#include <bits/stdc++.h>
using namespace std;
int dp[2][1001][90];
int distinct[1001][90];
int y[1001][90];
int ans[1001][1001];
void preprocess() {
  dp[0][0][0] = 1;
  dp[0][0][1] = 1;
  y[0][0] = 1;
  for (int i = 1; i < 1001; i++) {
    for (int j = 0; j < 1001; j++) {
      for (int k = 0; k < 90; k++) {
        dp[i & 1][j][k] =
            (dp[1 - (i & 1)][j][k] +
             1LL * k * (k and j >= i ? dp[1 - (i & 1)][j - i][k - 1] : 0)) %
            1000000007;
      }
    }
  }
  for (int j = 0; j < 1001; j++) {
    for (int k = 0; k < 90; k++) {
      distinct[j][k] = dp[0][j][k];
      if (j) distinct[j][k] += distinct[j - 1][k];
      if (distinct[j][k] >= 1000000007) distinct[j][k] -= 1000000007;
      for (int l = 1; l < j + 1; l++) {
        y[j][k] = ((k ? y[j - l][k - 1] : 0) + y[j][k]);
        if (y[j][k] >= 1000000007) y[j][k] -= 1000000007;
      }
    }
  }
  for (int i = 1; i < 1001; i++) {
    for (int j = 1; j < 90; j++) {
      for (int r = j; r < i + 1; r++) {
        ans[i][j] =
            (ans[i][j] + 1LL * y[r][j] * distinct[i - r][j]) % 1000000007;
      }
    }
  }
}
signed main() {
  preprocess();
  int test;
  cin >> test;
  while (test--) {
    int n, k;
    cin >> n >> k;
    cout << ans[n][k] << endl;
  }
  return 0;
}

### Prompt

Create a solution in cpp for 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;
int dp[2][1001][90];
int distinct[1001][90];
int y[1001][90];
int ans[1001][1001];
void preprocess() {
  dp[0][0][0] = 1;
  dp[0][0][1] = 1;
  y[0][0] = 1;
  for (int i = 1; i < 1001; i++) {
    for (int j = 0; j < 1001; j++) {
      for (int k = 0; k < 90; k++) {
        dp[i & 1][j][k] =
            (dp[1 - (i & 1)][j][k] +
             1LL * k * (k and j >= i ? dp[1 - (i & 1)][j - i][k - 1] : 0)) %
            1000000007;
      }
    }
  }
  for (int j = 0; j < 1001; j++) {
    for (int k = 0; k < 90; k++) {
      distinct[j][k] = dp[0][j][k];
      if (j) distinct[j][k] += distinct[j - 1][k];
      if (distinct[j][k] >= 1000000007) distinct[j][k] -= 1000000007;
      for (int l = 1; l < j + 1; l++) {
        y[j][k] = ((k ? y[j - l][k - 1] : 0) + y[j][k]);
        if (y[j][k] >= 1000000007) y[j][k] -= 1000000007;
      }
    }
  }
  for (int i = 1; i < 1001; i++) {
    for (int j = 1; j < 90; j++) {
      for (int r = j; r < i + 1; r++) {
        ans[i][j] =
            (ans[i][j] + 1LL * y[r][j] * distinct[i - r][j]) % 1000000007;
      }
    }
  }
}
signed main() {
  preprocess();
  int test;
  cin >> test;
  while (test--) {
    int n, k;
    cin >> n >> k;
    cout << ans[n][k] << endl;
  }
  return 0;
}

```