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:
t = int(input())
while t > 0:
	n,k= map(int,input().split())
	l = []
	
	if n%2 != 0 and k%2 == 0 :
		print("NO")

	elif n%2 != 0 and k%2 != 0:
		temp = n
		while k > 1 and n >0 :
			l.append(1)
			k -= 1
			n -= 1
		if n>0:
			l.append(n)
			k -= 1
		if k > 0 or sum(l) != temp:
			print("NO")
		else:
			print("YES")
			print(*l)

	elif n%2 == 0 and k%2 != 0:
		temp = n
		while k > 1 and n>0:
			l.append(2)
			n -= 2
			k -= 1
		if n > 0:
			l.append(n)
			k -= 1
		if k > 0 or sum(l) != temp:
			print("NO")
		else:
			print("YES")
			print(*l)

	else:

		if n//2*2 >= k :
			temp = n
			while k > 1 and n >0 :
				l.append(1)
				k -= 1
				n -= 1
			if n>0:
				l.append(n)
				k -= 1
			if k > 0 or sum(l) != temp:
				print("NO")
			else:
				print("YES")
				print(*l)
		else:
			temp = n
			while k > 1 and n>0:
				l.append(2)
				n -= 2
				k -= 1
			if n>0:
				l.append(n)
				k -= 1
			if k > 0 or sum(l) != temp:
				print("NO")
			else:
				print("YES")
				print(*l)



	t -= 1