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 = map(int,input().split())
    summ1= (k-1)
    rem1 = n-summ1
    flag = 0
    if rem1%2==1 and rem1>0:
        print("YES")
        ans = [1]*(k-1)
        ans+=[rem1]
        print(*ans)
        flag = 1
    else:
        summ2 = 2*summ1
        rem2 = n-summ2
        if rem2>0 and rem2%2==0:
            print("YES")
            ans = [2]*(k-1)
            ans+=[rem2]
            print(*ans)
            flag=1
        else:
            print("NO")
    t-=1