#include <bits/stdc++.h>
const int mod = 1000000007;
long long dp[1010][1010], c[1010][1010], fac[1010];
int T, n, k;
using namespace std;
int main() {
  dp[0][0] = 1;
  for (int add = 1; add <= 1000; add++)
    for (int i = 1000; i >= add; i--) {
      int j = 1;
      while (j * (j - 1) / 2 <= i - add) {
        dp[i][j] += dp[i - add][j - 1];
        dp[i][j] %= mod;
        j++;
      }
    }
  c[0][0] = 1;
  for (int i = 1; i <= 1000; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= i; j++)
      c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod;
  }
  fac[0] = 1;
  for (int i = 1; i <= 1000; i++) fac[i] = fac[i - 1] * i % mod;
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &n, &k);
    long long ans = 0;
    for (int i = k * (k + 1) / 2; i <= n; i++) {
      ans += dp[i][k] * fac[k] % mod * c[k + 1 + n - i - 1][n - i] % mod;
      ans %= mod;
    }
    printf("%I64d\n", ans);
  }
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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.

### Response

```cpp
#include <bits/stdc++.h>
const int mod = 1000000007;
long long dp[1010][1010], c[1010][1010], fac[1010];
int T, n, k;
using namespace std;
int main() {
  dp[0][0] = 1;
  for (int add = 1; add <= 1000; add++)
    for (int i = 1000; i >= add; i--) {
      int j = 1;
      while (j * (j - 1) / 2 <= i - add) {
        dp[i][j] += dp[i - add][j - 1];
        dp[i][j] %= mod;
        j++;
      }
    }
  c[0][0] = 1;
  for (int i = 1; i <= 1000; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= i; j++)
      c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod;
  }
  fac[0] = 1;
  for (int i = 1; i <= 1000; i++) fac[i] = fac[i - 1] * i % mod;
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &n, &k);
    long long ans = 0;
    for (int i = k * (k + 1) / 2; i <= n; i++) {
      ans += dp[i][k] * fac[k] % mod * c[k + 1 + n - i - 1][n - i] % mod;
      ans %= mod;
    }
    printf("%I64d\n", ans);
  }
  return 0;
}

```