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.*;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public final class B implements Runnable {


    public void solveCase() {
        int n = nextInt(), k = nextInt();
        int[] ans = null;
        if (n >= k && n % 2 == k % 2) {
            ans = new int[k];
            Arrays.fill(ans, 1);
            ans[ans.length - 1] = n - (k - 1);
        } else if (n >= 2 * k && n % 2 == 0) {
            ans = new int[k];
            Arrays.fill(ans, 2);
            ans[ans.length - 1] = n - (k - 1) * 2;
        }
        if (ans != null) {
            pw.println("YES");
            for (int x : ans)
                pw.print(x + " ");
            pw.println();
        } else {
            pw.println("NO");
        }
    }

    public void solve() {
        int t = nextInt();
        for (int i = 0; i < t; ++i) {
            solveCase();
        }
    }

    static final String filename = "A";
    static final boolean fromConsole = true;

    public void run() {
        try {
            if (!fromConsole) {
                in = new BufferedReader(new FileReader(filename + ".in"));
                pw = new PrintWriter(filename + ".out");
            } else {
                in = new BufferedReader(new InputStreamReader(System.in));
                pw = new PrintWriter(System.out);
            }
            st = new StringTokenizer("");
            long st = System.currentTimeMillis();
            solve();
            //pw.printf("\nWorking time: %d ms\n", System.currentTimeMillis() - st);
            pw.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    private StringTokenizer st;
    private BufferedReader in;
    private PrintWriter pw;

    boolean hasNext() {
        try {
            while (!st.hasMoreTokens()) {
                String line = in.readLine();
                if (line == null) {
                    return false;
                }
                st = new StringTokenizer(line);
            }
            return st.hasMoreTokens();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    String next() {
        return hasNext() ? st.nextToken() : null;
    }

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

    BigInteger nextBigInteger() {
        return new BigInteger(next());
    }

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

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

    public static void main(String[] args) {
        new Thread(new B()).start();
    }
}