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.Map;
import java.util.Map.Entry;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Pranay2516
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(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, FastReader in, PrintWriter out) {
            int n = in.nextInt(), k = in.nextInt();
            HashMap<Integer, Integer> ans = new HashMap<>();
            ArrayDeque<Integer> bits = new ArrayDeque<>();
            int t = n, j = 0;
            while (t > 0) {
                if (t % 2 == 1) {
                    if (j > 0) bits.add(1 << j);
                    ans.put(1 << j, ans.getOrDefault(1 << j, 0) + 1);
                }
                t /= 2;
                j++;
            }
            if (ans.size() > k) {
                out.println("NO");
                return;
            }
            int cnt = ans.size();
            while (cnt < k && !bits.isEmpty()) {
                int num = bits.pollFirst();
                ans.put(num, ans.get(num) - 1);
                ans.put(num / 2, ans.getOrDefault(num / 2, 0) + 2);
                if (num / 2 > 1) {
                    bits.add(num / 2);
                    bits.add(num / 2);
                }
                cnt++;
            }
            if (cnt < k) {
                out.println("NO");
                return;
            }
            out.println("YES");
            for (Map.Entry<Integer, Integer> entry : ans.entrySet()) {
                int key = entry.getKey(), v = entry.getValue();
                if (v > 0) {
                    for (int i = 0; i < v; ++i) {
                        out.print(key + " ");
                    }
                }
            }
            out.println();
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}