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:
class Solution():
    def even(self, n, t):
        if t < 1:
            return None
        x = (t - 1) * 2
        if (n - x) % 2 != 0:
            return None
        if n - x < 1:
            return None
        res = ([2] * (t - 1)) + [n - x]
        if sum(res) != n:
            return None
        return res

    def odd(self, n, t):
        if t < 1:
            return None
        x = (t - 1) * 1
        if (n - x) % 2 == 0:
            return None
        if n - x < 1:
            return None
        res = ([1] * (t - 1)) + [n - x]
        if sum(res) != n:
            return None
        return res

tests = int(input())
solution = Solution()
for test in range(tests):
    splits = str(input()).split(' ')
    n = int(splits[0])
    t = int(splits[1])
    even = solution.even(n, t)
    odd = solution.odd(n, t)
    if even is not None:
        print('YES')
        print(' '.join(map(str, even)))
    elif odd is not None:
        print('YES')
        print(' '.join(map(str, odd)))
    else:
        print('NO')