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:
# May the Speedforce be with us...
'''
for _ in range(int(input())):
arr=list(map(int,input().split()))
n,k=map(int,input().split())
n=int(input())
s=input()

from collections import defaultdict
d=defaultdict()

d=dict()
s=set()
s.intersection()
s.union()
s.difference()


problem statement achhe se padhna hai
age se bhi dekhna hai, piche se bhi dekhna hai
'''
from math import gcd,ceil
from collections import defaultdict as dd
def lcm(a,b):
	return (a*b)//gcd(a,b)
def inin():
	return int(input())
def inar():
	return list(map(int,input().split()))
def ar(element,size):
	return [element for i in range(size)]
def digitsum(num):
	su=0
	while(num):
		su+=num%10
		num//=10
	return su

for i in range(inin()):
	n,k=inar()
	if n%2==0:
		if n<k:
			print('NO')
		else:
			if k%2==0:
				print('YES')
				for i in range(k-1):
					print(1,end=' ')
				print(n-k+1)
			if k%2==1:
				if 2*k>n:
					print('NO')
				else:
					print('YES')
					for i in range(k-1):
						print(2,end=' ')
					print(n-2*(k-1))




	if n%2==1:
		if n<k:
			print('NO')
		else:
			if k%2==1:
				print('YES')
				for i in range(k-1):
					print(1, end=' ')
				print(n-k+1)
			else:
				print('NO')