A. Sum of Odd Integers
math
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.