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:
GI = lambda: int(input()); GIS = lambda: map(int, input().split()); LGIS = lambda: list(GIS())

def main():
    pass
    ## if n is odd and k is even then NO
    ## if n is odd and k is odd then parity is odd
    #n = 1 + 1 + [k * 1] + n - (k-1)
    ## if n is even and k is even then parity can be odd or even
    #12 4
    #1 1 1 9
    #2 2 2 6
    ## if n is odd and k is odd then parity is odd
    #7 3
    #1 1 5

    ## Strategy: try with ai 1 and 2, if both fail: NO

    for t in range(GI()):
        n, k = GIS()
        # Try odd
        last = n - k + 1
        if last <= 0 or (last % 2) == 0:
            # Odd didn't work, try even
            last = n - ((k - 1) * 2)
            if last <= 0 or (last % 2) == 1:
                res = []
            else:
                res = [2] * (k - 1) + [last]
        else:
            res = [1] * (k - 1) + [last]

        if res:
            print("YES")
            print(' '.join(map(str, res)))
        else:
            print("NO")

main()