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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <class T>
ostream& operator<<(ostream& out, vector<T> v) {
  out << "[";
  for (int(i) = int(0); i < int(int((v).size())); ++i) {
    if (i) out << ", ";
    out << v[i];
  }
  out << "]";
  return out;
}
template <class A, class B>
ostream& operator<<(ostream& out, pair<A, B> p) {
  out << "<" << p.first << ", " << p.second << ">";
  return out;
}
template <class T>
ostream& operator<<(ostream& out, set<T> s) {
  out << "(";
  for (typeof((s).begin()) it = (s).begin(); it != (s).end(); ++it) {
    if (it != s.begin()) out << ", ";
    out << *it;
  }
  out << ")";
  return out;
}
template <class A, class B>
ostream& operator<<(ostream& out, map<A, B> m) {
  out << "{";
  for (typeof((m).begin()) it = (m).begin(); it != (m).end(); ++it) {
    if (it != m.begin()) out << ", ";
    out << *it;
  }
  out << "}";
  return out;
}
int N;
int A[100];
int brute() {
  int mask = 0;
  for (int(i) = int(0); i < int(N); ++i)
    if (A[i]) mask |= (1 << (i));
  int res = 0;
  for (int(i) = int(0); i < int((1 << (N))); ++i)
    for (int(k) = int(i + 1); k < int((1 << (N))); ++k)
      if ((i ^ mask) > (k ^ mask)) res++;
  return res;
}
int M(long long a, long long b) { return (a * b) % 1000000007; }
int ADD(long long a, long long b) { return (a + b) % 1000000007; }
int main() {
  string s;
  cin >> s;
  N = int((s).size());
  memset(A, 0, sizeof(A));
  int pow2[N + 1];
  pow2[0] = 1;
  for (int(i) = int(1); i < int(N + 1); ++i) pow2[i] = M(pow2[i - 1], 2);
  int ans = 0;
  for (int(i) = int(0); i < int(N); ++i) {
    if (s[i] == '1') {
      ans = ADD(ans, M(pow2[i], M(pow2[N - 1 - i], pow2[N - 1 - i])));
    }
  }
  cout << ans << endl;
}