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:
import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__

def gift():
    for _ in range(t):
        n,k=map(int,input().split())
        if n<k:
            yield 'NO'
        else:
            if n%2==0:
                if n>=k*2:
                    ans=[2]*(k-1)+[n-2*(k-1)]
                    yield 'YES'
                    yield " ".join(str(x) for x in ans)
                else:
                    dd=(3*k-n)//2
                    dl=(3*k-n)/2
                    if dd==dl:
                        ans=[1]*(dd)+[3]*(k-dd)
                        yield 'YES'
                        yield " ".join(str(x) for x in ans)
                    else:
                        yield 'NO'
            else:
                if n>=k and k%2:
                    yield 'YES'
                    ans=[1]*(k-1)+[n-(k-1)]
                    yield " ".join(str(x) for x in ans)
                else:
                    yield 'NO'
if __name__ == '__main__':
    t= int(input())
    ans = gift()
    print(*ans,sep='\n')



##100 55
##1 3 5
##33  22

##x+3*(k-x)=n
##n=3*k-2*x
##x=(3*k-n)//2
##1 3 1 3 1 3 49