#include <bits/stdc++.h>
using namespace std;
const long long mo = 1e9 + 7;
long long f[1001][46], fac[1001], c[1101][1101], ans[1101][46];
int main() {
  c[0][0] = 1;
  for (int i = 1; i <= 1100; i++)
    for (int j = 1; j <= i; j++) c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mo;
  f[0][0] = 1;
  fac[0] = 1;
  for (int i = 1; i <= 1000; i++) fac[i] = fac[i - 1] * i % mo;
  for (int i = 1; i <= 1000; i++)
    for (int j = 1; j <= 45; j++) {
      f[i][j] = 0;
      for (int k = 1; k <= i / j; k++)
        f[i][j] = (f[i][j] + f[i - k * j][j - 1]) % mo;
      f[i][j] = f[i][j];
    }
  for (int i = 1; i <= 1000; i++)
    for (int j = 1; j <= 45; j++) f[i][j] = f[i][j] * fac[j] % mo;
  for (int i = 1; i <= 1000; i++)
    for (int j = 1; j <= 45; j++)
      for (int k = i; k <= 1000; k++) {
        ans[k][j] += f[i][j] * c[k - i + j + 1][j + 1];
        ans[k][j] %= mo;
      }
  int t;
  scanf("%d", &t);
  while (t--) {
    int n, k;
    scanf("%d%d", &n, &k);
    k = min(k, 45);
    printf("%lld\n", ans[n][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 long long mo = 1e9 + 7;
long long f[1001][46], fac[1001], c[1101][1101], ans[1101][46];
int main() {
  c[0][0] = 1;
  for (int i = 1; i <= 1100; i++)
    for (int j = 1; j <= i; j++) c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mo;
  f[0][0] = 1;
  fac[0] = 1;
  for (int i = 1; i <= 1000; i++) fac[i] = fac[i - 1] * i % mo;
  for (int i = 1; i <= 1000; i++)
    for (int j = 1; j <= 45; j++) {
      f[i][j] = 0;
      for (int k = 1; k <= i / j; k++)
        f[i][j] = (f[i][j] + f[i - k * j][j - 1]) % mo;
      f[i][j] = f[i][j];
    }
  for (int i = 1; i <= 1000; i++)
    for (int j = 1; j <= 45; j++) f[i][j] = f[i][j] * fac[j] % mo;
  for (int i = 1; i <= 1000; i++)
    for (int j = 1; j <= 45; j++)
      for (int k = i; k <= 1000; k++) {
        ans[k][j] += f[i][j] * c[k - i + j + 1][j + 1];
        ans[k][j] %= mo;
      }
  int t;
  scanf("%d", &t);
  while (t--) {
    int n, k;
    scanf("%d%d", &n, &k);
    k = min(k, 45);
    printf("%lld\n", ans[n][k]);
  }
  return 0;
}

```