#include <bits/stdc++.h>
using namespace std;
const int N = 1010;
const int Mod = 1000000007;
int dp[N][N][2], f[N], c[N][N];
int main() {
  dp[0][0][0] = 0;
  dp[0][1][1] = 1;
  for (int i = 1; i < N; i++) {
    for (int k = 1; k <= i + 1; k++) {
      if (i >= k) dp[i][k][0] = dp[i - k][k][0] + dp[i - k][k][1];
      if (dp[i][k][0] >= Mod) dp[i][k][0] -= Mod;
      dp[i][k][1] = dp[i][k - 1][0];
      if (dp[i][k][1] >= Mod) dp[i][k][1] -= Mod;
    }
  }
  for (int i = 0; i < N; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= i; j++) {
      c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
      if (c[i][j] >= Mod) c[i][j] -= Mod;
    }
  }
  f[1] = 1;
  for (int i = 2; i < N; i++) {
    f[i] = ((long long)f[i - 1] * 1ll * i) % Mod;
  }
  int t, k, n;
  cin >> t;
  while (t--) {
    cin >> n >> k;
    int ans = 0;
    for (int sum = 0; sum + k <= n; sum++) {
      long long temp = 1ll * f[k] * c[n - sum][k];
      temp %= Mod;
      temp *= 1ll * (dp[sum][k][0] + dp[sum][k][1]);
      temp %= Mod;
      ans += temp;
      if (ans >= Mod) ans -= Mod;
    }
    cout << ans << endl;
  }
}

### Prompt

Please formulate 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 N = 1010;
const int Mod = 1000000007;
int dp[N][N][2], f[N], c[N][N];
int main() {
  dp[0][0][0] = 0;
  dp[0][1][1] = 1;
  for (int i = 1; i < N; i++) {
    for (int k = 1; k <= i + 1; k++) {
      if (i >= k) dp[i][k][0] = dp[i - k][k][0] + dp[i - k][k][1];
      if (dp[i][k][0] >= Mod) dp[i][k][0] -= Mod;
      dp[i][k][1] = dp[i][k - 1][0];
      if (dp[i][k][1] >= Mod) dp[i][k][1] -= Mod;
    }
  }
  for (int i = 0; i < N; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= i; j++) {
      c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
      if (c[i][j] >= Mod) c[i][j] -= Mod;
    }
  }
  f[1] = 1;
  for (int i = 2; i < N; i++) {
    f[i] = ((long long)f[i - 1] * 1ll * i) % Mod;
  }
  int t, k, n;
  cin >> t;
  while (t--) {
    cin >> n >> k;
    int ans = 0;
    for (int sum = 0; sum + k <= n; sum++) {
      long long temp = 1ll * f[k] * c[n - sum][k];
      temp %= Mod;
      temp *= 1ll * (dp[sum][k][0] + dp[sum][k][1]);
      temp %= Mod;
      ans += temp;
      if (ans >= Mod) ans -= Mod;
    }
    cout << ans << endl;
  }
}

```