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:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Enumeration;
import java.util.Iterator;
import java.util.Properties;
import java.util.Stack;

/**
 * Works good for CF
 * 
 * @author cykeltillsalu
 */
public class B139 {

	// some local config
	static boolean test = false;
	static String testDataFile = "testdata.txt";
	static String feedFile = "feed.txt";
	CompetitionType type = CompetitionType.CF;
	private static String ENDL = "\n";

	// solution
	private void solve() throws Throwable {
		int len = 200;
		long[] num = new long[200];
		num[0] = 1;
		int s = iread(), k = iread();
		for (int pas = 0; pas < len; pas++) {
			long sum = 0;
			for (int i = Math.max(0, pas - k); i <= pas; i++) {
				sum += num[i];
			}
			if (sum > 1000000000) {
				break;
			}
//			System.out.print(sum + " ");
			num[pas] = sum;
		}

		Stack<Integer> vals = new Stack<Integer>();
		vals.push(0);
		for (int i = len - 1; i >= 0; i--) {
			if (num[i] != 0 && (num[i] <= s)) {
				vals.push((int) num[i]);
				s -= num[i];
			}
		}
		
		System.out.println(vals.size());
		for (Integer integer : vals) {
			System.out.print(integer + " ");
		}
		System.out.println();
		out.flush();
	}

	public int iread() throws Exception {
		return Integer.parseInt(wread());
	}

	public double dread() throws Exception {
		return Double.parseDouble(wread());
	}

	public long lread() throws Exception {
		return Long.parseLong(wread());
	}

	public String wread() throws IOException {
		StringBuilder b = new StringBuilder();
		int c;
		c = in.read();
		while (c >= 0 && c <= ' ')
			c = in.read();
		if (c < 0)
			return "";
		while (c > ' ') {
			b.append((char) c);
			c = in.read();
		}
		return b.toString();
	}

	public static void main(String[] args) throws Throwable {

		if (test) { // run all cases from testfile:
			BufferedReader testdataReader = new BufferedReader(new FileReader(testDataFile));
			String readLine = testdataReader.readLine();
			int casenr = 0;
			out: while (true) {
				BufferedWriter w = new BufferedWriter(new FileWriter(feedFile));
				if (!readLine.equalsIgnoreCase("input")) {
					break;
				}
				while (true) {
					readLine = testdataReader.readLine();
					if (readLine.equalsIgnoreCase("output")) {
						break;
					}
					w.write(readLine + "\n");
				}
				w.close();
				System.out.println("Answer on case " + (++casenr) + ": ");

				new B139().solve();
				System.out.println("Expected answer: ");

				while (true) {
					readLine = testdataReader.readLine();

					if (readLine == null) {
						break out;
					}
					if (readLine.equalsIgnoreCase("input")) {
						break;
					}
					System.out.println(readLine);
				}
				System.out.println("----------------");
			}
			testdataReader.close();
		} else { // run on server
			new B139().solve();
		}
		out.close();
	}

	public B139() throws Throwable {
		if (test) {
			in = new BufferedReader(new FileReader(new File(feedFile)));
		}
	}

	InputStreamReader inp = new InputStreamReader(System.in);
	BufferedReader in = new BufferedReader(inp);
	static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

	enum CompetitionType {
		CF, OTHER
	};
}