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:
//package com.company;
import com.sun.nio.sctp.SctpStandardSocketOptions;
import javax.swing.*;
import java.math.BigInteger;
import java.util.Calendar;
import java.net.StandardSocketOptions;
import java.util.*;
import java.util.Calendar;
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.text.SimpleDateFormat;
import java.util.Arrays;
import java.util.Calendar;
import java.util.Random;
import java.util.StringTokenizer;
import java.io.*;
import java.util.ArrayList;
import java.math.BigInteger;
    /*
                                                DOMINGO_GIRL :)
                                                ─────────▄──────────────▄
                                                ────────▌▒█───────────▄▀▒▌
                                                ────────▌▒▒▀▄───────▄▀▒▒▒▐
                                                ───────▐▄▀▒▒▀▀▀▀▄▄▄▀▒▒▒▒▒▐
                                                ─────▄▄▀▒▒▒▒▒▒▒▒▒▒▒█▒▒▄█▒▐
                                                ───▄▀▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▀██▀▒▌
                                                ──▐▒▒▒▄▄▄▒▒▒▒▒▒▒▒▒▒▒▒▒▀▄▒▒▌
                                                ──▌▒▒▐▄█▀▒▒▒▒▄▀█▄▒▒▒▒▒▒▒█▒▐
                                                ─▐▒▒▒▒▒▒▒▒▒▒▒▌██▀▒▒▒▒▒▒▒▒▀▄▌
                                                ─▌▒▀▄██▄▒▒▒▒▒▒▒▒▒▒▒░░░░▒▒▒▒▌
                                                ─▌▀▐▄█▄█▌▄▒▀▒▒▒▒▒▒░░░░░░▒▒▒▐ Wow
                                                ▐▒▀▐▀▐▀▒▒▄▄▒▄▒▒▒▒▒░░░░░░▒▒▒▒▌
                                                ▐▒▒▒▀▀▄▄▒▒▒▄▒▒▒▒▒▒░░░░░░▒▒▒▐
                                                ─▌▒▒▒▒▒▒▀▀▀▒▒▒▒▒▒▒▒░░░░▒▒▒▒▌
                                                ─▐▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▐
                                                ──▀▄▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▄▒▒▒▒▌
                                                ────▀▄▒▒▒▒▒▒▒▒▒▒▄▄▄▀▒▒▒▒▄▀
                                                ───▐▀▒▀▄▄▄▄▄▄▀▀▀▒▒▒▒▒▄▄▀
                                                ──▐▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▀▀
                                            */

    public class Main {
        //static final int mod = (int)1e9+7;
        public static void main(String[] arg) {
            Scanner sc = new Scanner(System.in);
            int t=sc.nextInt();
            while (t-->0){
                long n=sc.nextLong(),k=sc.nextLong();
                if(k>n)System.out.println("NO");

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



                    }

                }



            }



        }




    }