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:
def main():
    t = int(input())

    for i in range(t):
        nk = list(map(int, input().split()))
        n = nk[0]
        m = nk[1]

        if n < m:
            print("NO")
        elif n % m == 0:
            print("YES")
            resultado = int(n / m)
            lista = [resultado] * m
            print(*lista)
        elif n %2 != 0  and m %2 == 0:
            print("NO")
        elif n%2 == 0 and m%2 != 0:
            if n/2 < m:
                print("NO")
            else:
                print("YES")
                lista = []
                for i in range(m-1):
                    lista.append(2)
                lista.append(n-2*(m-1))
                print(*lista)

        else:
            print("YES")
            lista = []
            for i in range(m-1):
                lista.append(1)
            lista.append(n-(m-1))
            print(*lista)


if __name__ == "__main__":
    main()