class UnionFind: def __init__(self, n): self.n = n self.parents = [-1] * n def find(self, x): """ 根を見つける関数を定義(同時にxを直接根にくっつける操作も行う)""" tmp = [] parents = self.parents while parents[x] >= 0: tmp.append(x) x = parents[x] for y in tmp: parents[y] = x return x def union(self, x, y): """ 二つの木をくっつける(子を多く持つ方を根とした親子関係)。これは破壊的操作を行う。""" x = self.find(x) y = self.find(y) if x == y: return False if self.parents[x] > self.parents[y]: x, y = y, x self.parents[x] += self.parents[y] self.parents[y] = x return True def same(self, x, y): """ xとyが同じ根の子かを判定 """ return self.find(x) == self.find(y) def size(self, x): """ xの根のparent(= 要素数)を返す """ return -self.parents[self.find(x)] def members(self, x): """ xが属するグループの要素をリストとして返す O(N)""" root = self.find(x) return [i for i in range(self.n) if self.find(i) == root] def roots(self): """ 全ての根の要素をリストとして返す O(N)""" return [i for i, x in enumerate(self.parents) if x < 0] def group_count(self): """ グループの数を返す O(N)""" return len(self.roots()) def size_list(self): """ 各グループの要素数のリストを返す(根の番号は返さない) O(N)""" return [-x for x in self.parents if x < 0] def all_group_members(self): """ {根:[根の子(根を含む)のリスト],...}を辞書で返す O(N)""" res = [[] for _ in range(self.n)] for i in range(self.n): x = self.find(i) res[x].append(i) return {r: res[r] for r in self.roots()} def __str__(self): return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots()) def dfs(start=0,goal=None): p,t=start,0 parents[p]=-2 next_set=[(p,t)] if p==goal: return t while next_set: p,t=next_set.pop() if p>=0: for q in edges[p]: if q in parents: continue if q==goal: return t+1 parents[q]=p next_set.append((~q,t+1)) next_set.append((q,t+1)) else: # 帰りがけ処理 p=~p par=parents[p] size[par]+=size[p] return -1 def example(): global input example = iter( """ 5 5 5 1 4 3 2 4 4 3 5 7 2 3 8 2 3 10 """ .strip().split("\n")) input = lambda: next(example) #####( main )#################################################################### import sys input=sys.stdin.readline # example() N,M,X=map(int,input().split()) data=[] for _ in range(M): p,q,cost=map(int,input().split()) p,q = p-1,q-1 data.append((p,q,cost)) size=[1]*N parents=[-1]*N UF=UnionFind(N) edges=[[] for _ in range(N)] used=[0]*M data2=[] for p,q,dist in data: if UF.union(p,q): edges[p].append(q) edges[q].append(p) data2.append((p,q,dist)) for i in range(N): if parents[i]==-1: dfs(start=i) MOD=10**9+7 res=0 for p,q,cost in data2: if parents[q]!=p: q,p=p,q n=UF.size(p) m=size[q] res+=m*(n-m)*pow(X,cost,MOD) res%=MOD print(res)