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:
// Jai Shri Ram
import javax.management.DynamicMBean;
import javax.print.DocFlavor;
import javax.print.attribute.HashAttributeSet;
import java.awt.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.net.Inet4Address;
import java.nio.file.attribute.FileAttribute;
import java.sql.SQLType;
import java.time.DayOfWeek;
import java.time.LocalDate;
import java.time.Month;
import java.time.temporal.TemporalAdjusters;
import java.util.List;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.*;
import java.util.Arrays;
import java.util.concurrent.Callable;
import java.time.DayOfWeek;
import java.time.LocalDate;
import java.time.Month;
import java.time.temporal.TemporalAdjusters;



public class Main {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static void main(String[] args) {
        FastReader sc = new FastReader();
         int t=sc.nextInt();
         for(int i=0;i<t;i++) {
             int n = sc.nextInt();
             int k=sc.nextInt();
             if(n%2!=0 && k%2==0){
                 System.out.println("NO");
             }
             else if(n%2!=0 && k%2!=0){
                 if(n<(k)){
                     System.out.println("NO");
                 }
                 else{
                     System.out.println("YES");
                     for(int j=1;j<=(k-1);j++){
                         System.out.print(1+" ");
                     }
                     System.out.print(n-(k-1));
                     System.out.println(" ");
                 }
             }
             else if(n%2==0 && k%2==0){
                 if(n>=(2*k)){
                     System.out.println("YES");
                     for(int j=1;j<=(k-1);j++){
                         System.out.print(2+" ");
                     }
                     System.out.print(n-2*(k-1));
                     System.out.println(" ");
                 }
                 else if(n>=k){
                     System.out.println("YES");
                     for(int j=1;j<=(k-1);j++){
                         System.out.print(1+" ");
                     }
                     System.out.print(n-(k-1));
                     System.out.println(" ");
                 }
                 else{
                     System.out.println("NO");
                 }
             }
             else{
                 if(n>=(2*k)){
                     System.out.println("YES");
                     for(int j=1;j<=(k-1);j++){
                         System.out.print(2+" ");
                     }
                     System.out.print(n-2*(k-1));
                     System.out.println(" ");
                 }else{
                     System.out.println("NO");
                 }
             }
         }
    }
}