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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.util.stream.Collectors;

public class ProbB {

    static void process(long number, int k) {
        var output = new ArrayList<Long>();
        if(k%2==0) {
            if(number%2==0) {
                if(number<k){
                    out.println("NO");
                    return;
                }
                out.println("YES");
                int temp = k;
                while(temp>1){
                    output.add((long) 1);
                    temp--;
                }
                output.add(number-(k-1));
            }
            else{
                out.println("NO");
                return;
            }
        }
        else {
            if(number%2==0){
                if(number<2*k){
                    out.println("NO");
                    return;
                }
                out.println("YES");
                int temp = k;
                while (temp>1){
                    output.add((long) 2);
                    temp--;
                }
                output.add(number- 2*(k-1));
            }
            else {
                if(number<k){
                    out.println("NO");
                    return;
                }
                out.println("YES");
                int temp = k;
                while(temp>1){
                    output.add((long) 1);
                    temp--;
                }
                output.add(number-(k-1));
            }
        }
        out.println(output.stream().map(String::valueOf).collect(Collectors.joining(" ")));
    }

    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        int t = sc.nextInt();
        var input = new long[t];
        var input2 = new int[t];
        for (int i = 0; i < t; i++) {
            input[i] = sc.nextLong();
            input2[i] = sc.nextInt();
        }
        for (int i = 0; i < t; i++) {
            process(input[i], input2[i]);
        }

        out.close();
    }



    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }

    }
    //--------------------------------------------------------
}