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.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.FileReader;
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;
        Scanner in = new Scanner(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, Scanner sc, PrintWriter pw) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            char[] temp = Integer.toBinaryString(n).toCharArray();
            int[] arr = new int[temp.length];
            for (int i = 0; i < temp.length; i++)
                arr[i] = temp[i] - '0';
            int sum = 0;
            for (int i = 0; i < arr.length; i++)
                if (arr[i] == 1)
                    sum++;
            if (sum > k) {
                pw.print("NO");
                return;
            }
            for (int i = 0; i < arr.length - 1 && sum < k; i++) {
                while (sum < k && arr[i] >= 1) {
                    sum++;
                    arr[i + 1] += 2;
                    arr[i]--;
                }
            }
            if (sum == k) {
                pw.println("YES");
                for (int i = arr.length - 1; i >= 0; i--) {
                    while (arr[i]-- >= 1)
                        pw.print((1 << (arr.length - 1 - i)) + " ");
                }
            } else {
                pw.println("NO");
            }
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

    }
}