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.