You are given a positive integer N. Find the number of the pairs of integers u and v (0≦u,v≦N) such that there exist two non-negative integers a and b satisfying a xor b=u and a+b=v. Here, xor denotes the bitwise exclusive OR. Since it can be extremely large, compute the answer modulo 10^9+7.

Constraints

* 1≦N≦10^{18}

Input

The input is given from Standard Input in the following format:


N


Output

Print the number of the possible pairs of integers u and v, modulo 10^9+7.

Examples

Input

3


Output

5


Input

1422


Output

52277


Input

1000000000000000000


Output

787014179
#include <bits/stdc++.h>
using namespace std;

using ll = long long;

int main()
{
    ll N; cin >> N;

    auto dp = map<ll, ll>();
    const function<ll(ll)> f = [&](const ll N)
    {
        if (N == 0) return 1LL;
        if (N == 1) return 2LL;

        if (dp.count(N)) return dp[N];

        return dp[N] = (f(N/2) + f((N-1)/2) + f((N-2)/2)) % int(1e9+7);
    };

    cout << f(N) << endl;
}
