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())
while t:
    n,k=list(map(int,input().split()))
    flag=0
    s=0
    a=[]
    if n%2!=0:
        s+=k-1
        if s>n:
            flag=1
        else:
            d=n-s
            if d!=0 and d%2!=0:
                a=[1]*(k-1)
                a.append(d)
            else:
                flag=1
    else:
        s1=k-1
        if s1>n:
            flag=1
        else:
            d=n-s1
            if d!=0 and d%2!=0:
                a=[1]*(k-1)
                a.append(d)
            else:
                flag=1
        if flag==1:
            s2=2*(k-1)
            if s2>n:
                flag=1
            else:
                d=n-s2
                if d!=0 and d%2==0:
                    a=[2]*(k-1)
                    a.append(d)
                else:
                    flag=1
    if a==[]:
        print("NO")
    else:
        print("YES")
        print(*a)
    t-=1