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.Arrays;
import java.util.LinkedHashMap;
import java.util.Scanner;
public class scratch_16{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t= sc.nextInt();
        for (int i = 0; i <t ; i++) {
            int n= sc.nextInt();
            int k= sc.nextInt();
            boolean b1=false;
            if(n<k){

                //    System.out.print("NO");
            }
            else if(n==k){
                b1=true;
                System.out.println("YES");
                for (int j = 0; j <n ; j++) {
                    System.out.print(1+" ");
                }
            }
            else if(k==1){
                b1=true;
                System.out.println("YES");
                System.out.print(n);
            }
            else{
                if(n%2==0){
                    if((k-1)*2>=n){
                        if(k%2==0){
                            b1=true;
                            System.out.println("YES");
                            for (int j = 0; j <k-1 ; j++) {
                                System.out.print(1+" ");
                            }
                            System.out.print(n-(k-1));


                        }
                    }
                    else{
                        b1=true;
                        System.out.println("YES");
                        for (int j = 0; j <k-1 ; j++) {
                            System.out.print(2+" ");
                        }
                        System.out.print(n-((k-1)*2));
                    }
                }
                else{
                    if((n-(k-1))%2!=1){
                        b1=false;
                        //System.out.print("NO");
                    }
                    else{
                        b1=true;

                        System.out.println("YES");
                        for (int j = 0; j <k-1 ; j++) {
                            System.out.print(1+" ");
                        }
                        System.out.print(n-(k-1));


                    }}


            }
            if(!b1){
                System.out.print("NO");
            }


            System.out.println();
        }



    }}