410679: GYM104076 E Identical Parity

Let the value of a sequence be the sum of all numbers in it.

Determine whether there exists a permutation of length $$$n$$$ such that the values of all subsegments of length $$$k$$$ of the permutation share the same parity. The values share the same parity means that they are all odd numbers or they are all even numbers.

A subsegment of a permutation is a contiguous subsequence of that permutation. A permutation of length $$$n$$$ is a sequence in which each integer from $$$1$$$ to $$$n$$$ appears exactly once.

The first line contains one integer $$$T~(1\le T \le 10^5)$$$, the number of test cases.

For each test case, the only line contains two integers $$$n,k~(1 \le k \le n \le 10^9)$$$.

For each test case, output "Yes" (without quotes) if there exists a valid permutation, or "No" (without quotes) otherwise.

You can output "Yes" and "No" in any case (for example, strings "YES", "yEs" and "yes" will be recognized as positive responses).

3
3 1
4 2
5 3

No
Yes
Yes

In the first test case, it can be shown that there does not exist any valid permutation.

In the second test case, $$$[1,2,3,4]$$$ is one of the valid permutations. Its subsegments of length $$$2$$$ are $$$[1,2],[2,3],[3,4]$$$. Their values are $$$3,5,7$$$, respectively. They share the same parity.

In the third test case, $$$[1,2,3,5,4]$$$ is one of the valid permutations. Its subsegments of length $$$3$$$ are $$$[1,2,3],[2,3,5],[3,5,4]$$$. Their values are $$$6,10,12$$$, respectively. They share the same parity.