#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 10;
const int maxm = 1e3 + 5;
const int mod = 1e9 + 7;
long long C[maxm][maxm], fac[maxm], f[maxm][maxm];
inline void init() {
  fac[0] = 1;
  for (int i = 1; i < maxm - 4; i++) fac[i] = fac[i - 1] * i % mod;
  C[0][0] = 1;
  for (int i = 1; i < maxm - 4; i++) {
    C[i][0] = C[i][i] = 1;
    for (int j = 1; j < i; j++) {
      C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % mod;
    }
  }
  f[0][0] = 1;
  for (int i = 1; i < maxm - 4; i++) {
    for (int j = 1; j < i + 1; j++)
      f[i][j] = (f[i - j][j] + f[i - j][j - 1]) % mod;
  }
}
inline void solve() {
  int n, k;
  scanf("%d%d", &n, &k);
  long long ans = 0;
  for (int len = k * (k + 1) / 2; len < n + 1; len++)
    ans = (ans + f[len][k] * C[n - len + k][k]) % mod;
  printf("%lld\n", ans * fac[k] % mod);
}
int main() {
  init();
  int t;
  scanf("%d", &t);
  while (t--) solve();
  return 0;
}

### Prompt

Your task is to create 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 maxn = 1e5 + 10;
const int maxm = 1e3 + 5;
const int mod = 1e9 + 7;
long long C[maxm][maxm], fac[maxm], f[maxm][maxm];
inline void init() {
  fac[0] = 1;
  for (int i = 1; i < maxm - 4; i++) fac[i] = fac[i - 1] * i % mod;
  C[0][0] = 1;
  for (int i = 1; i < maxm - 4; i++) {
    C[i][0] = C[i][i] = 1;
    for (int j = 1; j < i; j++) {
      C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % mod;
    }
  }
  f[0][0] = 1;
  for (int i = 1; i < maxm - 4; i++) {
    for (int j = 1; j < i + 1; j++)
      f[i][j] = (f[i - j][j] + f[i - j][j - 1]) % mod;
  }
}
inline void solve() {
  int n, k;
  scanf("%d%d", &n, &k);
  long long ans = 0;
  for (int len = k * (k + 1) / 2; len < n + 1; len++)
    ans = (ans + f[len][k] * C[n - len + k][k]) % mod;
  printf("%lld\n", ans * fac[k] % mod);
}
int main() {
  init();
  int t;
  scanf("%d", &t);
  while (t--) solve();
  return 0;
}

```