Problem: You are given two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100). Represent the number n as the sum of k positive integers of the same parity (have the same remainder when divided by 2).

In other words, find a_1, a_2, …, a_k such that all a_i>0, n = a_1 + a_2 + … + a_k and either all a_i are even or all a_i are odd at the same time.

If such a representation does not exist, then report it.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Next, t test cases are given, one per line.

Each test case is two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100).

Output

For each test case print:

  * YES and the required values a_i, if the answer exists (if there are several answers, print any of them); 
  * NO if the answer does not exist. 



The letters in the words YES and NO can be printed in any case.

Example

Input


8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9


Output


YES
4 2 4
YES
55 5 5 35
NO
NO
YES
1 1 1 1 1 1 1 1
NO
YES
3 1 1
YES
111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111120

Solution (in PYTHON3):

Solution:
T = int(input())
while T:
	T = T -1
	n,k = input().split()
	N = int(n)
	K = int(k)
	
	#If N== even, K = even
	# Try parity = even, if N >= 2*K 
	# Else try parity = odd, if N >=K
	# else report NO
	if N%2 == 0 and K%2 == 0:
		if N>=2*K:
			print('YES')
			for i in range(K-1):
				print(2,end=' ')
			print(N-2*(K-1)) 
			continue
		elif N>=K:
			print('YES')
			for i in range(K-1):
				print(1,end=' ')
			print(N-(K-1))
			continue
		else:
			print('NO')
	elif N%2 ==0 and K%2 == 1:
		if N>=2*K:
			print('YES')
			for i in range(K-1):
				print(2,end=' ')
			print(N-2*(K-1))
			continue
		else:
			print('NO')
			continue
	elif N%2 == 1 and K%2 == 0:
		print('NO')
		continue
	else:
		if N>=K:
			print('YES')
			for i in range(K-1):
				print(1,end=' ')
			print(N-(K-1))
			continue
		else:
			print('NO')
			continue
	#If N = even, K = odd
	#Try parity = even, if N>=2*K
	# else report NO

	#If N = odd, K = even
	# odd+odd = even, even+even = even
	# report NO
	
	# If N = odd, K = odd
	# parity = odd, if N>=K
	# else report NO