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
import sys

input = sys.stdin.readline

F = [None]*101
F[0] = 1
for i in range(1,len(F)):
	F[i] = (F[i-1] * i) % int(1e9+7)

def rec(x, p, g, c, s):
	c[s] += 1
	for v in g[x]:
		if v != p:
			rec(v, x, g, c, s+1)

def solve():
	input()
	n, k = map(int, input().split())
	g = [[] for i in range(n+1)]
	for i in range(n-1):
		u, v = map(int, input().split())
		g[u].append(v)
		g[v].append(u)
	MOD = int(1e9+7)
	if k == 2:
		print((n * (n-1) // 2) % MOD)
		return
	r = 0
	for x in range(1,n+1):
		d = [[0]*n for i in range(k+1)]
		d[0] = [1]*n
		for v in g[x]:
			c = [0] * n
			rec(v, x, g, c, 0)
			#print(x, v, c)
			for i in range(k-1,-1,-1):
				for j in range(n):
					d[i+1][j] = (d[i+1][j] + d[i][j] * c[j]) % MOD
		#print(x,d)
		for j in range(n):
			r = (r + d[k][j]) % MOD
	print(r)

for i in range(int(input())):
	solve()
