Easy

26.92%

Given an array, an inversion is defined as a pair a[i], a[j] such that a[i] > a[j] and i < j. We are given two numbers N and k, we need to tell how many permutation of first N number have exactly K inversion.

**Input:**

The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. The first line of each test case contains integers N and K.

**Output:**

Print the count of the number of permutations for the first N numbers which have exactly K inversions. Since the answer can be quite large print the answer modulo 10^{9}+7. Print the answer for each testcase in a new line.

**Constraints:**

1<= T <=100

1<= N, K <=100

**Example:**

**Input:**

1

3 1

**Output:**

2

```
Explanation :
Total Permutation of first N number,
123, 132, 213, 231, 312, 321
Permutation with 1 inversion : 132 and 213
```