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 PYTHON):

Solution:
from sys import stdin,stdout
input = stdin.readline
T=int(input())

def Output(A,B):
    last = A-(B-1)
    if last >0 and last % 2:

        return ['YES', [1 for i in range(B-1)] +[last]]

    last = A-(B-1)*2
    if last >0 and last % 2==0:

        return ['YES',[2 for i in range(B-1)] +[last]]
    return ['NO', None]
for i in range(1,T+1):
    A,B=list(map(int,input().split()))
    can, l = Output(A,B)
    if can =='YES':
        print("YES")
        print(" ".join(map(str,l)))
    else:
        print("NO")