Break the Stick solution codechef

Chef has a stick of length N.

He can break the stick into 2 or more parts such that the parity of length of each part is same. For example, a stick of length 11 can be broken into three sticks of lengths {3,3,5} since each part is odd, but it cannot be broken into two sticks of lengths {5,6} since one is even and the other is odd.

Chef can then continue applying this operation on the smaller sticks he obtains, as many times as he likes.

Can Chef obtain a stick of length exactly X by doing this?

Input Format

Break the Stick solution codechef

• The first line of input will contain a single integer T, denoting the number of test cases. The description of the test cases follows.
• Each test case consists of a single line of input, containing two space-separated integers N,X.

Output Format

For each test case, output on a new line YES if Chef can obtain a stick of length exactly X, and NO otherwise.

Each letter of the output may be printed in either lowercase or uppercase. For example, the strings YES, yEs, and Yes will be considered identical.

Constraints

• 1≤T≤1000
• 1≤X<N≤109

Sample Input 1

Break the Stick solution codechef

3
6 1
3 2
4 3

Sample Output 1

YES
NO
YES

Explanation

Test case 1: Chef can initially break the stick into 3 parts of length 2 each. After that, Chef can pick any segment of length 2 and break it into 2 sticks of length 1each.

Test case 2: Chef cannot obtain a stick of length 2, since the only way to break a stick of length 3 following the given conditions is into three parts of length 1 each.

Test case 3: Chef can break the stick into lengths 3 and 1.