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 _ in range(int(input())):
    l=[]
    n,k=map(int,input().split())
    flag=1
    if k>n:
        print("NO")
        continue
    else:
        if n==k:
            while n>0:
                l.append(1)
                n-=1
        else:
            f=n
            if n%2==0:
                k1=k
                while k1>1:
                    l.append(2)
                    f-=2
                    k1-=1
                if f>0:
                    l.append(f)
                    flag=0
            if flag==1:
                l=[]
                f=n
                while k>1:
                    l.append(1)
                    f-=1
                    k-=1
                if f%2==0:
                    print("NO")
                    continue
                l.append(f)
    print("YES")
    print(*l)