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:
for t in range(int(input())):
    n,k=list(map(int,input().split()))
    rem=n%k
    x=n//k
    ans=[x]*k
    if rem==0:
        ans=[x]*k
    elif (x%2==0 and rem%2==1) or (x%2==1 and rem%2==1):
        x1=[x+rem]
        x2=[x-1]*((k-1)//2)
        x3=[x+1]*(k-1-((k-1)//2))
        ans=x1+x2+x3
    else:
        ans[0]+=rem
    #print(ans)
    cnte,cnto,zero=0,0,0
    for i in ans:
        if i<=0:
            zero+=1
        if i%2==0:
            cnte+=1
        else:
            cnto+=1
    if zero==0 and (cnte==0 or cnto==0 ) and sum(ans)==n:
        print('YES')
        print(*ans)
    else:
        print('NO')