Problem: As a tradition, every year before IOI all the members of Natalia Fan Club are invited to Malek Dance Club to have a fun night together. Malek Dance Club has 2n members and coincidentally Natalia Fan Club also has 2n members. Each member of MDC is assigned a unique id i from 0 to 2n - 1. The same holds for each member of NFC.

One of the parts of this tradition is one by one dance, where each member of MDC dances with a member of NFC. A dance pair is a pair of numbers (a, b) such that member a from MDC dances with member b from NFC.

The complexity of a pairs' assignment is the number of pairs of dancing pairs (a, b) and (c, d) such that a < c and b > d.

You are given a binary number of length n named x. We know that member i from MDC dances with member <image> from NFC. Your task is to calculate the complexity of this assignment modulo 1000000007 (109 + 7).

Expression <image> denotes applying «XOR» to numbers x and y. This operation exists in all modern programming languages, for example, in C++ and Java it denotes as «^», in Pascal — «xor».

Input

The first line of input contains a binary number x of lenght n, (1 ≤ n ≤ 100).

This number may contain leading zeros.

Output

Print the complexity of the given dance assignent modulo 1000000007 (109 + 7).

Examples

Input

11


Output

6


Input

01


Output

2


Input

1


Output

1

Solution (in JAVA):

Solution:
/* Codeforces Template */

import java.io.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.fill;
import static java.util.Arrays.binarySearch;
import static java.util.Arrays.sort;

public class Main {
	
	static long initTime;
	static final Random rnd = new Random(7777L);
	static boolean writeLog = false;
	
	public static void main(String[] args) throws IOException {
		initTime = System.currentTimeMillis();
		try {
			writeLog = "true".equals(System.getProperty("LOCAL_RUN_7777"));
		} catch (SecurityException e) {}
		new Thread(null, new Runnable() {
			public void run() {
				try {
					try {
						if (new File("input.txt").exists())
							System.setIn(new FileInputStream("input.txt"));
					} catch (SecurityException e) {}
					long prevTime = System.currentTimeMillis();
					new Main().run();
					log("Total time: " + (System.currentTimeMillis() - prevTime) + " ms");
					log("Memory status: " + memoryStatus());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
		}, "1", 1L << 24).start(); 
	}

	void run() throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.close();
		in.close();
	}
	
	/*************************************************************** 
	 * Solution
	 **************************************************************/

	final long MOD = 1000000007L;
	
	void solve() throws IOException  {
		
		char[] s = in.readLine().toCharArray();
		int n = s.length;

		long answer = 0L;
		long pow = 1L;
		
		for (int i = 0; i < n; i++) {
			answer = answer * 2L % MOD;
			if (s[n - 1 - i] == '1')
				answer = (answer + pow * pow % MOD) % MOD;
			pow = pow * 2L % MOD;
		}
		
		out.println(answer);
	}
	
	/*************************************************************** 
	 * Input 
	 **************************************************************/
	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");
	
	String nextToken() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}
	
	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}
	
	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}
	
	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
	
	int[] nextIntArray(int size) throws IOException {
		int[] ret = new int [size];
		for (int i = 0; i < size; i++)
			ret[i] = nextInt();
		return ret;
	}
	
	long[] nextLongArray(int size) throws IOException {
		long[] ret = new long [size];
		for (int i = 0; i < size; i++)
			ret[i] = nextLong();
		return ret;
	}
	
	double[] nextDoubleArray(int size) throws IOException {
		double[] ret = new double [size];
		for (int i = 0; i < size; i++)
			ret[i] = nextDouble();
		return ret;
	}
	
	String nextLine() throws IOException {
		st = new StringTokenizer("");
		return in.readLine();
	}
	
	boolean EOF() throws IOException {
		while (!st.hasMoreTokens()) {
			String s = in.readLine();
			if (s == null)
				return true;
			st = new StringTokenizer(s);
		}
		return false;
	}
	
