1327A. Sum of Odd Integers

math, 1100, https://codeforces.com/problemset/problem/1327/A

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.

Input

The first line of the input contains one integer 𝑡 (1≤𝑡≤105) — 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≤𝑛,𝑘≤107).

Output

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.

Example

input

6
3 1
4 2
10 3
10 2
16 4
16 5

output

YES
YES
NO
YES
YES
NO

Note

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.

t = int(input())
for i in range(t):
    n, k = map(int, input().split())
    if (n+k) % 2 == 0 and n >= k**2:
        print('YES')
    else:
        print('NO')