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
import itertools
from functools import lru_cache
import sys
import math
###############################################################################
#Helper
def helper():
    pass
###############################################################################
#Solver
def solve():
    n,k = map(int,input().split(' '))
    if k==1:
        print('YES')
        print(n)
        return
    if n%2==0:
        #odds even time
        left = n
        if k%2 == 0 and k<=n:
            print('YES')
            for i in range(k-2):
                print('1',end=' ')
                left-=1
            print(1,left-1)
            
        #evens k times
        elif k%2==1 and n/2>=k:
            print('YES')
            for  i in range(k-1):
                print('2',end=" ")
                left-=2
            print(left)

        else:
            print('NO')
    else:
        # try
        if k>n: 
            print('NO')
            return
        left = n
        ans = []
        for i in range(k-1):
            ans.append('1')
            left-=1
        if left%2==1:
            print('YES')
            print(' '.join(ans),left)
        else:
            print('NO') 





################################################################################
#Driver
t = int(input())
for _ in range(t):
    solve()
###############################################################################