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: Accepted)

#include<bits/stdc++.h>
using namespace std;
long long dp[62][2][2], mod = 1e9 + 7;
long long n;
long long solve(int idx, int carry, int flag){
    long long &ans = dp[idx][carry][flag];
    if(ans != -1){
        return ans;
    }
    if(idx == 60){
        return ans = (carry == 0 && flag == 0);
    }
    int bit = (n >> idx) & 1;
    ans = 0;
    for(int a = 0; a <= 1; a++){
        for(int b = 0; b <= a; b++){
            int curbit = (a + b + carry) % 2;
            int curcarry = (a + b + carry) / 2;
            int curflag = flag;
            if(curbit > bit){
                curflag = 1;
            }
            if(curbit < bit){
                curflag = 0;
            }
            ans = (ans + solve(idx + 1, curcarry, curflag)) % mod;
        }
    }
    return ans;
}
int main(){
    cin >> n;
    memset(dp, -1, sizeof(dp));
    cout << solve(0, 0, 0);
    return 0;
}