CF1327A.Sum of Odd Integers

You are given two integers $n$ and $k$ . Your task is to find if $n$ can be represented as a sum of $k$ distinct positive odd (not divisible by $2$ ) integers or not.

You have to answer $t$ independent test cases.

The first line of the input contains one integer $t$ ( $1 \le t \le 10^5$ ) — the number of test cases.

The next $t$ lines describe test cases. The only line of the test case contains two integers $n$ and $k$ ( $1 \le n, k \le 10^7$ ).

For each test case, print the answer — "YES" (without quotes) if $n$ can be represented as a sum of $k$ distinct positive odd (not divisible by $2$ ) integers and "NO" otherwise.

In the first test case, you can represent $3$ as $3$ .

In the second test case, the only way to represent $4$ is $1+3$ .

In the third test case, you cannot represent $10$ as the sum of three distinct positive odd integers.

In the fourth test case, you can represent $10$ as $3+7$ , for example.

In the fifth test case, you can represent $16$ as $1+3+5+7$ .

In the sixth test case, you cannot represent $16$ as the sum of five distinct positive odd integers.