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():
    n_t = int(input())
    for t in range(n_t):
        n, k = map(int, input().split(" "))
        if n < k:
            ans = "NO"
        else:
            rem = n % k
            m = n // k
            div = [m for _ in range(k)]
            div[-1] += rem
            ans = "YES"
            if m % 2 != div[-1] % 2:
                if (k-1) % 2 != 0:
                    ans = "NO"
                else:
                    for i in range(0, k-1, 2):
                        div[i] += 1
                        div[i+1] -= 1
                    if 0 in div:
                        ans = "NO"
        print(ans)

        if ans == "YES":
            print(" ".join([str(item) for item in div]))

if __name__ == '__main__':
    main()