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.*;
import java.lang.*;
import java.io.*;
 
 
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
    	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 && k>n/2) || (n%2==1 && k%2==0) || n<k) {
					System.out.println("NO");
				}
				else {
					System.out.println("YES");
					int nnn =0;
					if(n%2==0 && k<=n/2) nnn = 2;
					else if(n%2==0 && k>n/2 && k<n)nnn = 1;
					else nnn =1;
					while(k>1) {
						System.out.print(nnn + " ");
						k--;
						n-=nnn;
					}
					System.out.print(n);
					System.out.println();
					
					
				}
				t--;
			}
		
    	
    	
	}
}