The sequence of integer pairs (a1, b1), (a2, b2), ..., (ak, bk) is beautiful, if the following statements are fulfilled: 

  * 1 ≤ a1 ≤ b1 < a2 ≤ b2 < ... < ak ≤ bk ≤ n, where n is a given positive integer; 
  * all numbers b1 - a1, b2 - a2, ..., bk - ak are distinct. 



For the given number n find the number of beautiful sequences of length k. As the answer can be rather large, print the remainder after dividing it by 1000000007 (109 + 7).

Input

The first line contains integer t (1 ≤ t ≤ 2·105) — the number of the test data.

Each of the next t lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000).

Output

For each test from the input print the answer to the problem modulo 1000000007 (109 + 7). Print the answers to the tests in the order in which the tests are given in the input.

Examples

Input

6
1 1
2 1
2 2
3 1
3 2
3 3


Output

1
3
0
6
2
0

Note

In the first test sample there is exactly one beautiful sequence: (1, 1).

In the second test sample, the following sequences are beautiful: 

  * (1, 1); 
  * (1, 2); 
  * (2, 2). 



In the fourth test sample, the following sequences are beautiful: 

  * (1, 1); 
  * (1, 2); 
  * (1, 3); 
  * (2, 2); 
  * (2, 3); 
  * (3, 3). 



In the fifth test sample, the following sequences are beautiful: 

  * (1, 1), (2, 3); 
  * (1, 2), (3, 3). 



In the third and sixth samples, there are no beautiful sequences.
import java.util.*;
import java.io.*;

public class BeautyPair {
	final static int mod = 1000000007;
	static long [][] dp = new long [1010][1010];
	static int [][] ans = new int [1010][1010];
	static int [][] c = new int [1010][1010];

	public static void main (String[] args) {
		Reader in = new Reader ();
		dp[0][0] = 1;
		for(int i = 0; i <= 1000; i++) {
			for(int j = 1; j <= 1000; j++) {
				dp[i][j] = 0;
				dp[i][j] += (i >= (j - 1)) ? dp[i - j + 1][j - 1] : 0;
				dp[i][j] += (i >= j) ?       dp[i - j][j] : 0;
				dp[i][j] %= mod;
			}
		}

		int test = in.nextInt();
		StringBuilder s = new StringBuilder ();

		for(int i = 0; i <= 1000; i++) c[i][0] = 1;
		for(int i = 1; i <= 1000; i++) {
			for(int j = 1; j <= i; j++) {
				c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
				if(c[i][j] >= mod) c[i][j] -= mod;
			}
		}		
		long f[] = new long [1005];		
		f[0] = 1;
		for(int i = 1; i <= 1000; i++) f[i] = (f[i - 1] * i) % mod; 
		
		for(int i = 1; i <= 1000; i++) {
			for(int j = 1; j <= 50; j++) {
				long res = 0;
				for(int k = 0; k <= i; k++) {
					res += dp[k][j] * c[i - k][j];
					res %= mod;
				}
				res *= f[j];
				res %= mod;
				ans[i][j] = (int) res;
			}
		}
		
		for(int q = 1; q <= test; q++) {
			int n = in.nextInt();
			int k = in.nextInt();
			s.append( ans[n][k] ).append("\n");
		}
		System.out.print(s.toString());
	}
	static class Reader {
		private BufferedReader a;
		private StringTokenizer b;
		Reader() {
			a = new BufferedReader (new InputStreamReader (System.in));
		} 
		public String next () {
			while(b == null || !b.hasMoreTokens()) {
				try {
					 b = new StringTokenizer (a.readLine());
				 } catch (IOException e) {
					 e.printStackTrace();
				 }
			 }
			 return b.nextToken();
		 }
		 public int nextInt () {
			 return Integer.parseInt(next());
		 }
		 public long nextLong () {
			 return Long.parseLong(next());
		 }
		 public double nextDouble () {
			 return Double.parseDouble(next());
		 }
		 public String nextLine () {
			try {
				return a.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return "Exception Occured";
		 }
	}
	static class Pair <P, Q> {
		P first;
		Q second;
		Pair () {}
		Pair (P first, Q second) {
			this.first = first;
			this.second = second;
		}	
	}
}
