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:
tes=int(input())
for i in range(tes):
	a=input().split()
	n,k=int(a[0]),int(a[1])
	flag=False
	if k==1:
		print("YES")
		print(n)
		flag=True
	else:
		nums=1*(k-1)
		if n-nums>0 and ((n-nums)%2)==1:
			a=[1]*(k-1)
			a.append(n-nums)
			print("YES")
			print(*a)
			flag=True
		if not flag:
			nums=2*(k-1)
			if n-nums>0 and ((n-nums)%2)==0:
				a=[2]*(k-1)
				a.append(n-nums)
				print("YES")
				print(*a)
				flag=True
	if not flag:
		print("NO")