Permutation Test#13035
Given two integers and , Determine if there exists a permutation of \{1,2,3,\ldots,n\} such that \sum\limits_{\underset{i \bmod 2=0}{i=1}}^n p_i=k
More Formally , The sum of elements placed in even indices equals to exactly.
The first line contains single integer (1 \le t \le 10^4) — the number of test cases.
The only line of each test case contains two integers (1 \le n,k \le 10^9) — the length of the permutation and the desired sum.
For each test case, print "YES" if there exists a permutation satisfying the conditions ; otherwise, print "NO".
You can output the answer in any case (For example,the strings "yEs" , "yes" , "yeS" , "Yes" will be recognized as positive answers).
Example 1
In the first test case , the permutation p=[1,\color{blue}{3},2,\color{blue}{4}] works.
In the second and third cases , It can be shown that no permutation works.
In the last test case , the permutation p=[1,\color{blue}{2},5,\color{blue}{3},6,\color{blue}{4},7] works.
Subtask ( points) : (1 \le n \le 6)
Subtask ( points) : No additional constraints