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 Mon Jun  1 20:15:32 2020

@author: Katherine
"""

testCases = int(input())

while testCases > 0:
    
    n, k = map(int, input().split())
    
    listA = []
    
    yes = True
    
    if n == k:
        
        x = 0
        while x < k:
            listA.append(1)
            x += 1
            
    elif k == 1:
        
        listA.append(n)
    
    elif n % 2 == 0:
        
        x = 1
        while x < k:
            listA.append(2)
            x += 1
            
        listA.append(n - len(listA) * 2)
        
        if listA[-1] <= 0:
            
            listA = []
            
            x = 1
            while x < k:
                listA.append(1)
                x += 1
            
            if (n - len(listA)) % 2 == 1:
                listA.append(n - len(listA))
            
            else:
            
                yes = False
            
            if listA[-1] <= 0:
                
                yes = False
        
    elif (n - k) > 0 and (n - k) % 2 == 0:
        
        x = 1
        while x < k:
            listA.append(1)
            x += 1
          
        
        listA.append(n - len(listA))
        
        
    else:
        
        yes = False
        
    if yes == False:
        
        print("NO")
        
    else:
        
        print("YES")
        
        print(*listA)
    
    testCases -= 1