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++14 (GCC 5.4.1) (judge verdict: Accepted)

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

int main()
{
	int64_t n, mod = 1000000007;
	cin >> n;
	map<pair<int64_t, int64_t>, int64_t> map;
	function<int64_t(int64_t, int64_t)> f = [&](int64_t s, int64_t t) {
		//a+b<=s
		//a^b<=t
		if (s < 0 || t < 0)
		{
			return int64_t(0);
		}
		if (map[make_pair(s, t)])
		{
			return map[make_pair(s, t)];
		}
		if (s == 0)
		{
			return map[make_pair(s, t)] = f(s / 2, t / 2);
		}
		return map[make_pair(s, t)] = (f(s / 2, t / 2) + f((s - 1) / 2, (t - 1) / 2) + f(s / 2 - 1, t / 2)) % mod;
	};
	map[make_pair(0, 0)] = 1;
	cout << f(n, n) << endl;
	return 0;
}