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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class _DIV4_B implements Runnable{
    public static void main(String[] args) {
	    new Thread(null, new _DIV4_B(),"Main",1<<27).start();
    }
    @Override
    public void run() {
        FastReader fd = new FastReader();
        PrintWriter out = new PrintWriter(System.out, true);

        int t = fd.nextInt();
        for(int te = 0; te < t; te++){
            int a = fd.nextInt();
            int b = fd.nextInt();

            if( b > a || (a-b) == 1 && b != 1){ System.out.println("NO");continue; }

            int ext = a - b;
            int sum = 0;

            StringBuilder ans = new StringBuilder();

            if(getSum(a, b, sum, ans,(ext % 2)+1)){
                System.out.println("YES");
                System.out.println(ans);
            }
            else{
                System.out.println("NO");
            }
        }
    }

    private boolean getSum(int a, int b, int sum, StringBuilder ans, int start) {
        int count = 0;
        for(int i = 1; i < b; i++){
            sum += start;
            count++;
            ans.append(start).append(" ");
        }
        if((a - sum) > 0 && (a-sum) % 2 == (start % 2)){
            ans.append(a - sum).append(" ");
            count++;
            sum += a - sum;
        }
        return count == b && sum == a;
    }


    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;
        }
    }
}