#include <bits/stdc++.h>
using namespace std;
const int MAX = 1000 + 9;
const long long MOD = 1e9 + 7;
long long fac[MAX], c[MAX][MAX];
long long dp[MAX][MAX], ans[MAX][MAX];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  for (int i = 0; i < MAX; i++) {
    c[i][0] = 1;
    for (int t = 1; t <= i; t++)
      c[i][t] = (c[i - 1][t] + c[i - 1][t - 1]) % MOD;
  }
  fac[0] = 1;
  for (long long i = 1; i < MAX; i++) fac[i] = fac[i - 1] * i % MOD;
  dp[0][0] = 1;
  for (int i = 0; i < MAX; i++)
    for (int t = 50; t >= 1; t--)
      for (int j = MAX - 1; j >= i; j--)
        dp[j][t] = (dp[j][t] + dp[j - i][t - 1]) % MOD;
  for (int i = 1; i < MAX; i++)
    for (int t = 1; t <= 50; t++)
      for (int j = 0; j <= i; j++) {
        long long f = dp[j][t] * fac[t] % MOD * c[i - j][t] % MOD;
        ans[i][t] = (ans[i][t] + f) % MOD;
      }
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int n, k;
    cin >> n >> k;
    cout << ans[n][k] << "\n";
  }
}

### Prompt

Please create a solution in cpp 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 MAX = 1000 + 9;
const long long MOD = 1e9 + 7;
long long fac[MAX], c[MAX][MAX];
long long dp[MAX][MAX], ans[MAX][MAX];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  for (int i = 0; i < MAX; i++) {
    c[i][0] = 1;
    for (int t = 1; t <= i; t++)
      c[i][t] = (c[i - 1][t] + c[i - 1][t - 1]) % MOD;
  }
  fac[0] = 1;
  for (long long i = 1; i < MAX; i++) fac[i] = fac[i - 1] * i % MOD;
  dp[0][0] = 1;
  for (int i = 0; i < MAX; i++)
    for (int t = 50; t >= 1; t--)
      for (int j = MAX - 1; j >= i; j--)
        dp[j][t] = (dp[j][t] + dp[j - i][t - 1]) % MOD;
  for (int i = 1; i < MAX; i++)
    for (int t = 1; t <= 50; t++)
      for (int j = 0; j <= i; j++) {
        long long f = dp[j][t] * fac[t] % MOD * c[i - j][t] % MOD;
        ans[i][t] = (ans[i][t] + f) % MOD;
      }
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int n, k;
    cin >> n >> k;
    cout << ans[n][k] << "\n";
  }
}

```