Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3

Sample Output 1

5

The five possible pairs of u and v are:

u=0,v=0 (Let a=0,b=0, then 0 xor 0=0, 0+0=0.)

u=0,v=2 (Let a=1,b=1, then 1 xor 1=0, 1+1=2.）

u=1,v=1 (Let a=1,b=0, then 1 xor 0=1, 1+0=1.）

u=2,v=2 (Let a=2,b=0, then 2 xor 0=2, 2+0=2.）

u=3,v=3 (Let a=3,b=0, then 3 xor 0=3, 3+0=3.）

Sample Input 2

1422

Sample Output 2

52277

Sample Input 3

1000000000000000000

Sample Output 3

787014179

Solution in C++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
template<typename A, typename B> ostream& operator<<(ostream &cout, pair<A, B> const &p) {
    return cout << "(" << p.first << ", " << p.second << ")";
}
template<typename A> ostream& operator<<(ostream &cout, vector<A> const &v) {
    cout << "{"; for (int i = 0; i < v.size(); i++) {if (i) cout << ", "; cout << v[i];} return cout << "}";
}

int main() {
    const int MOD = 1e9 + 7;
    ll n; cin >> n;
    map<ll, ll> store;
    function<ll(int)> eval = [&](ll x) -> ll {
        if (store.find(x) != store.end()) return store[x];
        ll ret;
        if (x == 1) {
            ret = 2;
        } else if (x == 2) {
            ret = 4;
        } else if (x == 3) {
            ret =  5;
        } else {
            if (x % 2 == 0) {
                ret = (2 * eval(x / 2 - 1) + eval(x / 2)) % MOD;
            } else {
                ret = (eval(x / 2 - 1) + 2 * eval(x / 2)) % MOD;
            }
        }
        store[x] = ret;
        return ret;
    };
    cout << eval(n) << '\n';
    return 0;
}