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:
from typing import List


def GetParity(n: int, k: int) -> List[int]:
    Element = list()
    if (1 + (n - k)) > 0 and (1 + (n - k)) % 2 == 1:
        for i in range(k):
            Element.append(1)
        Element[k - 1] += n - k
    elif (2 + (n - 2*k)) > 0 and (2 + (n - 2 * k)) % 2 == 0:
        for i in range(k):
            Element.append(2)
        Element[k - 1] += (n - 2 * k)
    return Element


t = int(input())
Result = list(list())
for i in range(t):
    number, num_elements = map(int, input().split())
    temp = GetParity(number, num_elements)
    Result.append(temp)
for el in Result:
    if len(el) == 0:
        print("NO")
    else:
        print("YES")
        for e in el:
            print(int(e), end=' ')
        print()