18763번 - Knowledge-Oriented Problem 다국어

문제

After gaining a lot of knowledge, you decided to write a knowledge-oriented problem.

You are given an undirected graph G with n vertices and m edges. You copy it k times and denote the copies by G₁, G₂, . . . , G_k. You add edges between vertex u in copy G_i and the same vertex u in copy G_i+1 for all 1 ≤ i ≤ k−1 and 1 ≤ u ≤ n.

Find the number of spanning trees of the new graph. The answer can be large, so output it modulo 10⁹ + 7.

입력

The first line contains three integers n, m, k (1 ≤ n ≤ 500, 0 ≤ m ≤ n(n−1)/2, 1 ≤ k ≤ 10¹⁸).

Each of the following m lines contains two integers u, v (1 ≤ u, v ≤ n, u ≠ v) indicating an undirected edge (u, v) in the graph. All edges are distinct.

출력

Output one integer: the answer.

제한

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