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 ≤ 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 ≤ n, k ≤ 10^7).

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.
def s(ord_a, ord_b):
    a = (ord_a - 1) * 2 + 1
    b = (ord_b - 1) * 2 + 1
    total_numbers = (ord_b - ord_a) + 1
    return int((a + b) * (total_numbers / 2))

def solve(n, k):
    if k % 2 != n % 2:
        return "NO" 

    min_ = s(1, k)
    max_ = s(1, n) - s(1, n - k)

    if min_ <= n <= max_:
        return "YES"
    else:
        return "NO"


if __name__ == "__main__":
    t = input()
    for i in range(int(t)):
        n, k = map(int, input().split())

        res = solve(n, k)
        print(res)

