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.
import bisect

if __name__ == "__main__":
    seq = []
    odd = 0
    i = 0
    j = 0
    while(True):
        i += 1
        if i % 2 == 1:
            odd += i
            j += 1
            seq.append((odd, j))
        if odd >= 10000000:
            break
    raw_seq = [i for i, _ in seq]

    t = int(input())
    for _ in range(t):
        n, k = tuple(map(int, input().split()))
        if (n%2 == 0 and k%2 == 1) or (n%2==1 and k%2 == 0):
            print("NO")
        else:
            i = bisect.bisect_left(raw_seq, n)
            if raw_seq[i] != n:
                i -= 1
            _, j = seq[i]
            if j < k:
                print("NO")
            else:
                print("YES")