|Codeforces Round #189 (Div. 1)|
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 from NFC. Your task is to calculate the complexity of this assignment modulo 1000000007 (109 + 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 (109 + 7).