	/*************************************************************** 
	 * Output 
	 **************************************************************/
	void printRepeat(String s, int count) {
		for (int i = 0; i < count; i++)
			out.print(s);
	}
	
	void printArray(int[] array) {
		if (array == null || array.length == 0)
			return;
		for (int i = 0; i < array.length; i++) {
			if (i > 0) out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}
	
	void printArray(long[] array) {
		if (array == null || array.length == 0)
			return;
		for (int i = 0; i < array.length; i++) {
			if (i > 0) out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}
	
	void printArray(double[] array) {
		if (array == null || array.length == 0)
			return;
		for (int i = 0; i < array.length; i++) {
			if (i > 0) out.print(' ');
			out.print(array[i]);
		}
		out.println();
	}
	
	void printArray(double[] array, String spec) {
		if (array == null || array.length == 0)
			return;
		for (int i = 0; i < array.length; i++) {
			if (i > 0) out.print(' ');
			out.printf(Locale.US, spec, array[i]);
		}
		out.println();
	}
	
	void printArray(Object[] array) {
		if (array == null || array.length == 0)
			return;
		boolean blank = false;
		for (Object x : array) {
			if (blank) out.print(' '); else blank = true;
			out.print(x);
		}
		out.println();
	}
	
	@SuppressWarnings("rawtypes")
	void printCollection(Collection collection) {
		if (collection == null || collection.isEmpty())
			return;
		boolean blank = false;
		for (Object x : collection) {
			if (blank) out.print(' '); else blank = true;
			out.print(x);
		}
		out.println();
	}
	
	/*************************************************************** 
	 * Utility
	 **************************************************************/
	static String memoryStatus() {
		return (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory() >> 20) + "/" + (Runtime.getRuntime().totalMemory() >> 20) + " MB";
	}
	
	static void checkMemory() {
		System.err.println(memoryStatus());
	}
	
	static long prevTimeStamp = Long.MIN_VALUE;
	
	static void updateTimer() {
		prevTimeStamp = System.currentTimeMillis();
	}
	
	static long elapsedTime() {
		return (System.currentTimeMillis() - prevTimeStamp);
	}
	
	static void checkTimer() {
		System.err.println(elapsedTime() + " ms");
	}
	
	static void chk(boolean f) {
		if (!f) throw new RuntimeException("Assert failed");
	}
	
	static void chk(boolean f, String format, Object ... args) {
		if (!f) throw new RuntimeException(String.format(format, args));
	}
	
	static void log(String format, Object ... args) {
		if (writeLog) System.err.println(String.format(Locale.US, format, args));
	}
	
	static void swap(int[] a, int i, int j) {
		int tmp = a[i];
		a[i] = a[j];
		a[j] = tmp;
	}
	
	static void swap(long[] a, int i, int j) {
		long tmp = a[i];
		a[i] = a[j];
		a[j] = tmp;
	}
	
	static void swap(double[] a, int i, int j) {
		double tmp = a[i];
		a[i] = a[j];
		a[j] = tmp;
	}
	
	static void shuffle(int[] a, int from, int to) {
		for (int i = from; i < to; i++)
			swap(a, i, rnd.nextInt(a.length));
	}
	
	static void shuffle(long[] a, int from, int to) {
		for (int i = from; i < to; i++)
			swap(a, i, rnd.nextInt(a.length));
	}
	
	static void shuffle(double[] a, int from, int to) {
		for (int i = from; i < to; i++)
			swap(a, i, rnd.nextInt(a.length));
	}
	
	static void shuffle(int[] a) {
		if (a == null) return;
		shuffle(a, 0, a.length);
	}
	
	static void shuffle(long[] a) {
		if (a == null) return;
		shuffle(a, 0, a.length);
	}
	
	static void shuffle(double[] a) {
		if (a == null) return;
		shuffle(a, 0, a.length);
	}
	
	
}