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:
# cook your dish here
for _ in range(int(input())):
	a,k = map(int,input().split())
	arr = []
	c = 0
	if a%2 ==0:
		if k%2==0:
			if k<=a:
				c = 1
				arr = [1]*(k-1) 
				arr.append(a-(k-1))
		else:
		    
		    if 2*k <=a and (a-(2*(k-1)))%2==0:
		        
		        
		        c =1
		        arr = [2]*(k-1)
		        arr.append(a-2*(k-1))
		        
		        
	elif a%2!=0:
		if k%2!=0:
			if k<=a:
				c =1
				arr = [1]*(k-1) 
				arr.append(a-(k-1))
	if c==0:
		print("NO")
	else:
		print("YES")
		print(*arr)