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 JAVA):

Solution:
import java.util.HashMap;
import java.util.Scanner;
import java.util.LinkedList;
import java.util.ArrayList;
import java.util.TreeSet;
import java.util.Stack;
public class Main
{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		
		int t = sc.nextInt();
		
		while(t != 0){
		
		    int n = sc.nextInt();
		    int k = sc.nextInt();
		    
		    if(n%2 == 0 && k%2 == 1)
		    {
		        if(k*2 > n)
		            System.out.println("NO");
		        else{
		            System.out.println("YES");
		            for(int i = 0;i<k-1;i++)
		            {
		                System.out.print("2 ");
		            }
		             System.out.println((n-2*k+2));
		        }
		    }
		    else if(n%2 == 1 && k%2 == 1)
		    {
		        if(k > n)
		            System.out.println("NO");
		        else{
		            System.out.println("YES");
		            for(int i = 0;i<k-1;i++)
		            {
		                System.out.print("1 ");
		            }
		             System.out.println((n-k+1));
		        }
		    }
		    else if(n%2 == 1 && k%2 == 0)
		    {
		        System.out.println("NO");
		    }
		    else{
		        if(k > n)
		            System.out.println("NO");
		        else{
		            System.out.println("YES");
		            for(int i = 0;i<k-1;i++)
		            {
		                System.out.print("1 ");
		            }
		             System.out.println((n-k+1));
		        }
		    }
		    
		    
		  
		    t--;
		        
    		
		}
		    
	}
}