human
Write me a Python program to find the number of ways to choose exactly k vertices in this tree (i given the following:
A tree is an undirected connected graph without cycles.

You are given a tree of n vertices. Find the number of ways to choose exactly k vertices in this tree (i. e. a k-element subset of vertices) so that all pairwise distances between the selected vertices are equal (in other words, there exists an integer c such that for all u, v (u ≠ v, u, v are in selected vertices) d_{u,v}=c, where d_{u,v} is the distance from u to v).

Since the answer may be very large, you need to output it modulo 10^9 + 7.

Input

The first line contains one integer t (1 ≤ t ≤ 10) — the number of test cases. Then t test cases follow.

Each test case is preceded by an empty line.

Each test case consists of several lines. The first line of the test case contains two integers n and k (2 ≤ k ≤ n ≤ 100) — the number of vertices in the tree and the number of vertices to be selected, respectively. Then n - 1 lines follow, each of them contains two integers u and v (1 ≤ u, v ≤ n, u ≠ v) which describe a pair of vertices connected by an edge. It is guaranteed that the given graph is a tree and has no loops or multiple edges.

Output

For each test case output in a separate line a single integer — the number of ways to select exactly k vertices so that for all pairs of selected vertices the distances between the vertices in the pairs are equal, modulo 10^9 + 7 (in other words, print the remainder when divided by 1000000007).

Example

Input

3

4 2
1 2
2 3
2 4

3 3
1 2
2 3

5 3
1 2
2 3
2 4
4 5

Output

6
0
1
Using python3 can you solve the prior task?
assistant
#Here is Python program to find the number of ways to choose exactly k vertices in this tree (i.

import sys
input=sys.stdin.readline
t=int(input())
mod=10**9+7
for _ in range(t):
    tmp=input()
    n,k=map(int,input().split())
    g=[[] for i in range(n)]
    for __ in range(n-1):
        u,v=map(int,input().split())
        g[u-1].append(v-1)
        g[v-1].append(u-1)
    f=[1]*101
    ans=0
    def dfs(u,depth):
        global ans
        f[u]=0
        for v in g[u]:
            if f[v]:
                dfs(v,depth+1)
                for j in range(n):
                    dp[u][j]+=dp[v][j]
        dp[u][depth]+=1
        if depth==0:
            for i in range(n):
                c=[0]*(k+1)
                c[0]=1
                for to in g[u]:
                    if f[to] and dp[to][i]:
                        for kk in range(1,k+1)[::-1]:
                            c[kk]+=c[kk-1]*dp[to][i]%mod
                            c[kk]%=mod
                ans=(ans+c[k])%mod
        f[u]=1
    for i in range(n):
        dp=[[0]*n for i in range(n)]
        dfs(i,0)
    if k==2:
        print(n*(n-1)//2)
    else:
        print(ans%mod)