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.
# ANSHUL GAUTAM
# IIIT-D

from math import *
from copy import *
from string import *				# alpha = ascii_lowercase
from random import *				# l.sort(key=lambda l1:l1[0]-l1[1]) => ex: sort on the basis difference
from bisect import *				# bisect_left(arr,x,start,end)  => start and end parameters are temporary
from sys import stdin				# bisect_left return leftmost position where x should be inserted to keep sorted
from sys import maxsize
from operator import *				# d = sorted(d.items(), key=itemgetter(1))
from itertools import *
from collections import Counter		# d = dict(Counter(l))
from collections import defaultdict # d = defaultdict(list)

'''
6
3 1
4 2
10 3
10 2
16 4
16 5
'''

def solve(l):
	n = len(l)
	
T = int(input())
for _ in range(T):
	N,K = list(map(int, stdin.readline().rstrip().split()))
	if(N < K**2):
		print('NO')
	elif(N%2 == 1 and K%2 == 1):
		print('YES')
	elif(N%2 == 0 and K%2 == 0):
		print('YES')
	else:
		print('NO')



