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 sys import stdin, stdout
import math,sys
from itertools import permutations, combinations
from collections import defaultdict,deque,OrderedDict
import bisect as bi
import heapq 

'''
#------------------PYPY FAst I/o--------------------------------#
 
def I():return (int(stdin.readline()))
def In():return(map(int,stdin.readline().split()))
'''
#------------------Sublime--------------------------------------#
 
#sys.stdin=open('input.txt','r');sys.stdout=open('output.txt','w');
def I():return (int(input()))
def In():return(map(int,input().split()))

def main():
    try:
        n,k=In()
        flag=0
        ans=[]
        q=0
        if n<k:
            flag=1
        else:
            if n==k:
                for i in range(k):
                    ans.append(1)
                    q=1
            if n&1!=1 and q==0:
                if k&1==1:
                    if n>=(2*k):
                        for i in range(k-1):
                            ans.append(2)
                        ans.append(n-(2*(k-1)))
                    else:
                        flag=1
                else:
                    for i in range(k-1):
                        ans.append(1)
                    ans.append(n-(k-1))

            elif q==0 and n&1==1:
                if k&1==1:
                    if n>=k:
                        for i in range(k-1):
                            ans.append(1)
                        ans.append(n-(k-1))
                else:
                    flag=1
        if flag==0:
            print('YES')
            print(*ans)
        else:
            print('NO')
    except:
        pass
        
M = 998244353
P = 1000000007
 
if __name__ == '__main__':
    for _ in range(I()):
        main()