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.
#  =========     /\       /|    |====/|
#      |        /  \       |    |   / |
#      |       /____\      |    |  /  |
#      |      /      \     |    | /   |
#  ========= /        \  =====  |/====|  
#  code

# MOD = 998244353
# def pow(base , exp):
#     if exp == -1:
#         return pow(base , MOD - 2)
#     res = 1
#     base %= MOD
#     while exp > 0:
#         if exp % 2:
#             res = (res * base) % MOD
#         exp //= 2
#         base = (base * base) % MOD
    
#     res %= MOD
    #   return res

def main():
    t = int(input())
    for _ in range(t):
        n , k = map(int , input().split())
        if k%2 == n%2:
            c = (k - 1) * (k - 1)
            if n >= c and (n - c) >= (2*k - 1):
                print('YES')
            else:
                print('NO')
        else:
            print('NO')
    return

if __name__ == "__main__":
    main()