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.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.util.PriorityQueue;
import java.util.Comparator;
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;
        ScanReader in = new ScanReader(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, ScanReader in, PrintWriter out) {
            long n = in.scanInt();
            long k = in.scanInt();


            PriorityQueue<Integer> pq = new PriorityQueue<>(new Comparator<Integer>() {

                public int compare(Integer o1, Integer o2) {
                    return o2.intValue() - o1.intValue();
                }
            });
            int p = 1;
            while (n > 0) {
                if (n % 2 == 1) {
                    pq.add(p);
                }
                n = n / 2;
                p = p * 2;
            }

            if (pq.size() > k) {
                out.println("NO");
                return;
            }

            while (pq.size() < k) {
                int t = pq.poll();
                if (t == 1) break;
                if (pq.size() > k) break;
                pq.add(t / 2);
                pq.add(t / 2);
            }


            if (pq.size() == k) {
                out.println("YES");
                while (pq.size() != 0) {
                    out.print(pq.poll() + " ");
                }
            } else {
                out.println("NO");
                return;
            }

        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int INDEX;
        private BufferedInputStream in;
        private int TOTAL;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (INDEX >= TOTAL) {
                INDEX = 0;
                try {
                    TOTAL = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (TOTAL <= 0) return -1;
            }
            return buf[INDEX++];
        }

        public int scanInt() {
            int I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}