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:
# -*- coding: utf-8 -*-
"""
Created on Tue May 12 03:19:56 2020

@author: Bilel Kanoun
"""

t=int(input())

for i in range(t):
    n,k = map(int, input().split())
    
    n1 = n - (k-1)
    if (n1>0 and n1%2==1):
        print("YES")
        ch1=""
        for i in range(k-1):
            ch1+="1 "
        
        print(ch1+str(n1))
        continue
    
    n2 = n - 2*(k-1)
    if (n2>0 and n2%2==0):
        print("YES")
        ch2=""
        for i in range(k-1):
            ch2+="2 "
            
        print(ch2+str(n2))
        continue
    
    print("NO")