#include <bits/stdc++.h>
using namespace std;
const int N = 1005;
const int MOD = 1000000007;
int ans[N + 11][N + 11], C[N + 11][N + 11];
int f[N + 11];
int main() {
  for (int i = 0; i <= N; 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;
    }
  }
  f[0] = 1;
  for (int k = 1; k <= N; k++) {
    if (k * (k - 1) / 2 > N) continue;
    long long fac = 1;
    for (int i = 1; i <= k; i++) {
      fac *= i;
      fac %= MOD;
    }
    for (int i = N; i >= 0; i--) {
      for (int times = 1; times * k + i <= N; times++) {
        (f[i + times * k] += f[i]) %= MOD;
      }
    }
    for (int n = 0; n <= N; n++) {
      int tot = k * (k - 1) / 2;
      ans[n][k] = 0;
      int nn = n - tot;
      for (int x = 0; x <= nn; x++) {
        (ans[n][k] += 1LL * f[x] * fac % MOD * C[nn - x + 1][k] % MOD) %= MOD;
      }
    }
  }
  int test;
  scanf("%d", &test);
  while (test--) {
    int n, k;
    scanf("%d %d", &n, &k);
    printf("%d\n", ans[n - 1][k]);
  }
  return 0;
}

### Prompt

Generate a Cpp solution to the following problem:

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>
using namespace std;
const int N = 1005;
const int MOD = 1000000007;
int ans[N + 11][N + 11], C[N + 11][N + 11];
int f[N + 11];
int main() {
  for (int i = 0; i <= N; 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;
    }
  }
  f[0] = 1;
  for (int k = 1; k <= N; k++) {
    if (k * (k - 1) / 2 > N) continue;
    long long fac = 1;
    for (int i = 1; i <= k; i++) {
      fac *= i;
      fac %= MOD;
    }
    for (int i = N; i >= 0; i--) {
      for (int times = 1; times * k + i <= N; times++) {
        (f[i + times * k] += f[i]) %= MOD;
      }
    }
    for (int n = 0; n <= N; n++) {
      int tot = k * (k - 1) / 2;
      ans[n][k] = 0;
      int nn = n - tot;
      for (int x = 0; x <= nn; x++) {
        (ans[n][k] += 1LL * f[x] * fac % MOD * C[nn - x + 1][k] % MOD) %= MOD;
      }
    }
  }
  int test;
  scanf("%d", &test);
  while (test--) {
    int n, k;
    scanf("%d %d", &n, &k);
    printf("%d\n", ans[n - 1][k]);
  }
  return 0;
}

```