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:
# b.py

def checkPossibility(n, k):
	ans = []
	if n%2 == 1 and k%2 == 0:
		return ans
	elif n%2 == 1:
		if n-k >= 0:
			ans = [1 for _ in range(k-1)]+[n-k+1]
	elif n%2 == 0 and k%2 == 1:
		# must be even
		if n-2*k >= 0:
			ans = [2 for _ in range(k-1)]+[n-2*k+2]
		pass
	elif n%2 == 0 and k%2 == 0:
		# can be odd
		if n-k >= 0:
			ans = [1 for _ in range(k-1)]+[n-k+1]
		pass

	return ans

def printList(lst):
	for v in lst:
		print(v, end=" ")
	print()


t = int(input())

for i in range(t):
	values = [int(a) for a in input().split(" ")]
	# print(values)
	n = values[0]
	k = values[1]
	lst = checkPossibility(n, k)
	if not lst:
		print("NO")
	else:
		print("YES")
		printList(lst)