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)

/*Whose woods these are I think I know.
His house is in the village though;
He will not see me stopping here
To watch his woods fill up with snow.

My little horse must think it queer
To stop without a farmhouse near
Between the woods and frozen lake
The darkest evening of the year.

He gives his harness bells a shake
To ask if there is some mistake.
The only other sound’s the sweep
Of easy wind and downy flake.

The woods are lovely, dark and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.*/

#include<bits/stdc++.h>
using namespace std;
#define lli long long int
#define pb push_back
#define fi first
#define se second
#define MOD 1000000007
const int maxn= 100010;
lli n;
map<pair<lli, lli>, lli> m;
lli dp(lli x, lli y)
{
    if(m.count({x,y}))
        return m[{x,y}];
    if(x==0ll&&y==0ll)
        return m[{x,y}]=1ll;
    lli res=dp(x/2ll,y/2ll);
    if(x>=1ll&&y>=1ll)
        res=(res+dp((x-1ll)/2ll,(y-1ll)/2ll))%MOD;
    if(x>=2ll)
        res=(res+dp((x-2ll)/2ll,y/2ll))%MOD;
    return m[{x,y}]=res;
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cin>>n;
    cout<<dp(n,n)<<endl;
}