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.*;
import java.util.*;

public class PowersOfTwo {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
    }

    static class Solver {
        private void solve(InputReader inp, PrintWriter out) {
            int n = inp.nextInt(), k = inp.nextInt();
            if (k > n) {
                out.print("NO");
                return;
            }
            int[] pow = new int[31];
            int i = pow.length - 1, tot = 0;
            while (n > 0) {
                if ((n&1)==1) pow[i]++;
                i--;
                n >>= 1;
            }
            for (int j: pow) tot += j;
            if (k < tot) {
                out.print("NO");
                return;
            }
            out.println("YES");
            for (int j = 0; j < pow.length - 1 && tot < k; j++) {
                while (pow[j] > 0 && tot < k) {
                    pow[j]--;
                    pow[j+1]+=2;
                    tot++;
                }
            }
            int power = 1;
            for (int j = pow.length - 1; j >= 0; j--) {
                for (int m = 0; m < pow[j]; m++) {
                    out.print(power + " ");
                }
                power <<= 1;
            }
        }
    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

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

        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());
        }

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