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:
#!/usr/bin/env python
# coding:utf-8
# Copyright (C) dirlt

from sys import stdin


def PR(x):
    print(x, end='')


def run(n, k):
    if n > (k - 1) and (n - k - 1) % 2 == 1:
        print('YES')
        PR('1 ' * (k - 1))
        print(str(n - k + 1))
        return

    if n > 2 * (k - 1) and (n - 2 * k + 2) % 2 == 0:
        print('YES')
        PR('2 ' * (k - 1))
        print(str(n - 2 * k + 2))
        return

    print('NO')


def main():
    t = int(stdin.readline())
    for _ in range(t):
        n, k = [int(x) for x in stdin.readline().split()]
        run(n, k)


if __name__ == '__main__':
    main()