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.Scanner;
import java.util.Arrays;

public class SameParitySummands {

	public static void main(String[] args) {
		Scanner scan =  new Scanner (System.in);
		int  t= scan.nextInt();
		String[] booleanSol = new String[t];
		String[] Sol = new String[t];
		int x=0;
		for(int i=0; i<t;i++){
			int  n= scan.nextInt();
			int  k= scan.nextInt();
			int[] sol =new int [k];
			for(int j=0;j<k;j++)sol[j]=n/k;
			if (n<k){
			    	booleanSol[i]="No";
					Sol[i]=null;
			}
			else if((k%2)!=0){
				if((n/k)==1){
					if((n%k)%2!=0) booleanSol[i]="No";
					else {
						booleanSol[i]="Yes";
						sol[0]=sol[0]+(n%k);
						//for(int solution: sol)System.out.print(solution);
						Sol[i]=Arrays.toString(sol);
					}
				}
				
				else {
					if((n%k)%2!=0){
						booleanSol[i]="Yes";
						sol[0]=sol[0]+(n%k);
						for(x=1;x<k-1;x=x+2){++sol[x];//System.out.print(sol[x]+" ");
						--sol[x+1];
						}
						//for(int solution: sol)System.out.print(solution);
						Sol[i]=Arrays.toString(sol);
					}
					else {
						booleanSol[i]="Yes";
						sol[0]=sol[0]+(n%k);
						//for(int solution: sol)System.out.print(solution);
						Sol[i]=Arrays.toString(sol);
					}		
					
				}
			}
			
			
			else {
				if((n%k)%2!=0){
					booleanSol[i]="No";
					Sol[i]=null;
				}
				else {
					booleanSol[i]="Yes";
					sol[0]=sol[0]+(n%k);
					//for(int solution: sol)System.out.print(solution);
					Sol[i]=Arrays.toString(sol);
				}
				
			}
				
		}
		for(x=0;x<t;x++){
			if(booleanSol[x]=="Yes"){
    			System.out.println(booleanSol[x]);
    			for(int y=1;y<Sol[x].length()-1;y++){
    			    if(Sol[x].charAt(y)!=',')System.out.print(Sol[x].charAt(y));
    			    else System.out.print(" ");
    			}
    			System.out.println();
			}
		    else System.out.println(booleanSol[x]); 	
		}

	}

}