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.io.*;
import  java.math.*;
import java.nio.Buffer;
import java.sql.SQLSyntaxErrorException;
import  java.util.*;
import  java.text.*;
import java.util.regex.Pattern;
import java.util.stream.Collectors;


public class Main {

    public static void main(String[] args) {
        Scanner cin = new Scanner(System.in);
        //h,l,H,L
        int T=cin.nextInt();
        while(T-->0){
            int n=cin.nextInt();
            int k=cin.nextInt();
            if(n<k){
                System.out.println("NO");
                continue;
            }

            if(n%2==0){
                int x=n/k;
                if((x*k)==n){
                    System.out.println("YES");
                    for(int i=0;i<k;i++){
                        if(i!=0){
                            System.out.print(" ");
                        }
                        System.out.print(x);
                    }
                    System.out.println();
                    continue;
                }
                else {
                    int sum=n%(x*k);
                    if(sum%2!=0){
                        if(x!=1&&k%2==1){
                            System.out.println("YES");
                            System.out.print(x-1+sum+k);
                            for(int i=1;i<k;i++){
                                System.out.print(" ");
                                System.out.print(x-1);
                            }
                            System.out.println();
                        }

                        else{
                            System.out.println("NO");
                            continue;
                        }
                    }
                    else{
                        System.out.println("YES");
                        System.out.print(sum+x);
                        for(int i=1;i<k;i++){
                            System.out.print(" ");
                            System.out.print(x);
                        }
                            System.out.println();
                        }

                }
            }
            else{
                int x=n/k;
                if(k%2==0){
                    System.out.println("NO");
                    continue;
                }

                if(x*k==n){
                    System.out.println("YES");
                    for(int i=0;i<k;i++){
                        if(i!=0){
                            System.out.print(" ");
                        }
                        System.out.print(x);
                    }
                    System.out.println();
                    continue;
                }
                else{
                    int sum=n%(x*k);
                    if(sum%2!=0){
                        if(x!=1&&k%2==1){
                            System.out.println("YES");
                            System.out.print(x-1+sum+k);
                            for(int i=1;i<k;i++){
                                System.out.print(" ");
                                System.out.print(x-1);
                            }
                            System.out.println();
                        }

                        else{
                            System.out.println("NO");
                            continue;
                        }
                    }
                    else{
                        System.out.println("YES");
                        System.out.print(sum+x);
                        for(int i=1;i<k;i++){
                            System.out.print(" ");
                            System.out.print(x);
                        }
                        System.out.println();
                    }
                }
            }
        }

    }
}