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 solution(n, k):
    # Если n нечетно, а k четно, то решения нет
    if n % 2 != 0 and k % 2 == 0:
        print("no")
        return
    # Если n < k, то решения нет (ai = 0)
    if n < k:
        print("no")
        return
    res = []
    # Если n - четное и k - четное, то слагаемые могут быть нечетными
    # аналогичное поведение, если n и k - нечетные
    if not ((n % 2 == 0) ^ (k % 2 == 0)):
        res = [1 for _ in range(k-1)]
        res.append(n - sum(res))
        print("yes")
        print(' '.join(map(str, res)))
        return

    # Если n - четно и k - нечетно, то числа должны быть четными
    if n % 2 == 0 and k % 2 != 0:
        res = [2 for _ in range(k-1)]
        if n - sum(res) <= 0:
            print("no")
            return
        res.append(n - sum(res))
        print("yes")
        print(' '.join(map(str, res)))


inp = int(input())
for _ in range(inp):
    input_ = tuple(map(int, input().split()))
    solution(input_[0], input_[1])