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:
t=int(input())
i=0
while i<t:
    n,k=map(int,input().split())
    a=False
    b=False
    r=False
    q=[1]*k
    if sum(q)==n:
        a=True
        print("YES")
        for x in q:
            print(x,end=" ")
    elif sum(q)>n:
        
        r=True
    else:
        s=n-k
        if s%2==0:
            print("YES")
            a=True
            q[k-1]=q[k-1]+s
            for x in q:
                print(x,end=" ")
            print()
        else:
            r=True


    if r==True:
        p=[2]*k
        if sum(p)==n:
            b=True
            print("YES")
            for x in p:
                print(x,end=" ")
            print()
        elif sum(p)>n:
        
            pass
        else:
            s=n-(2*k)
            if s%2==0:
                b=True
                print("YES")
            
                p[k-1]=p[k-1]+s
                for x in p:
                    print(x,end=" ")
                print()
            else:
                pass
            
        
        
    


    if a==False and b==False:
        print("NO")
    


    i=i+1