Possible?

Time Limit: 0.5 sec

 

The Problem

Let's say P= [P₁, P₂ . . . P_N] is a permutations of all positive integers less than or equal to N. A function called "special count" F(P) is defined as:

 

Now Hiya gives a N and K to Diya and asks if K is a possible special count for any permutation of first N positive integers.

 

The Input

First line contains T(1 ≤ T ≤ 100), the number of test cases. Each test case consists of N(1 ≤ N ≤ 40) and K(0 ≤ K ≤ 2000)  in one line.

 

The Output

For each test case, print "YES" or "NO", denoting whether K is a possible special count or not.

 

Sample Input

2

2 1

3 2

 

Sample Output

NO

YES

 

 

Explanation

First test case: None of the two permutations [1, 2] and [2, 1] have special count 1.

Second test case: Permutations [1, 3, 2] and [2, 1, 3] have special count 2.

 

 

Inter University Programming Contest - 2016 [BGC Trust University Bangladesh]

Problem Setter: Parag Paul