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.
"""
from collections import Counter

t=int(input())
for i in range(t):
    n = int(input())
    nums = list(map(int, input().split()))
    c = Counter(nums)
    ans = 0
    for i,j in c.items():
        ans += j//i
        c[i] = j%i
    print(c)
    print(ans)"""


"""
from functools import lru_cache

@lru_cache(maxsize=None)
def findMinMax(s):
    if len(s)==1:
        return int(s[0])**2
    return int(s[0])*int(s[-1])



t = int(input())
for i in range(t):
    a,k = list(map(int, input().split()))
    for i in range(k-1):
        l = "".join(sorted(str(a)))
        if "0" in l:
            break
        else:
            a += findMinMax(l)
    print(a)"""

t = int(input())
for i in range(t):
    n,k = list(map(int, input().split()))
    if k**2 > n:
        print("NO")
    else:
        if n%2==1:
            if k%2==1:
                print("YES")
            else:
                print("NO")
        else:
            if k%2==1:
                print("NO")
            else:
                print("YES")













