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:
for _ in range(int(input())):
	n, k = list(map(int, input().split(' ')))
	if n < k:
		print('NO')
	elif k % 2: # k is odd  3 + 3+ 3 -> odd  4 + 4+ 4 -> even
		if n % 2: # n is odd
			# print('YES')
			# must use odd
			# n 
			# 1 1 1 1 n-(k-1)
			if (n-(k - 1)) % 2 == 0:  # 1 1 [n-(k -1)]
				print('NO')
			else:
				print('YES')
				print(' '.join(['1']* (k-1)) +' '+str(n-(k-1)) )
		else:
			# print('YES')
			# must use even
			# 2 2 2 2 2
			if (n-2*(k - 1)) < 2 or (n-2*(k - 1)) % 2:
				print('NO')
			else:
				print('YES')
				print(' '.join(['2']* (k-1)) +' '+str(n-2*(k - 1)) )
	else:
		# even or odd is ok 
		if n % 2: # n must be even  even + even -> even, odd + odd -> even
			print('NO')
		else:
			# k -> even
			# n -> even 
			# even + even + ... or odd + odd + ...
			# even: 2 + 2 + 2 + [n - 2*(k - 1)]

			if not ((n-2*(k - 1)) < 2 or (n-2*(k - 1)) % 2):
				print('YES')
				print(' '.join(['2']* (k-1)) +' '+str(n-2*(k - 1)) )
			elif not ((n-(k - 1)) % 2 == 0):
				print('YES')
				print(' '.join(['1']* (k-1)) +' '+str(n-(k-1)) )
			else:
				print('NO')