#include <bits/stdc++.h>
using namespace std;
const int NMax = 1010;
long long INF = 1000000007LL;
long long dp[NMax][NMax], C[NMax * 2][NMax];
void INIT() {
  C[0][0] = 1;
  for (int i = 1; i <= 2000; i++) {
    C[i][0] = 1;
    for (int j = 1; j <= i; j++)
      C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % INF;
  }
  dp[0][0] = 1;
  for (int i = 1; i <= 1000; i++)
    for (int j = 1; j <= i; j++)
      dp[i][j] = (dp[i - j][j] + dp[i - j][j - 1]) % INF;
}
int main() {
  INIT();
  int T;
  scanf("%d", &T);
  while (T--) {
    int N, K;
    scanf("%d%d", &N, &K);
    long long ret = 0;
    for (int i = ((K - 1) * K) / 2; i <= N - K; i++)
      ret = (ret + (((long long)dp[i + K][K] * (long long)C[N - i][K]) % INF)) %
            INF;
    for (int i = 1; i <= K; i++)
      ret = (((long long)ret * (long long)i) % INF) % INF;
    printf("%I64d\n", ret);
  }
  getchar();
  getchar();
  return 0;
}

### Prompt

Your challenge is to write 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 NMax = 1010;
long long INF = 1000000007LL;
long long dp[NMax][NMax], C[NMax * 2][NMax];
void INIT() {
  C[0][0] = 1;
  for (int i = 1; i <= 2000; i++) {
    C[i][0] = 1;
    for (int j = 1; j <= i; j++)
      C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % INF;
  }
  dp[0][0] = 1;
  for (int i = 1; i <= 1000; i++)
    for (int j = 1; j <= i; j++)
      dp[i][j] = (dp[i - j][j] + dp[i - j][j - 1]) % INF;
}
int main() {
  INIT();
  int T;
  scanf("%d", &T);
  while (T--) {
    int N, K;
    scanf("%d%d", &N, &K);
    long long ret = 0;
    for (int i = ((K - 1) * K) / 2; i <= N - K; i++)
      ret = (ret + (((long long)dp[i + K][K] * (long long)C[N - i][K]) % INF)) %
            INF;
    for (int i = 1; i <= K; i++)
      ret = (((long long)ret * (long long)i) % INF) % INF;
    printf("%I64d\n", ret);
  }
  getchar();
  getchar();
  return 0;
}

```