Problem: A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input


9 4


Output


YES
1 2 2 4 


Input


8 1


Output


YES
8 


Input


5 1


Output


NO


Input


3 7


Output


NO

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.AbstractCollection;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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);
        CPowersOfTwo solver = new CPowersOfTwo();
        solver.solve(1, in, out);
        out.close();
    }

    static class CPowersOfTwo {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            String b = Integer.toBinaryString(n);
            int counter = 0;
            int e = 0;
            PriorityQueue<Integer> q = new PriorityQueue<>();
            StringBuilder ans = new StringBuilder();
            for (int i = b.length() - 1; i > -1; i--) {
                if (b.charAt(i) == '1') {
                    int p = power(2, counter);
                    if (p > 1) {
                        q.add(p);
                    } else {
                        ans.append(1 + " ");
                    }
                    e++;
                }
                counter++;
            }
            if (e > k)
                out.println("NO");
            else {
                while (!q.isEmpty() && e < k) {
                    int w = q.poll();
                    int w1 = w / 2;
                    e++;
                    if (w1 > 1) {
                        q.add(w1);
                        q.add(w1);
                    } else {
                        ans.append(1 + " " + 1 + " ");
                    }
                }
                if (e == k) {
                    out.println("YES");
                    while (!q.isEmpty())
                        ans.append(q.poll() + " ");
                    out.println(ans.toString());
                } else
                    out.println("NO");
            }
        }

        int power(int x, int y) {
            int temp;
            if (y == 0)
                return 1;
            temp = power(x, y / 2);
            if (y % 2 == 0)
                return temp * temp;
            else
                return x * temp * temp;
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            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());
        }

    }
}