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 math import ceil,floor 
for _ in range(int(input())):
	n,k=map(int,input().split())
	#L=list(map(int,input().split()))
	"""
	if n&1 !=0 and k&1==0:
		print('NO')
		continue
	if n<k:
		print('NO')
		continue
	if n==k:
		print('YES')
		ans=[1]*n
		print(*ans)
		continue
	"""
	ans1=[]
	ans2=[]
	flag=0
	flag2=0
	if n&1 == 1:
		flag = 1
	
	#if flag==1:
	ans1=[1]*(k-1)
	val1=n-(1*(k-1))
	
	ans2=[2]*(k-1)
	val2=n-(2*(k-1))
	if val1 > 0 and val1&1==1:
		flag2 = 1
		ans1.append(val1)
		if sum(ans1)==n:
			print('YES')
			print(*ans1)
			continue
	

	if val2 >0 and val2&1==0:
		flag2 = 1
		ans2.append(val2)
		if sum(ans2)==n:
			print('YES')
			print(*ans2)
			continue

	if flag2==0:
		print('NO')
		continue
	
	
	"""
	if flag==0:
		ans1=[1]*(k-1)
		val1=n-(1*(k-1))
		
		ans2=[2]*(k-1)
		val2=n-(2*(k-1))
		if val1 > 0 and val1&1==1:
			flag2 = 1
			ans.append(val1)
			if sum(ans1)==n:
				print('YES')
				print(*ans1)
				continue
		

		if val2 >0 and val2&1==0:
			flag2=1
			ans.append(val2)
			if sum(ans2)==n:
				print('YES')
				print(*ans2)
				continue
		if flag2==1:
			print('NO')
			continue
	"""