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:
#lannisters don't act like fools

import math
'''And who are you, the proud lord said,
That I must bow so low?
Only a cat of a different coat,
That's all the truth I know.
In a coat of gold or a coat of red,
A lion still has claws,
And mine are long and sharp, my lord,
As long and sharp as yours.
And so he spoke, and so he spoke,
That lord of Castamere,
But now the rains weep o'er his hall,
With no one there to hear.
Yes now the rains weep o'er his hall,
And not a soul to hear.
'''


t=int(input())
for _ in range(0,t):
    str1=input()
    str1=str1.split()
    n=int(str1[0])
    k=int(str1[1])
    sum1=(k-1)
    sum2=(k-1)*2
    if (n-sum1)>0 and (n-sum1)%2==1:
        print("YES")
        for i in range(0,k-1):
            print(1,end=' ')
        print(n-sum1)
    elif (n-sum2)>0 and (n-sum2)%2==0:
        print("YES")
        for i in range(0,k-1):
            print(2,end=' ')
        print(n-sum2)
    else:
        print("NO")