#define MOD_TYPE 1 #pragma region Macros #include using namespace std; #if 0 #include #include using Int = boost::multiprecision::cpp_int; using lld = boost::multiprecision::cpp_dec_float_100; #endif #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") using ll = long long int; using ld = long double; using pii = pair; using pll = pair; using pld = pair; template using smaller_queue = priority_queue, greater>; constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353); //constexpr ll MOD = 1; constexpr int INF = (int)1e9 + 10; constexpr ll LINF = (ll)4e18; constexpr double PI = acos(-1.0); constexpr double EPS = 1e-11; constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0}; constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0}; #define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i) #define rep(i, n) REP(i, 0, n) #define REPI(i, m, n) for (int i = m; i < (int)(n); ++i) #define repi(i, n) REPI(i, 0, n) #define MP make_pair #define MT make_tuple #define YES(n) cout << ((n) ? "YES" : "NO") << "\n" #define Yes(n) cout << ((n) ? "Yes" : "No") << "\n" #define possible(n) cout << ((n) ? "possible" : "impossible") << "\n" #define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n" #define Yay(n) cout << ((n) ? "Yay!" : ":(") << "\n" #define all(v) v.begin(), v.end() #define NP(v) next_permutation(all(v)) #define dbg(x) cerr << #x << ":" << x << "\n"; struct io_init { io_init() { cin.tie(0); ios::sync_with_stdio(false); cout << setprecision(30) << setiosflags(ios::fixed); }; } io_init; template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } inline ll CEIL(ll a, ll b) { return (a + b - 1) / b; } template inline void Fill(A (&array)[N], const T &val) { fill((T *)array, (T *)(array + N), val); } template constexpr istream &operator>>(istream &is, pair &p) noexcept { is >> p.first >> p.second; return is; } template constexpr ostream &operator<<(ostream &os, pair &p) noexcept { os << p.first << " " << p.second; return os; } #pragma endregion #pragma region mint template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) v += MOD; } constexpr int getmod() { return MOD; } constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; } constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; } constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; } constexpr Fp &operator+=(const Fp &r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp &operator-=(const Fp &r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp &operator*=(const Fp &r) noexcept { val = val * r.val % MOD; if (val < 0) val += MOD; return *this; } constexpr Fp &operator/=(const Fp &r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator==(const Fp &r) const noexcept { return this->val == r.val; } constexpr bool operator!=(const Fp &r) const noexcept { return this->val != r.val; } friend constexpr ostream &operator<<(ostream &os, const Fp &x) noexcept { return os << x.val; } friend constexpr istream &operator>>(istream &is, Fp &x) noexcept { return is >> x.val; } }; Fp modpow(const Fp &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } using mint = Fp; #pragma endregion struct UnionFind { vector par, rank_; UnionFind() {} UnionFind(int n) : par(n), rank_(n, 0) { iota(begin(par), end(par), 0); } int root(int x) { return par[x] == x ? x : par[x] = root(par[x]); } bool same(int x, int y) { return root(x) == root(y); } void unite(int x, int y) { x = root(x); y = root(y); if (x == y) return; if (rank_[x] < rank_[y]) { par[x] = y; } else { par[y] = x; if (rank_[x] == rank_[y]) rank_[x]++; } } }; template struct kruskal { UnionFind uf; kruskal(int n = 200010) : uf(n) {} struct edge { int u, v; T cost; int num; }; vector E; set used_num; void add_E(int s, int t, T w) { static int i = 0; E.push_back({s, t, w, i++}); } T calc() { sort(E.begin(), E.end(), [](edge &e1, edge &e2) { return e1.cost < e2.cost; }); T res = 0; for (auto e : E) { if (!uf.same(e.u, e.v)) { uf.unite(e.u, e.v); res += e.cost; used_num.insert(e.num); } } return res; } bool used(int i) { return used_num.count(i); } }; template struct Tree { int V; using P = pair; vector> E; vector par; vector depth; vector sub; vector dist; vector> par_double; Tree(int V_) : V(V_) { E.resize(V); depth.resize(V); dist.resize(V); sub.resize(V); } void add_E(int a, int b, T w = T(1), bool direction = false) { E[a].push_back(make_pair(b, w)); if (!direction) E[b].push_back(make_pair(a, w)); } int dfs(int p, int d, T w) { sub[p] = 1; for (auto pi : E[p]) { int v = pi.first; if (par[p] == v) continue; par[v] = p; depth[v] = d + 1; dist[v] = w + pi.second; sub[p] += dfs(v, depth[v], dist[v]); } return sub[p]; } void make_tree(int root = 0) { calculated = false; par.assign(V, -1); par_double.assign(V, vector(25)); depth[root] = 0; dist[root] = T(0); dfs(root, 0, 0); } bool calculated; void calc_double() { for (int i = 0; i < V; i++) par_double[i][0] = par[i]; for (int k = 0; k < 24; k++) { for (int i = 0; i < V; i++) { if (par_double[i][k] == -1) par_double[i][k + 1] = -1; else par_double[i][k + 1] = par_double[par_double[i][k]][k]; } } } int getLCA(int a, int b) { if (!calculated) { calc_double(); calculated = true; } if (a == b) return a; if (depth[a] < depth[b]) swap(a, b); for (int k = 24; k >= 0; k--) { if (par_double[a][k] != -1 && depth[par_double[a][k]] >= depth[b]) a = par_double[a][k]; } if (a == b) return a; for (int k = 24; k >= 0; k--) { if (par_double[a][k] != -1 && par_double[a][k] != par_double[b][k]) { a = par_double[a][k]; b = par_double[b][k]; } } return par_double[a][0]; } int length(int a, int b) { return depth[a] + depth[b] - 2 * depth[getLCA(a, b)]; } int distance(int a, int b) { return dist[a] + dist[b] - 2 * dist[getLCA(a, b)]; } T diameter(int &a, int &b) { T Max(-1); for (int i = 0; i < V; i++) { if (Max < distance(0, i)) Max = distance(0, i), a = i; } for (int i = 0; i < V; i++) { if (Max < distance(a, i)) Max = distance(a, i), b = i; } return Max; } T diameter() { int a, b; return diameter(a, b); } int diameter_l(int &a, int &b) { int Max = -1; for (int i = 0; i < V; i++) { if (Max < length(0, i)) Max = length(0, i), a = i; } for (int i = 0; i < V; i++) { if (Max < length(a, i)) Max = length(a, i), b = i; } return Max; } int diameter_l() { int a, b; return diameter_l(a, b); } }; void solve() { ll n, m; ll x; cin >> n >> m >> x; kruskal ks(n); rep(i, m) { int x, y; ll z; cin >> x >> y >> z; x--, y--; ks.add_E(x, y, z); } ks.calc(); Tree tr(n); for (auto i : ks.used_num) { auto [u, v, z, num] = ks.E[i]; tr.add_E(u, v, z); } tr.make_tree(); mint ans = 0; for (auto i : ks.used_num) { auto [u, v, z, num] = ks.E[i]; if (tr.par[v] == u) swap(u, v); ll t = tr.sub[u] * (n - tr.sub[u]); ans += modpow(x, z) * t; } cout << ans << "\n"; } int main() { solve(); }