weird-permutations

You have N numbers from 1 to N. Now Permutations of N numbers of having length N means Reorder all numbers in all possible orders. Like for N=3 ,
 6 Permutations are possible.  

1 2 3
1 3 2  
2 1 3  
2 3 1  
3 1 2  
3 2 1    

In General for N numbers you can represent Permutations as P1 , P2 , P3 .... PN  

Now You need  to find number of permutations of length N such that  

| 3*P(i)-2*P(i+1) | ≤ k for 1 ≤ i ≤ n-1

considering P1,P2,P3….,Pn to be number in respective Permutations.

Input :
First line contains T- No of test cases. 
Next T lines contains two space separated integers - N and K.   

Output:
Print the no of permutations satisfying the conditions given in problem sratement in separate lines.  

Constraints : 
1 ≤ T ≤ 10  
1 ≤ N ≤ 16 
0 ≤ K ≤ 60   

SAMPLE INPUT
3
2 3
2 4
5 6

SAMPLE OUTPUT
1
2
7

Explanation

Test Case #1:  N=2 and K=3
now all possible Permutation of Lengh 2 are
1) 1 2
2) 2 1    

For (1) : | 3(1) - 2(2) | = 1 ≤3 . Hence valid.
For (2 ): | 3(2) - 2(1) | = 4 ≰ 3 . Hence not valid.  

So answer is 1.

Source: hackerearth | Difficulty: UNKNOWN_DIFFICULTY


Solutions: