Problem Description
You are given a directed graph, which is constructed as follows:
- Pick an connected undirected graph with exactly n vertices and n edges. The vertices are numbered 1 through n.
- Convert each undirected edge into a directed edge, satisfying each vertice's outdegree equals 1.
Also you're given m different colors to color the vertices. Your task is to calculate the number of different colored graphs that can be made.
Two colored graphs A and B are considered the same if and only if there exists a mapping P satisfying the following constraints:
- Vertice u in graph A has the same color as vertice P(u) in graph B.
- For any two different vertices u and v in graph A, P(u) and P(v) are different vertices in graph B.
- For any directed edge u -> v in graph A, there exists a corresponding directed edge P(u) -> P(v) in graph B.
Print the answer module 10^9 + 7.
Input
The first line contains a number T(1 <= T <= 10), denoting the number of testcases.
For each testcase, the first line contains two space-seperated integers n and m(3 <= n <= 10^5, 1 <= m <= 10^9), representing the number of vertices in the graph and the number of colors you have.
Then, n lines follow. The i-th of them contains an integer f_i, denoting a directed edge from vertice i to vertice f_i in the given graph.(1 <= f_i <= n, f_i != i)
Output
For each testcase, print a line containing the answer.
Sample Input
1
6 3
2
3
4
1
1
3
Sample Output
378
