A8971 | Malek Dance Club

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 $2^{n}$ 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».

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

This number may contain leading zeros.

Print the complexity of the given dance assignent modulo $1000000007$ $(10^{9}+7)$ .