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
/**
 * author: derrick20
 * created: 8/3/21 10:50 PM
 */
import java.io.*;
import java.util.*;
import static java.lang.Math.*;

public class F_EquidistantVertices {
    static FastScanner sc = new FastScanner();
    static PrintWriter out = new PrintWriter(System.out);
    
    public static void main(String[] args) {
        int T = sc.nextInt();
        while (T-->0) {
            int N = sc.nextInt();
            int K = sc.nextInt();
            adjList = new ArrayList[N];
            Arrays.setAll(adjList, i -> new ArrayList<>());
            for (int i = 0; i < N - 1; i++) {
                int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
                adjList[u].add(v);
                adjList[v].add(u);
            }
            if (K == 2) {
                out.println(N * (N - 1) / 2);
                continue;
            }
            long ans = 0;
            for (int node = 0; node < N; node++) {
                long[][] depthWays = new long[K + 1][N];
                Arrays.fill(depthWays[0], 1);
                for (int adj : adjList[node]) { // this and prev loop sum to 2(N-1)
                    int[] branchFreq = new int[N];
                    dfs(adj, node, 0, branchFreq);
                    // then KN
                    for (int k = K; k >= 1; k--) {
                        for (int depth = 0; depth < N; depth++) {
                            depthWays[k][depth] = (depthWays[k][depth] + depthWays[k - 1][depth] * branchFreq[depth] % mod) % mod;
                        }
                    }
                }
                // So, O(KN^2)
                for (int depth = 0; depth < N; depth++) {
                    ans = (ans + depthWays[K][depth]) % mod;
                }
            }
            out.println(ans);
        }
        out.close();
    }

    static ArrayList<Integer>[] adjList;
    static long mod = (long) 1e9 + 7;

    static void dfs(int node, int par, int depth, int[] freq) {
        freq[depth]++;
        for (int adj : adjList[node]) {
            if (adj != par) {
                dfs(adj, node, depth + 1, freq);
            }
        }
    }

    static class FastScanner {
        private int BS = 1 << 16;
        private char NC = (char) 0;
        private byte[] buf = new byte[BS];
        private int bId = 0, size = 0;
        private char c = NC;
        private double cnt = 1;
        private BufferedInputStream in;
    
        public FastScanner() {
            in = new BufferedInputStream(System.in, BS);
        }
    
        public FastScanner(String s) {
            try {
                in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
            } catch (Exception e) {
                in = new BufferedInputStream(System.in, BS);
            }
        }
    
        char getChar() {
            while (bId == size) {
                try {
                    size = in.read(buf);
                } catch (Exception e) {
                    return NC;
                }
                if (size == -1) return NC;
                bId = 0;
            }
            return (char) buf[bId++];
        }
    
        int nextInt() {
            return (int) nextLong();
        }
    
        long nextLong() {
            cnt = 1;
            boolean neg = false;
            if (c == NC) c = getChar();
            for (; (c < '0' || c > '9'); c = getChar()) {
                if (c == '-') neg = true;
            }
            long res = 0;
            for (; c >= '0' && c <= '9'; c = getChar()) {
                res = (res << 3) + (res << 1) + c - '0';
                cnt *= 10;
            }
            return neg ? -res : res;
        }
    
        double nextDouble() {
            boolean neg = false;
            if (c == NC) c = getChar();
            for (; (c < '0' || c > '9'); c = getChar()) {
                if (c == '-') neg = true;
            }
            double cur = nextLong();
            if (c != '.') {
                return neg ? -cur : cur;
            } else {
                double frac = nextLong() / cnt;
                return neg ? -cur - frac : cur + frac;
            }
        }
    
        String next() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c > 32) {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }
    
        String nextLine() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c != '\n') {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }
    
        boolean hasNext() {
            if (c > 32) return true;
            while (true) {
                c = getChar();
                if (c == NC) return false;
                else if (c > 32) return true;
            }
        }
    }
    
    static void ASSERT(boolean assertion, String message) {
        if (!assertion) throw new AssertionError(message);
    }
    
    static void ASSERT(boolean assertion) {
        if (!assertion) throw new AssertionError();
    }
}