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:
def check(x, k, on):
	ans = []
	summ = 0
	while k>0:
		if k==1:
			if on==2:
				on=0
			val = x - summ
			if val <= 0:
				return False, []
			elif val%2==on:
				ans.append(val)
				return True, ans
			else:
				return False, []
				
		k-=1
		summ += on
		ans.append(on)
		
	
t = int(input())
while t>0:
	t-=1
	inp = input()
	x, k = inp.split(" ")
	x = int(x)
	k = int(k)
	o1, l1 = check(x, k, 1)
	if (o1):
		print("YES")
		for v in l1:
			print(v, end=" ")
		print()
	else:
		o2, l2 = check(x, k, 2)
		if (o2):
			print("YES")
			for v in l2:
				print(v, end=" ")
			print()
		else:
			print("NO")