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:
# ANSHUL GAUTAM
# IIIT-D

from math import *
from copy import *					# ll = deepcopy(l)
from heapq import *					# heappush(hp,x)
from string import *				# alpha = ascii_lowercase
from random import *				# l.sort(key=lambda l1:l1[0]-l1[1]) => ex: sort on the basis difference
from bisect import *				# bisect_left(arr,x,start,end)  => start and end parameters are temporary
from sys import stdin				# bisect_left return leftmost position where x should be inserted to keep sorted
from sys import maxsize				# minn = -maxsize
from operator import *				# d = sorted(d.items(), key=itemgetter(1))
from itertools import *				# pre = [0] + list(accumulate(l))
from collections import Counter		# d = dict(Counter(l))
from collections import defaultdict # d = defaultdict(list)

'''
8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9

'''

def solve(n,k):
	if(k > n):
		print('NO')
		return
	else:
		ans = []
		if(n&1):
			if(k&1):
				print('YES')
				for i in range(k-1):
					ans.append(1)
				ans.append(n-sum(ans))
			else:
				print('NO')
				return
		else:
			if(k&1):
				if(2*k > n):
					print('NO')
					return
				else:
					print('YES')
					for i in range(k-1):
						ans.append(2)
					ans.append(n-sum(ans))
			else:
				print('YES')
				for i in range(k-1):
					ans.append(1)
				ans.append(n-sum(ans))
		print(*ans)

T = int(input())
for _ in range(T):
	N,K = list(map(int, stdin.readline().rstrip().split()))
	solve(N,K)