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.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Reader;
import java.io.StreamTokenizer;
import java.io.Writer;
import java.util.ArrayDeque;
import java.util.Deque;

public class PowersOfTwo {
    private static Reader reader = new InputStreamReader(System.in);
    private static Writer writer = new OutputStreamWriter(System.out);
    private static StreamTokenizer in = new StreamTokenizer(new BufferedReader(reader));
    private static PrintWriter out = new PrintWriter(writer);

    private static int nextInt() throws IOException {
        in.nextToken();
        return (int) in.nval;
    }

    public static void main(String[] args) throws IOException {
        int n = nextInt();
        int k = nextInt();

        String s = solve(n, k);
        if (s.isEmpty()) {
            out.println("NO");
        } else {
            out.println("YES");
            out.println(solve(n, k));
        }
        out.flush();

    }

    public static String solve(int n, int k) {
        StringBuilder sb = new StringBuilder();
        if (n == k) {
            for (int i = 0; i < n; i++) {
                sb.append("1 ");
            }
            return sb.toString();
        } else if (k > n) {
            return "";
        } else {
            int curr = n;
            int tmpK = k;
            Deque<Integer> l = new ArrayDeque<>();
            if (curr % 2 == 1) {
                l.push(0);
                curr--;
                tmpK--;
            }
            int p;
            for (int i = 30; i > 0; i--) {
                if (curr == 0) {
                    break;
                }
                if (tmpK == 0) {
//                    System.out.println(l);
//                    System.out.println(curr);
                    return "";
                }

                p = 1 << i;
                if (p == curr) {
//                    System.out.println("p="+p+";curr="+curr+";i="+i);
                    l.push(i);
                    curr = 0;
                    tmpK--;
                } else if (p < curr) {
//                    System.out.println("-----------");
//                    System.out.println(p);
//                    System.out.println(curr);
//                    System.out.println(i);
//                    System.out.println(tmpK);
//                    System.out.println("===========");

                    l.add(i);
                    curr -= p;
                    tmpK--;
                }
            }
//            System.out.println("xxx");
//            System.out.println(l);
//            System.out.println(tmpK);
//            System.out.println("xxx");
            while (tmpK > 0 && !l.isEmpty()) {
                p = l.pop();
                if (p > 0) {
                    l.push(p - 1);
                    l.push(p - 1);
                    tmpK--;
                } else {
                    l.addLast(p);
                }
            }
//            System.out.println("===========");
//            System.out.println(l);

            while (!l.isEmpty())
                sb.append(1 << l.pop()).append(" ");

            return sb.toString();
        }
    }

}