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:
from sys import stdin

def solve(n,k):
	ans="NO"
	f=True
	if (n%2)==1:
		if (k%2)==1 and n>=k:
			f=False
			print("YES")
			for i in range(k-1):
				print(1,end=' ')
				n-=1
			print(n)
	else:
		if (k%2)==1 and n>=2*k:
			f=False
			print("YES")
			for i in range(k-1):
				print(2,end=' ')
				n-=2
			print(n)
		if (k%2)==0:
			if n>=k and n<2*k:
				f=False
				print("YES")
				for i in range(k-1):
					print(1,end=' ')
					n-=1
				print(n)
			if n>=2*k:
				f=False
				print("YES")
				for i in range(k-1):
					print(2,end=' ')
					n-=2
				print(n)
	if f:
		print("NO")		
	return

def main():
	inp=stdin.readline
	for _ in range(int(inp())):
		n,k=map(int, inp().split())
		solve(n,k)
	

main()