Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Malek Dance Club

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAs 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 2^{n} members and coincidentally Natalia Fan Club also has 2^{n} members. Each member of MDC is assigned a unique id *i* from 0 to 2^{n} - 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 from NFC. Your task is to calculate the complexity of this assignment modulo 1000000007 (10^{9} + 7).

Expression 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 (10^{9} + 7).

Examples

Input

11

Output

6

Input

01

Output

2

Input

1

Output

1

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/24/2019 06:48:53 (d1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|