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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class PowersOfTwo {
    static BufferedReader _in = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer _stk;
    static String next() {
        try {
            while (_stk == null || !_stk.hasMoreTokens())
                _stk = new StringTokenizer(_in.readLine());

            return _stk.nextToken();
        } catch(Exception ex) {
            throw new RuntimeException("Failed reading input", ex);
        }
    }
    static int nextInt() { return Integer.parseInt(next()); }
    static long nextLong() { return Long.parseLong(next()); }
    static double nextDouble() { return Double.parseDouble(next()); }

    public static void main(String [] args) throws IOException {
        final int N = nextInt(), K = nextInt();


        PriorityQueue<Integer> pq = new PriorityQueue<>(K, Comparator.reverseOrder());
        for(int bit=1; bit<=N; bit<<=1) {
            if((N&bit) != 0) {
                pq.add(bit);
            }
        }


        while(pq.size()<K) {
            int toDecompose = pq.poll();
            if(toDecompose==1) break;
            pq.add(toDecompose>>1);
            pq.add(toDecompose>>1);
        }

        if(pq.size()!=K) {
            System.out.println("NO");
            return;
        }

        System.out.println("YES");
        PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        String sep="";
        for(int x : pq) {
            pw.print(sep);
            pw.print(x);
            sep = " ";
        }
        pw.println();
        pw.flush();
    }


}