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 java.io.*;
import java.util.*;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Task solver = new Task();
		int tcCnt = in.nextInt();
		for (int tc = 1; tc <= tcCnt; tc++)
			solver.solve(tc, in, out);
		out.close();
	}

	static class Task {
		final long MOD = (long)(1e9 + 7);
		int n, k;
		List<Integer>[] list;
		public void solve(int testNumber, InputReader in, PrintWriter out) {
			n = in.nextInt();
			k = in.nextInt();
			list = new ArrayList[n+1];
			for (int i = 1; i <= n; i++) {
				list[i] = new ArrayList<Integer>();
			}
			for (int i = 1; i < n; i++) {
				int u = in.nextInt();
				int v = in.nextInt();
				list[u].add(v);
				list[v].add(u);
			}
			if (k == 2) {
				out.println(((1l * n * (n-1)) / 2) % MOD);
				return;
			}
			long ans = 0;
			for (int i = 1; i <= n; i++) {
				ans = (ans + noOfSets(i)) % MOD;
			}
			out.println(ans);
		}
		long noOfSets(int node) {
			Queue<Integer> queue = new LinkedList<>();
			int[] subtreeIndex = new int[n+1];
			subtreeIndex[node] = -1;
			for (int i = 0; i < list[node].size(); i++) {
				int next = list[node].get(i);
				subtreeIndex[next] = i+1;
				queue.add(next);
			}

			int nn = list[node].size();
			int[] cnt = new int[nn+1];
			Arrays.fill(cnt, 1);

			// dp[i][j] is the number of sets of length j from the first i subtrees
			long[][] dp = new long[nn+1][k+1];
			long ans = 0;

			while(!queue.isEmpty()) {

				for (int i = 0; i <= nn; i++) {
					for (int j = 0; j <= i && j <= k; j++) {
						if (i == 0) {
							if (j == 0) {
								dp[i][j] = 1;
							} else {
								dp[i][j] = 0;
							}
						} else {
							dp[i][j] = (dp[i-1][j] + (j > 0 ? (dp[i-1][j-1] * cnt[i]) % MOD : 0)) % MOD;
						}
					}
				}

				ans = (ans + dp[nn][k]) % MOD;

				for (int i = queue.size(); i > 0 ; i--) {
					int curr = queue.remove();
					cnt[subtreeIndex[curr]]--;
					for (int next: list[curr]) {
						if (subtreeIndex[next] == 0) {
							cnt[subtreeIndex[curr]]++;
							subtreeIndex[next] = subtreeIndex[curr];
							queue.add(next);
						}
					}
				}
			}
			return ans;
		}

	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}

		public String nextToken() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				tokenizer = new StringTokenizer(nextLine());
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextToken());
		}

		public double nextDouble() {
			return Double.parseDouble(nextToken());
		}

		public long nextLong() {
			return Long.parseLong(nextToken());
		}

		public int[] nextIntArray(int size) {
			int[] arr = new int[size];
			for (int i = 0; i < size; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

	}
}