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.*;
import java.math.BigInteger;
import java.util.InputMismatchException;

public class Main {
	static PrintWriter out;
	static Reader in;
	public static void main(String[] args) throws IOException {
		input_output();
		Main solver = new Main();
		solver.solve();
		out.close();

		out.flush();
	} 

	static long INF = (long)1e18;
	static int MAXN = (int)1e5 + 5;
	static int MOD = (int)1e9 + 7;
	static int q, t, n, m, k;
	static double pi = Math.PI;

	static List<Integer> adj[];
	static long ans;

	void solve() throws IOException {
		t = in.nextInt();
		
		while (t --> 0) {
			n = in.nextInt();
			k = in.nextInt();

			adj = new ArrayList[n+1];
			for (int i = 1; i <= n; i++) adj[i] = new ArrayList<Integer>();

			for (int i = 0; i < n-1; i++) {
				int u = in.nextInt(),
					v = in.nextInt();
				adj[u].add(v);
				adj[v].add(u);
			}

			ans = 0;

			if (k == 2) {
				ans = (((long)n*(n-1))/2L)%MOD;
				out.println(ans);
				continue;
			}
			int[] par = new int[n+1];
			int[][] down = new int[n+1][n+1],
				    up   = new int[n+1][n+1];
			
			boolean[] vis = new boolean[n+1];
			DFS_DOWN(1, vis, down, par);
			vis = new boolean[n+1];
			BFS_UP(1, vis, up, down, par);

			long[] res = new long[k+1];
			res[0] = 1;
			for (int root = 1; root <= n; root++) {
				for (int depth = 1; depth < n; depth++) {
					for (int i = 1; i <= k; i++) res[i] = 0;

					for (int e: adj[root]) {
						if (e != par[root]) {
							for (int i = k; i >= 1; i--) {
								res[i] = (res[i] + (res[i-1]*down[e][depth-1])%MOD)%MOD;
							}
						} else {
							for (int i = k; i >= 1; i--) {
								res[i] = (res[i] + (res[i-1]*up[root][depth])%MOD)%MOD;
							}
						}
					}
					ans = (ans + res[k])%MOD;
				}
			}

			out.println(ans);
		}	
	}

	static void BFS_UP(int s, boolean[] vis, int[][] up, int[][] down, int[] par) {
		ArrayDeque<Integer> dq = new ArrayDeque<>();
		dq.add(s);
		vis[s] = true;

		while (dq.size() != 0) {
			int e = dq.pollFirst();
			up[e][0] = 1;
			for (int i = 0; i < n; i++) {
				up[e][i+1] += down[par[e]][i]+up[par[e]][i]-(i == 0 || e == 1 ? 0: down[e][i-1])-(i == 0 && e != 1 ? 1: 0);
			}

			for (int ee: adj[e]) {
				if (!vis[ee]) {
					vis[ee] = true;
					dq.addLast(ee);
				}
			}
		}
	}

	static void DFS_DOWN(int s, boolean[] vis, int[][] down, int[] par) {
		vis[s] = true;
		down[s][0] = 1;

		for (int e: adj[s]) {
			if (vis[e]) continue;
			par[e] = s;
			DFS_DOWN(e, vis, down, par);
			for (int i = 0; i < n; i++) down[s][i+1] += down[e][i];
		}
	}

	static class Reader {
		private InputStream mIs;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public Reader() {
			this(System.in);
		}

		public Reader(InputStream is) {
			mIs = is;
		}

		public int read() {
			if (numChars == -1) {
				throw new InputMismatchException();

			}
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = mIs.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String next() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

	}
	static void input_output() throws IOException {
		File f = new File("in.txt");
		if (f.exists() && !f.isDirectory()) {
			in = new Reader(new FileInputStream("in.txt"));
		} else in = new Reader();
		f = new File("out.txt");
		if (f.exists() && !f.isDirectory()) {
			out = new PrintWriter(new File("out.txt"));
		} else out = new PrintWriter(System.out);
	}
}