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.
"""
NTC here
"""
import sys
inp = sys.stdin.readline


def input(): return inp().strip()


flush = sys.stdout.flush
# import threading
# sys.setrecursionlimit(10**6)
# threading.stack_size(2**25)


def iin(): return int(input())


def lin(): return list(map(int, input().split()))

# range = xrange
# input = raw_input


def main():
    T = iin()
    while T:
        T-=1
        n, k = lin()
        ch = 0
        if k%2:
            ch = 1
        # print(ch, (k-1)*(k+1), n)
        if n%2==ch and (k-1)*(k+1)<=n:
            print('YES')
        else:
            print('NO')


"""
TEST-
4 4 1
1111
1111
1111
1111
"""


main()
# threading.Thread(target=main).start()
