from typing import List class UnionFind: """0-indexed""" def __init__(self, n): self.n = n self.parent = [-1] * n self.__group_count = n def unite(self, x, y) -> bool: """xとyをマージ""" x = self.root(x) y = self.root(y) if x == y: return False self.__group_count -= 1 if self.parent[x] > self.parent[y]: x, y = y, x self.parent[x] += self.parent[y] self.parent[y] = x return True def is_same(self, x, y) -> bool: """xとyが同じ連結成分か判定""" return self.root(x) == self.root(y) def root(self, x) -> int: """xの根を取得""" if self.parent[x] < 0: return x else: # 経路圧縮あり # self.parent[x] = self.root(self.parent[x]) # return self.parent[x] # 経路圧縮なし return self.root(self.parent[x]) def size(self, x) -> int: """xが属する連結成分のサイズを取得""" return -self.parent[self.root(x)] def all_sizes(self) -> List[int]: """全連結成分のサイズのリストを取得 O(N)""" sizes = [] for i in range(self.n): size = self.parent[i] if size < 0: sizes.append(-size) return sizes def members(self, x) -> List[int]: """xが属するグループのリストを返す O(N)""" mem = [] r = self.root(x) for i in range(self.n): if self.root(i) == r: mem.append(i) return mem def groups(self) -> List[List[int]]: """全連結成分の内容のリストを取得 O(N・α(N))""" groups = dict() for i in range(self.n): p = self.root(i) if not groups.get(p): groups[p] = [] groups[p].append(i) return list(groups.values()) @property def group_count(self) -> int: """連結成分の数を取得 O(1)""" return self.__group_count N, M, X = map(int, input().split()) uf = UnionFind(N) G = [list() for _ in range(N)] for i in range(M): x, y, z = map(int, input().split()) x-=1;y-=1 if uf.is_same(x,y):continue uf.unite(x,y) G[x].append((y,z)) G[y].append((x,z)) sub_tree = [0]*N def dfs(v, p): for next_v,_ in G[v]: if next_v == p: continue dfs(next_v, v) sub_tree[v] = 1 for c,_ in G[v]: if c== p: continue sub_tree[v] += sub_tree[c] res = 0 mod = 10**9+7 def dfs2(v, p): for nex, cost in G[v]: if nex==p:continue global res res += pow(X,cost,mod)*(sub_tree[nex]*(N-sub_tree[nex])) res %= mod dfs2(nex,v) dfs(0,-1) dfs2(0,-1) print(res)