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 _ in range(T):
        N, K = list(map(int, input().split()))
        #print(N, K)
        verdict = False
        res = []
        n = N
        k = K
        #print(not N & 1, K & 1)
        if (not N & 1) and (K  & 1):
            if N > 2 *(K - 1):
                for i in range(K - 1):
                    res.append(2)
                res.append(N - 2*(K - 1))
                verdict = True
        elif (not N & 1 and (not K & 1)):
            if N > (K - 1):
                for i in range(K - 1):
                    res.append(1)
                res.append(N - (K - 1))
                verdict = True
        elif (N & 1 and K & 1):
            if N > K - 1:
                for i in range(K - 1):
                    res.append(1)
                res.append(N - (K - 1))
                verdict = True
        if (verdict):
            print("YES")
            for i in res:
                print(i, end = " ")
        else:
            print("NO")
if __name__ == "__main__":
    main()