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:
// hazaro phool barsao div 4 aaya hai
import java.util.*;
import java.util.regex.*;

public class Codechef
{
	public static void main (String[] args)
	{
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		//int t = Integer.valueOf(sc.nextLine());
		while(t-- != 0)
		{
		    int n = sc.nextInt();
		    int k = sc.nextInt();
		    int q = n/k;
		    int r = n%k;
		    if(r==0)
		    {
		        System.out.println("YES");
		        for(int i = 0; i < k; i++)
		        {
		            System.out.print(q+" ");
		        }
		        System.out.println();
		    }
		    else
		    {
		        if(q>1)
		        {
		            String ans = "";
		            boolean isEven = false;
		            if(q%2==0)
		                isEven = true;
		            int sum = 0;
		            for(int i = 0; i < k-1; i++)
		            {
		                ans = ans + q + " ";
		                sum = sum + q;
		            }
		            int remain = n - sum;
		            if(remain%2==0 && isEven)
		            {
		                ans = ans+remain;
		                System.out.println("YES");
		                System.out.println(ans);
		            }
		            else if(remain%2 != 0 && !isEven)
		            {
		                ans = ans + remain;
		                System.out.println("YES");
		                System.out.println(ans);
		            }
		            else
		            {
		                q--;
    		            ans = "";
    		            isEven = false;
    		            if(q%2==0)
    		                isEven = true;
    		            sum = 0;
    		            for(int i = 0; i < k-1; i++)
    		            {
    		                ans = ans + q + " ";
    		                sum = sum + q;
    		            }
                        remain = n - sum;
    		            if(remain%2==0 && isEven)
    		            {
    		                ans = ans+remain;
    		                System.out.println("YES");
    		                System.out.println(ans);
    		            }
    		            else if(remain%2 != 0 && !isEven)
    		            {
    		                ans = ans + remain;
    		                System.out.println("YES");
    		                System.out.println(ans);
    		            }
    		            else
    		            {
    		                System.out.println("NO");
    		            }
		            }
		        }
		        else if(q>0)
		        {
		            String ans = "";
		            int sum = 0;
		            for(int i = 0; i < k-1; i++)
		            {
		                sum = sum + q;
		                ans = ans + q + " ";
		            }
		            if((n-sum)%2 != 0)
		            {
		                ans = ans + (n-sum);
		                System.out.println("YES");
		                System.out.println(ans);
		            }
		            else
		            {
		                System.out.println("NO");
		            }
		        }
		        else
		        {
		            System.out.println("NO");
		        }
		    }
		}
	}
}