#include using namespace std; using ll = long long; #define ALL(obj) (obj).begin(),(obj).end() template using priority_queue_reverse = priority_queue,greater>; constexpr long long MOD = 1'000'000'000LL + 7; constexpr long long MOD2 = 998244353; constexpr long long HIGHINF = (long long)1e18; constexpr long long LOWINF = (long long)1e15; constexpr long double PI = 3.1415926535897932384626433L; template vector multivector(size_t N,T init){return vector(N,init);} template auto multivector(size_t N,T... t){return vector(N,multivector(t...));} template void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}} template ostream &operator<<(ostream &o, const map&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;} template ostream &operator<<(ostream &o, const set&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} template ostream &operator<<(ostream &o, const multiset&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} template ostream &operator<<(ostream &o, const vector&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;} template ostream &operator<<(ostream &o, const pair&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;} void print(void) {cout << endl;} template void print(Head&& head) {cout << head;print();} template void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward(tail)...);} template void chmax(T& a, const T b){a=max(a,b);} template void chmin(T& a, const T b){a=min(a,b);} vector split(const string &str, const char delemiter) {vector res;stringstream ss(str);string buffer; while( getline(ss, buffer, delemiter) ) res.push_back(buffer); return res;} int msb(int x) {return x?31-__builtin_clz(x):-1;} void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;} void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;} void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;} /* * @title ModInt */ template class ModInt { public: long long x; constexpr ModInt():x(0) { // do nothing } constexpr ModInt(long long y) : x(y>=0?(y%mod): (mod - (-y)%mod)%mod) { // do nothing } ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator+=(const long long y) { ModInt p(y); if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator+=(const int y) { ModInt p(y); if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const long long y) { ModInt p(y); if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const int y) { ModInt p(y); if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (x * p.x % mod); return *this; } ModInt &operator*=(const long long y) { ModInt p(y); x = (x * p.x % mod); return *this; } ModInt &operator*=(const int y) { ModInt p(y); x = (x * p.x % mod); return *this; } ModInt &operator^=(const ModInt &p) { x = (x ^ p.x) % mod; return *this; } ModInt &operator^=(const long long y) { ModInt p(y); x = (x ^ p.x) % mod; return *this; } ModInt &operator^=(const int y) { ModInt p(y); x = (x ^ p.x) % mod; return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inv(); return *this; } ModInt &operator/=(const long long y) { ModInt p(y); *this *= p.inv(); return *this; } ModInt &operator/=(const int y) { ModInt p(y); *this *= p.inv(); return *this; } ModInt operator=(const int y) { ModInt p(y); *this = p; return *this; } ModInt operator=(const long long y) { ModInt p(y); *this = p; return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator++() { x++; if(x>=mod) x-=mod; return *this; } ModInt operator--() { x--; if(x<0) x+=mod; return *this; } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } ModInt operator^(const ModInt &p) const { return ModInt(*this) ^= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inv() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(long long n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { long long t; is >> t; a = ModInt(t); return (is); } }; using modint = ModInt; /* * @title UnionFindTree */ class UnionFindTree { vector parent,maxi,mini; inline int root(int n) { return (parent[n]<0?n:parent[n] = root(parent[n])); } public: UnionFindTree(int N = 1) : parent(N,-1),maxi(N),mini(N){ iota(maxi.begin(),maxi.end(),0); iota(mini.begin(),mini.end(),0); } inline bool connected(int n, int m) { return root(n) == root(m); } inline void merge(int n, int m) { n = root(n); m = root(m); if (n == m) return; if(parent[n]>parent[m]) swap(n, m); parent[n] += parent[m]; parent[m] = n; maxi[n] = std::max(maxi[n],maxi[m]); mini[n] = std::min(mini[n],mini[m]); } inline int min(int n) { return mini[root(n)]; } inline int max(int n) { return maxi[root(n)]; } inline int size(int n){ return (-parent[root(n)]); } inline int operator[](int n) { return root(n); } inline void print() { for(int i = 0; i < parent.size(); ++i) cout << root(i) << " "; cout << endl; } }; /* * @title Tree * @docs md/graph/Tree.md */ template class Tree { using TypeDist = typename Operator::TypeDist; size_t num; size_t ord; enum METHODS{ MAKE_DEPTH, MAKE_CHILD, MAKE_PARENT, MAKE_SIZE, MAKE_SUBTREE, MAKE_ANCESTOR, MAKE_EOULERTOUR, MAKE_HEAVY_LIGHT_DECOMPOSITION, METHODS_SIZE, }; array executed_flag; public: vector>> edge; vector depth; vector order; vector reorder; vector dist; vector> parent; vector>> child; vector,Operator::bit>> ancestor; vector size; vector> subtree; vector head; vector hldorder; vector eulertour; vector> eulertour_range; Tree(const int num):num(num),edge(num),depth(num,-1),order(num),dist(num),executed_flag(){} //O(1) anytime void make_edge(const int& from, const int& to, const TypeDist w = 1) { edge[from].push_back({to,w}); } //O(N) anytime void make_depth(const int root) { executed_flag[MAKE_DEPTH]++; depth[root] = 0; dist[root] = Operator::unit_dist; ord = 0; dfs(root,-1); order[ord++] = root; reverse_copy(order.begin(),order.end(),back_inserter(reorder)); } //O(N) anytime for forest void make_depth(void) { executed_flag[MAKE_DEPTH]++; ord = 0; for(size_t root = 0; root < num; ++root) { if(depth[root] != -1) continue; depth[root] = 0; dist[root] = Operator::unit_dist; dfs(root,-1); order[ord++] = root; } reverse_copy(order.begin(),order.end(),back_inserter(reorder)); } //for make_depth void dfs(int curr, int prev){ for(auto& e:edge[curr]){ int next = e.first; if(next==prev) continue; depth[next] = depth[curr] + 1; dist[next] = Operator::func_dist(dist[curr],e.second); dfs(next,curr); order[ord++] = next; } } //for make_eulertour void dfs(int from){ eulertour.push_back(from); for(auto& e:child[from]){ int to = e.first; dfs(to); eulertour.push_back(from); } } //O(N) after make_depth void make_parent(const int root = 0) { if(executed_flag[MAKE_PARENT]++) return; if(!executed_flag[MAKE_DEPTH]) make_depth(root); parent.resize(num,make_pair(num,Operator::unit_dist)); for (size_t i = 0; i < num; ++i) for (auto& e : edge[i]) if (depth[i] > depth[e.first]) parent[i] = e; } //O(N) after make_depth void make_child(const int root = 0) { if(executed_flag[MAKE_CHILD]++) return; if(!executed_flag[MAKE_DEPTH]) make_depth(root); child.resize(num); for (size_t i = 0; i < num; ++i) for (auto& e : edge[i]) if (depth[i] < depth[e.first]) child[i].push_back(e); } //O(NlogN) after make_parent void make_ancestor(const int root = 0) { if(executed_flag[MAKE_ANCESTOR]++) return; if(!executed_flag[MAKE_PARENT]) make_parent(root); ancestor.resize(num); for (size_t i = 0; i < num; ++i) ancestor[i][0] = (parent[i].first!