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:


if __name__ == '__main__':

    num = int(input())
    for i in range(num):
        t, k = map(int, input().split(" "))
        # even
        res = list()
        if t % 2 == 0:
            if t / 2 < k:
                if t - (k - 1) > 0 and (t - (k - 1)) % 2 == 1:
                    print('YES')
                    for j in range(k-1):
                        res.append(str('1'))
                    res.append(str(t - (k - 1)))
                    print(' '.join([str(h) for h in res]))
                else:
                    print('NO')
            else:
                for j in range(k-1):
                    res.append('2')
                    t -= 2
                res.append(str(t))
                print('YES')
                print(' '.join([str(h) for h in res]))
        else:
            if t - (k-1) > 0 and (t - (k-1)) % 2 == 1:
                print('YES')
                for j in range(k - 1):
                    res.append(str('1'))
                res.append(str(t - (k - 1)))
                print(' '.join([str(h) for h in res]))
            else:
                print('NO')