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 collections import Counter as C,defaultdict as D,deque as Q
from operator import itemgetter as I
from itertools import product as P
from bisect import bisect_left as BL,bisect_right as BR
from heapq import heappush as HPUSH,heappop as HPOP
from math import floor as MF,ceil as MC, gcd as MG,factorial as F,sqrt as SQRT, inf as INFINITY,log as LOG
from sys import stdin, stdout
INPUT=stdin.readline
PRINT=stdout.write

def player1():
	print("")

def player2():
	print("")

def isPrime(n):

	for i in range(2,MC(SQRT(n))+1):
		if n%i==0:
			return False
	return True

def factors(x):

	ans=[]

	for i in range(1,MC(SQRT(x))+1):
		if x%i==0:
			ans.append(i)
			if x%(x//i)==0:
				ans.append(x//i)
	return ans


def main():

	for _ in range(int(INPUT())):
		n,k=map(int,input().split( ))
		ans=[1]*(k-1)
		left=n-sum(ans)
		if left>0 and left&1:
			ans.append(left)
		else:
			ans=[2]*(k-1)
			left=n-sum(ans)
			if left>0 and (not left&1):
				ans.append(left)
			else:
				ans="NO"
		if ans=="NO":
			PRINT(ans+"\n")
		else:
			PRINT("yes\n")
			print(*ans)

main()