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 solve_old(n, k):
    if k == 1:
        return [n]
    if n < k:
        return None
    if n == k:
        return [1] * k

    if k % 2 == 0:
        if n % 2 != 0:
            return None

        assert n % 2 == 0
        if n < k * 2:
            return None
        a = [2] * k
        a[0] += n - 2 * k
        assert a[0] % 2 == 0
        return a

    assert k % 2 != 0
    if n % 2 == 0:
        if n < k * 2:
            return None
        a = [2] * k
        a[0] += n - 2 * k
        assert a[0] % 2 == 0
        return a

    assert n % 2 != 0
    if n < k:
        return None
    a = [1] * k
    a[0] += n - k
    assert a[0] % 2 != 0
    return a


def solve(n, k):
    if n < k:
        return None

    a_odd = [1] * k
    a_odd[0] += n - k
    if a_odd[0] % 2 != 0:
        return a_odd

    if n < 2 * k:
        return None

    a_even = [2] * k
    a_even[0] += n - 2 * k
    if a_even[0] % 2 == 0:
        return a_even

    return None


def main():
    T = int(input())
    for _ in range(T):
        n, k = map(int, input().split())
        arr = solve(n, k)
        if not arr:
            print("NO")
        else:
            # assert sum(arr) == n
            # assert len(arr) == k
            # assert all(0 < a <= n for a in arr), arr
            # assert all(a % 2 == arr[0] % 2 for a in arr), arr
            print("YES")
            print(" ".join(map(str, arr)))


if __name__ == "__main__":
    main()