#pragma GCC optimize("O3") #include #define ll long long #define rep(i,n) for(ll i=0;i<(n);i++) #define pll pair #define pii pair #define pq priority_queue #define pb push_back #define eb emplace_back #define fi first #define se second #define endl '\n' #define ios ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0); #define lb(c,x) distance(c.begin(),lower_bound(all(c),x)) #define ub(c,x) distance(c.begin(),upper_bound(all(c),x)) using namespace std; inline int topbit(unsigned long long x){ return x?63-__builtin_clzll(x):-1; } inline int popcount(unsigned long long x){ return __builtin_popcountll(x); } inline int parity(unsigned long long x){//popcount%2 return __builtin_parity(x); } template inline bool chmax(T& a,T b){if(a inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} const ll INF=1e15; const ll mod=1e9+7; struct mint { ll x; // typedef long long ll; mint(ll x=0):x((x%mod+mod)%mod){} mint operator-() const { return mint(-x);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; istream& operator>>(istream& is, mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} // combination mod prime // https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619 struct combination { vector fact, ifact; combination(ll n):fact(n+1),ifact(n+1) { assert(n < mod); fact[0] = 1; for (ll i = 1; i <= n; ++i) fact[i] = fact[i-1]*i; ifact[n] = fact[n].inv(); for (ll i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i; } mint operator()(ll n, ll k) { if (k < 0 || k > n) return 0; return fact[n]*ifact[k]*ifact[n-k]; } mint p(ll n, ll k) { return fact[n]*ifact[n-k]; } } c(1000005); class DisjointSet{ public: vector rank,p,sz; DisjointSet(){} DisjointSet(ll size){ //作られうる木の頂点数の最大値を入れる。 rank.resize(size,0); p.resize(size,0); sz.resize(size,0); rep(i,size) makeSet(i); } void makeSet(ll x){ //xだけが属する木を作る。 p[x]=x; rank[x]=0; } bool same(ll x,ll y){ //xとyが同じ木に属するかどうか return findSet(x)==findSet(y); } void unite(ll x, ll y){ link(findSet(x),findSet(y)); } void link(ll x, ll y){ //rankが大きい方の根に小さい方の根をつける。 if(rank[x]>rank[y]){ p[y]=x; } else{ p[x]=y; if(rank[x]==rank[y]){ rank[y]++; //xとyの木のrankが同じであれば、統合するとrankが1増える。 } } sz[x]+=sz[y]; sz[y]=sz[x]; } ll findSet(ll x){ //xが属する木の根の番号を返す if(x!=p[x]){ p[x]=findSet(p[x]); } return p[x]; } }; vector> to; vector memo; ll dfs(ll v,ll p=-1){ ll res=1; for(auto q:to[v]){ if(q.fi==p) continue; res+=dfs(q.fi,v); } return memo[v]=res; } int main(){ ll n,m; mint X; cin >> n >> m >> X; DisjointSet ds=DisjointSet(n+1); vector> edges(m); memo.resize(n); to=vector>(n); vector not_need(m); rep(i,m){ cin >> edges[i].se.fi >> edges[i].se.se >> edges[i].fi; edges[i].se.fi--; edges[i].se.se--; if(ds.same(edges[i].se.fi,edges[i].se.se)){ not_need[i]=1; } else{ ds.unite(edges[i].se.fi,edges[i].se.se); } } rep(i,m){ if(not_need[i]) continue; to[edges[i].se.fi].push_back({edges[i].se.se,edges[i].fi}); to[edges[i].se.se].push_back({edges[i].se.fi,edges[i].fi}); } ll d=dfs(0LL); mint ans=0; rep(i,m){ if(not_need[i]) continue; mint val=X.pow(edges[i].fi); ll s=memo[edges[i].se.fi]; ll t=memo[edges[i].se.se]; if(s