Let's say P= [P1, P2 . . . PN] 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
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.
