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:
import sys
def eprint(*args):
    print(*args, file=sys.stderr)
zz=1
from math import *
#sys.setrecursionlimit(10**6)
if zz:
	input=sys.stdin.readline
else:	
	sys.stdin=open('input.txt', 'r')
	sys.stdout=open('all.txt','w')

 
 
t=int(input())
while t>0:
	t-=1
	n,k=map(int,input().split())
	if k>n :
		print("NO")
		continue
	else:
		if n%2==k%2:
			
				print("YES")
				for i in range(k):
					if i==k-1:
						print(n,end=" ")
					else:
						print(1,end=' ')
						n-=1
				print()			

		else:
			if n%2==1:
				print("NO")	
				continue	
			else:
				if k*2>n:
					print("NO")
					continue
				else:
					print("YES")
					for i in range(k):
						if i==k-1:
							print(n,end=" ")
						else:
							print(2,end=' ')
							n-=2	
				print()