human
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

mod 
=====
Can you provide a Python code to find the number of ways to choose exactly k vertices in this tree (i?
assistant
#Here is Python code to find the number of ways to choose exactly k vertices in this tree (i.
= 1000000007 

# def power(x, m):
#     if m == 0:
#         return 1
#     if m == 1:
#         return x % mod
#     if m % 2 == 1:
#         return x * power(x, m - 1) % mod
#     tmp = power(x, m // 2)
#     return tmp * tmp % mod

# def C(k, n):
#     if k > n:
#         return 0
#     return gt[n] * pgt[k] % mod * pgt[n - k] % mod

# def build():
#     gt[0] = 1
#     for i in range(1, 101):
#         gt[i] = gt[i - 1] * i % mod
#     pgt[100] = power(gt[100], mod - 2)
#     for i in range(99, -1, -1):
#         pgt[i] = pgt[i + 1] * (i + 1) % mod

def min(x, y):
    if x < y:
        return x
    return y

def solve(m, x):
    if m < k:
        return 0
    f = [[0 for _ in range(k + 1)] for _ in range(m + 1)]
    f[0][0] = 1
    # print(m, k, f[m][k], "ccccc")
    for i in range(1, m + 1):
        for j in range(0, min(k + 1, i + 1)):
            if j == 0:
                f[i][j] = 1
            else:
                f[i][j] = (f[i - 1][j] + cnt[i] * f[i - 1][j - 1] % mod) % mod
            # print(i, j)
    # print(f[m][k], "ccc", x)
    return f[m][k]

def process(x):
    # print(x)
    check[x] = 1
    res = 0
    q = []
    for i in range(len(a[x])):
        v = a[x][i]
        check[v] = 1
        q.append([v, i + 1])
    # print(q)
    res = solve(len(a[x]), x)
    while len(q):
        cur = []
        for i in range(len(q)):
            u = q[i][0]
            j = q[i][1]
            cnt[j] -= 1
            for v in a[u]:
                if check[v] == 0:
                    cur.append([v, j])
                    check[v] = 1
                    cnt[j] += 1
        # print(cur)
        q = cur
        res += solve(len(a[x]), x)
        # print(cnt[1:(len(a[x]) + 1)], x)
        res %= mod
    return res

if __name__ == '__main__':
    test = int(input())
    # gt = [0 for _ in range(104)]
    # pgt = [0 for _ in range(104)]
    # build()
    for _ in range(test):
        input()
        n, k = map(int, input().split())
        a = [[] for _ in range(n + 1)]
        
        for _ in range(n -...