Construct Sequence from Powers of Two

You are given two positive integers n and s. Your goal is to determine whether it is possible to construct a sequence of n numbers, where each number is a power of two (with the smallest value being 2^0=1), such that the sum of the sequence is exactly s.

The minimum possible sum is achieved when every element is 1 (i.e. n), and the maximum sum is achieved when each element is the largest possible power of two in the sequence, which gives a sum of n\times 2^{n-1}. In other words, a valid sequence exists if and only if:

n\le s\le n\times 2^{n-1}

Determine whether s falls within this range (inclusive). If it does, output YES; otherwise, output NO.

inputFormat

The first line contains an integer t representing the number of test cases. Each of the next t lines contains two space-separated integers n and s.

outputFormat

For each test case, output a single line containing YES if it is possible to construct the sequence with the sum s, or NO otherwise.

## sample

4
3 12
4 16
2 1
5 31

YES
YES
NO
YES

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