Mahamba is nervous! He didn't prepare for BTS exam (which is super-important in his school) and now has a hard time. His teacher is very angry at him and told him that if he fails, he would be expelled! Mahamba still needs to solve one last programming question, but he has only a couple of minutes left. So, he called you, the best programmer in Lalalandia, to help him out!
You are given T test cases, each containing three numbers N, S and X. You need to say whether it is possible to construct such sequence A of length N, where each \(a_i >= 0\) for \(1<=i<=N\), the sum of all numbers in a sequence is equal to S, and the XOR of sequence equals to X.
Input format
The first line contains T - the number of test cases. The next T lines each contain three numbers N, S and X.
Output format
For each test case, output "Yes" if it is possible to construct such sequence A of length N, or "No" otherwise (without quotes).
Constraints
\(1 <= T <=1000\)
\(1 <= N <= 10^5\)
\(0 <= S,X <= 10^9\)
Details
More information on XOR operation: https://en.wikipedia.org/wiki/Exclusive_or
3 1 3 2 2 10 0 3 9 3
No Yes Yes
In the second test case, we can use the sequence "5 5", because the XOR of all elements will be 0, and sum - 10. For the third test case, we can use the sequence "3 3 3", because 3^3^3=3 and 3+3+3=9
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