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

Input
First line contains T, the number of test cases. Each test case consists of N and K in one line.

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

Constraints
1 ≤ T ≤ 100
20% testdata: 1 ≤ N ≤ 10
20% testdata: 1 ≤ N ≤ 20
60% testdata: 1 ≤ N ≤ 40
0 ≤ K ≤ 2000