=num?parent[i]:make_pair(i,Operator::unit_lca)); for (size_t j = 1; j < Operator::bit; ++j) { for (size_t i = 0; i < num; ++i) { size_t k = ancestor[i][j - 1].first; ancestor[i][j] = Operator::func_lca(ancestor[k][j - 1],ancestor[i][j - 1]); } } } //O(logN) after make_ancestor //return {lca,lca_dist} l and r must be connected pair lca(size_t l, size_t r) { assert(executed_flag[MAKE_ANCESTOR]); if (depth[l] < depth[r]) swap(l, r); int diff = depth[l] - depth[r]; auto ancl = make_pair(l,Operator::unit_lca); auto ancr = make_pair(r,Operator::unit_lca); for (int j = 0; j < Operator::bit; ++j) { if (diff & (1 << j)) { ancl = Operator::func_lca(ancestor[ancl.first][j],ancl); } } if(ancl.first==ancr.first) return ancl; for (int j = Operator::bit - 1; 0 <= j; --j) { if(ancestor[ancl.first][j].first!=ancestor[ancr.first][j].first) { ancl = Operator::func_lca(ancestor[ancl.first][j],ancl); ancr = Operator::func_lca(ancestor[ancr.first][j],ancr); } } ancl = Operator::func_lca(ancestor[ancl.first][0],ancl); ancr = Operator::func_lca(ancestor[ancr.first][0],ancr); return Operator::func_lca(ancl,ancr); } //O(N) anytime //pair pair> diameter(void){ make_depth(0); int root = max_element(dist.begin(), dist.end()) - dist.begin(); make_depth(root); int leaf = max_element(dist.begin(), dist.end()) - dist.begin(); make_parent(); TypeDist d = dist[leaf]; vector v; while (leaf != root) { v.push_back(leaf); leaf = parent[leaf].first; } v.push_back(root); return make_pair(d,v); } //O(N^2) after make_depth void make_subtree(const int root = 0) { if(executed_flag[MAKE_SUBTREE]++) return; if(!executed_flag[MAKE_DEPTH]) make_depth(root); subtree.resize(num); for (size_t i = 0; i < num; ++i) subtree[i].push_back(i); for (size_t i = 0; i < num; ++i) for (auto& e : edge[order[i]]) if (depth[order[i]] < depth[e.first]) for(auto k: subtree[e.first]) subtree[order[i]].push_back(k); } //O(N) after make_child void make_size(const int root = 0) { if(executed_flag[MAKE_SIZE]++) return; if(!executed_flag[MAKE_CHILD]) make_child(root); size.resize(num,1); for (size_t i:order) for (auto e : child[i]) size[i] += size[e.first]; } //(N) after make_depth and make_child template vector rerooting(vector rerootdp,vector rerootparent) { assert(executed_flag[MAKE_CHILD]); for(size_t pa:order) for(auto& e:child[pa]) rerootdp[pa] = Operator::func_reroot(rerootdp[pa],rerootdp[e.first]); for(size_t pa:reorder) { if(depth[pa]) rerootdp[pa] = Operator::func_reroot(rerootdp[pa],rerootparent[pa]); size_t m = child[pa].size(); for(int j = 0; j < m && depth[pa]; ++j){ size_t ch = child[pa][j].first; rerootparent[ch] = Operator::func_reroot(rerootparent[ch],rerootparent[pa]); } if(m <= 1) continue; vector l(m),r(m); for(int j = 0; j < m; ++j) { size_t ch = child[pa][j].first; l[j] = rerootdp[ch]; r[j] = rerootdp[ch]; } for(int j = 1; j+1 < m; ++j) l[j] = Operator::func_reroot_merge(l[j],l[j-1]); for(int j = m-2; 0 <=j; --j) r[j] = Operator::func_reroot_merge(r[j],r[j+1]); size_t chl = child[pa].front().first; size_t chr = child[pa].back().first; rerootparent[chl] = Operator::func_reroot(rerootparent[chl],r[1]); rerootparent[chr] = Operator::func_reroot(rerootparent[chr],l[m-2]); for(int j = 1; j+1 < m; ++j) { size_t ch = child[pa][j].first; rerootparent[ch] = Operator::func_reroot(rerootparent[ch],l[j-1]); rerootparent[ch] = Operator::func_reroot(rerootparent[ch],r[j+1]); } } return rerootdp; } //O(N) after make_depth,make_parent,make_child void make_heavy_light_decomposition(const int root = 0){ if(executed_flag[MAKE_HEAVY_LIGHT_DECOMPOSITION]++) return; if(!executed_flag[MAKE_SIZE]) make_size(root); if(!executed_flag[MAKE_PARENT]) make_parent(root); head.resize(num); hldorder.resize(num); iota(head.begin(),head.end(),0); for(size_t& pa:reorder) { pair maxi = {0,num}; for(auto& e:child[pa]) maxi = max(maxi,{size[e.first],e.first}); if(maxi.first) head[maxi.second] = head[pa]; } stack st_head,st_sub; size_t cnt = 0; for(size_t& root:reorder){ if(depth[root]) continue; st_head.push(root); while(st_head.size()){ size_t h = st_head.top(); st_head.pop(); st_sub.push(h); while (st_sub.size()){ size_t pa = st_sub.top(); st_sub.pop(); hldorder[pa] = cnt++; for(auto& e:child[pa]) { if(head[e.first]==head[pa]) st_sub.push(e.first); else st_head.push(e.first); } } } } } //after hld type 0: vertex, 1: edge vector> path(size_t u,size_t v,int type = 0) { assert(executed_flag[MAKE_HEAVY_LIGHT_DECOMPOSITION]); vector> path; while(1){ if(hldorder[u]>hldorder[v]) swap(u,v); if(head[u]!=head[v]) { path.push_back({hldorder[head[v]],hldorder[v]}); v=parent[head[v]].first; } else { path.push_back({hldorder[u],hldorder[v]}); break; } } reverse(path.begin(),path.end()); if(type) path.front().first++; return path; } size_t hld_lca(size_t u,size_t v){ assert(executed_flag[MAKE_HEAVY_LIGHT_DECOMPOSITION]); while(1){ if(hldorder[u]>hldorder[v]) swap(u,v); if(head[u]==head[v]) return u; v=parent[head[v]].first; } } //O(N) after make_child and make_parent void make_eulertour(const int root = 0){ if(executed_flag[MAKE_EOULERTOUR]++) return; if(!executed_flag[MAKE_CHILD]) make_child(root); if(!executed_flag[MAKE_PARENT]) make_parent(root); dfs(reorder.front()); eulertour_range.resize(num); for(int i = 0; i < eulertour.size(); ++i) eulertour_range[eulertour[i]].second = i; for(int i = eulertour.size()-1; 0 <= i; --i) eulertour_range[eulertour[i]].first = i; } }; //depth,dist //https://atcoder.jp/contests/abc126/tasks/abc126_d //child //https://atcoder.jp/contests/abc133/tasks/abc133_e //lca //https://atcoder.jp/contests/abc014/tasks/abc014_4 //weighted lca //https://atcoder.jp/contests/code-thanks-festival-2017-open/tasks/code_thanks_festival_2017_h //https://atcoder.jp/contests/cf16-tournament-round1-open/tasks/asaporo_c //diameter //https://atcoder.jp/contests/agc033/tasks/agc033_c //subtree //https://atcoder.jp/contests/code-thanks-festival-2018/tasks/code_thanks_festival_2018_f //rerooting //https://yukicoder.me/problems/no/922 //size //https://yukicoder.me/problems/no/872 //eulerTour //https://yukicoder.me/problems/no/900 //hld //https://yukicoder.me/problems/no/399 //https://yukicoder.me/problems/no/650 template struct TreeOperator{ using TypeDist = T; inline static constexpr size_t bit = 20; inline static constexpr TypeDist unit_dist = 0; inline static constexpr TypeDist unit_lca = 0; inline static constexpr TypeDist func_dist(const TypeDist& parent,const TypeDist& w){return parent+w;} inline static constexpr pair func_lca(const pair& l,const pair& r){return make_pair(l.first,l.second+r.second);} template inline static constexpr TypeReroot func_reroot(const TypeReroot& l,const TypeReroot& r) { return {l.first+r.first+r.second,l.second+r.second}; } template inline static constexpr TypeReroot func_reroot_merge(const TypeReroot& l,const TypeReroot& r) { return {l.first+r.first,l.second+r.second}; } }; /* * @title Mod */ class Mod{ public: //Pow_Mod O(log(n)) inline static long long pow(long long x, long long n, long long mod) { long long res = 1; for (x %= mod; n > 0; n >>= 1, (x *= x) %= mod) if (n & 1) (res *= x) %= mod; return res; } //Inv_Mod O(log(mod)) inline static long long inv(long long x, long long mod){ return pow(x,mod-2,mod); } }; int main() { cin.tie(0);ios::sync_with_stdio(false); ll N,M,X; cin >> N >> M >> X; vector u(M),v(M),w(M); for(int i = 0; i < M; ++i) cin >> u[i] >> v[i] >> w[i]; for(int i = 0; i < M; ++i) u[i]--,v[i]--; vector idx(M); iota(ALL(idx),0); sort(ALL(idx),[&](int l,int r){return w[l]> tree(N); for(int i:idx) { int l=u[i],r=v[i]; if(uf.connected(l,r)) continue; uf.merge(l,r); modint c = Mod::pow(X,w[i],MOD); tree.make_edge(l,r,c); tree.make_edge(r,l,c); } tree.make_size(0); tree.make_parent(); modint ans = 0; for(int pa:tree.order) { if(!tree.depth[pa]) continue; modint c = tree.parent[pa].second; ll sz = tree.size[pa]; ans += c * sz * (N-sz); } cout << ans << endl; return 0; }