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:
/*
    Arnab Chanda 
*/

// All imports here

import java.io.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.InputStream;
import java.util.*;
import java.util.stream.Collectors;

// Template code starts here //

//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Debugger debug = new Debugger(out);
        Objectify objectify = new Objectify(debug);
        Task solver = new Task();
        int test = in.nextInt();
        while(test-->0){
            solver.solve(1, in, out, debug, objectify);
        }
		out.close();
	}
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
 
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }
 
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
 
    public int nextInt() {
        return Integer.parseInt(next());
    }

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

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

    public float nextFloat() {
        return Float.parseFloat(next());
    }
 
}

class Debugger{
    PrintWriter out;

    Debugger(PrintWriter out){    
        this.out = out;
    }

    public <T> void printList(List<T> arrayList){
        for( Object ob: arrayList){
            out.print(ob+" ");
        }
        out.println();
    }

    public <T> void printSet(Set<T> set){
        for(Object ob: set){
            out.print(ob+" ");
        }
        out.println();
    }

    public <T> void printMap(Map<?,?> map){
        for(Object ob: map.keySet()){
            System.out.println(ob+" : "+map.get(ob));
        }
    }
}

class Objectify{
    
    Debugger debug;

    Objectify(Debugger ob){ debug = ob; }

    public void printArr(int[] arr){ debug.printList(Arrays.stream(arr).boxed().collect(Collectors.toList())); }
    public void printArr(double[] arr){ debug.printList(Arrays.stream(arr).boxed().collect(Collectors.toList())); }
    public void printArr(long[] arr){ debug.printList(Arrays.stream(arr).boxed().collect(Collectors.toList())); }
    public void printArr(char[] arr){ debug.printList( String.valueOf(arr).chars().mapToObj(c -> (char) c).collect(Collectors.toList())); }
    public void printArr(String[] arr){ debug.printList(Arrays.asList(arr)); }

    public void printMatrix(int[][] arr){ for(int a[]:arr) printArr(a); }
    public void printMatrix(double[][] arr){ for(double a[]:arr) printArr(a); }
    public void printMatrix(long[][] arr){ for(long a[]:arr) printArr(a); }
    public void printMatrix(char[][] arr){ for(char a[]:arr) printArr(a); }
    public void printMatrix(String[][] arr){ for(String a[]:arr) printArr(a); }

}

//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

// Template code ends here


class Task {

    final long MOD = (int)Math.pow(10,9)+7;

    public void solve(int testNumber, InputReader sc, PrintWriter out, Debugger debug, Objectify objectify) {
        
        // write your code here
        int n = sc.nextInt();
        int k = sc.nextInt();

        if ( k > n){
            out.println("NO");
        }
        else{
            int sum = 0;
            int sum2 = 0;
            for(int i = 1; i <= k-1; i++){
                sum++;
                sum2+=2;
            }

            if (1%2 == (n-sum)%2 && (n-sum) > 0){
                out.println("YES");
                for(int i = 0; i < k-1; i++){
                    out.print(1+" ");
                }
                out.println(n - sum);
            }
            else if((n-sum2)%2 == 0 && (n-sum2) > 0){
                out.println("YES");
                for(int i = 0; i < k-1; i++){
                    out.print(2+" ");
                }
                out.println(n - sum2);
            }
            else{
                out.println("NO");
            }

            
        }
    }
}