Problem: Numbers k-bonacci (k is integer, k > 1) are a generalization of Fibonacci numbers and are determined as follows:

  * F(k, n) = 0, for integer n, 1 ≤ n < k; 
  * F(k, k) = 1; 
  * F(k, n) = F(k, n - 1) + F(k, n - 2) + ... + F(k, n - k), for integer n, n > k. 



Note that we determine the k-bonacci numbers, F(k, n), only for integer values of n and k.

You've got a number s, represent it as a sum of several (at least two) distinct k-bonacci numbers. 

Input

The first line contains two integers s and k (1 ≤ s, k ≤ 109; k > 1).

Output

In the first line print an integer m (m ≥ 2) that shows how many numbers are in the found representation. In the second line print m distinct integers a1, a2, ..., am. Each printed integer should be a k-bonacci number. The sum of printed integers must equal s.

It is guaranteed that the answer exists. If there are several possible answers, print any of them.

Examples

Input

5 2


Output

3
0 2 3


Input

21 5


Output

3
4 1 16

Solution (in JAVA):

Solution:
//package codeforces;

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.StringTokenizer;

public class A implements Closeable {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    A() throws IOException {
//        reader = new BufferedReader(new FileReader("input.txt"));
//        writer = new PrintWriter(new FileWriter("output.txt"));
    }

    StringTokenizer stringTokenizer;

    String next() throws IOException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(reader.readLine());
        }
        return stringTokenizer.nextToken();
    }

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

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

    double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    private int MOD = 1000 * 1000 * 1000 + 7;

    int sum(int a, int b) {
        a += b;
        return a >= MOD ? a - MOD : a;
    }

    int product(int a, int b) {
        return (int) (1l * a * b % MOD);
    }

    int pow(int x, int k) {
        int result = 1;
        while (k > 0) {
            if (k % 2 == 1) {
                result = product(result, x);
            }
            x = product(x, x);
            k /= 2;
        }
        return result;
    }

    int inv(int x) {
        return pow(x, MOD - 2);
    }

    void solve() throws IOException {
        int s = nextInt(), k = nextInt();
        List<Long> f = new ArrayList<>();
        if(k > 30) {
            for(int i = 0; i < 30; i++) {
                f.add(1l << i);
            }
        } else {
            for (int i = 0; i < k - 1; i++) {
                f.add(0l);
            }
            f.add(1l);
            f.add(1l);
            for (int i = f.size(); ; i++) {
                long x = 2l * f.get(i - 1) - f.get(i - k - 1);
                if (x > s) {
                    break;
                }
                f.add(x);
            }
        }
        List<Long> answer = new ArrayList<>();
        Collections.reverse(f);
        for (Long x : f) {
            if(x <= s) {
                answer.add(x);
                s -= x;
            }
            if(s == 0) {
                break;
            }
        }
        answer.add(0l);
        writer.println(answer.size());
        for (Long x : answer) {
            writer.print(x + " ");
        }
    }

    public static void main(String[] args) throws IOException {
        try (A a = new A()) {
            a.solve();
        }
    }

    @Override
    public void close() throws IOException {
        reader.close();
        writer.close();
    }
}