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».

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 $1000000007$ $(10^{9} + 7)$.