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:
# **************************************************************************** #
#                                                                              #
#                                            __   __ .____  .__  __.  ____     #
#    B-SameParitySummands.py                |  | |  ||  _ \ |  \/  | /    |    #
#                                           |  | |  || |_| || \  / ||  ,--'    #
#    By: ayahyao <y.anas1997@gmail.com>     |  | |  ||  __/ | |\/| ||  |       #
#                                           |  `-'  || |    | |  | ||  `--.    #
#    Created: 2020/05/11 15:09 by Anas       \_____/ |_|    |_|  |_| \____|    #
#    Updated: 2020/05/11 15:31 by Anas                                         #
#                                                                              #
# **************************************************************************** #


def     process(n, k):
    if ((n % 2 == 1 and k % 2 == 0) or
       (k > n) or  (n % 2 == 0 and 2 * k > n and k % 2 == 1)):
        print("NO")
        return
    print("YES")
    if (n % 2 == 0 and k % 2 == 1):
        a = 2
    else:
        a = 1
    for i in range(k-1):
        print(a, end=' ')
    print (n - a * (k-1))
    return


T = int(input())

for i in range(T):
    data = input().split()
    n,k = int(data[0]), int(data[1])
    process(n,k)