] < sz[y]) swap(x, y); par[y] = x; sz[x] += sz[y]; sz[y] = 0; } bool issame(int x, int y) { return root(x) == root(y); } int size(int x) { return sz[root(x)]; } }; vector> tree; vector nodes; int dfs(int v, int p = -1) { int ret = 1; for (auto e : tree[v]) { if (e != p) { ret += dfs(e, v); } } nodes[v] = ret; return ret; } void solve() { int N, M; ll X; cin >> N >> M >> X; tree.resize(N); nodes.resize(N); vector> tapi(M); REP(i, M) { ll x, y, z; cin >> x >> y >> z; x--, y--; tapi[i] = tie(x, y, z); } sort(all(tapi), [](auto l, auto r) { return get<2>(l) < get<2>(r); }); UnionFind uf(N); vector> edges; for (int i = 0; i < M; ++i) { ll x, y, z; tie(x, y, z) = tapi[i]; if (!uf.issame(x, y)) { uf.merge(x, y); tree[x].push_back(y); tree[y].push_back(x); edges.push_back(tuple(x, y, z)); } } dfs(0); Mint ans = 0; for (auto edge : edges) { ll x, y, z; tie(x, y, z) = edge; if (nodes[x] < nodes[y]) swap(x, y); ll sz1 = N - nodes[y]; ll sz2 = nodes[y]; Mint cost = Mint(X).pow(z) * sz1 * sz2; ans += cost; } cout << ans.value() << endl; } int main() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(10); // std::ifstream in("input.txt"); // std::cin.rdbuf(in.rdbuf()); solve(); return 0; }