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 Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;

const MOD: i64 = 1000_000_007;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn dfs(s: i64, x: i64, memo: &mut HashMap<i64, HashMap<i64, i64>>) -> i64 {
    if memo.contains_key(&s) && memo[&s].contains_key(&x) {
        return memo[&s][&x];
    }
    if s == 0 {
        return 1;
    }

    if s < 0 {
        return 0;
    }
    let mut ret = dfs(s / 2, x / 2, memo);
    ret += dfs((s - 1) / 2, (x - 1) / 2, memo);
    ret %= MOD;
    if s >= 2 {
        ret += dfs((s - 2) / 2, x / 2, memo);
        ret %= MOD;
    }
    if !memo.contains_key(&s) {
        memo.insert(s, HashMap::new());
    }
    memo.get_mut(&s).unwrap().insert(x, ret);
    ret
}

fn main() {
    let n = read::<i64>();
    let mut memo = HashMap::new();
    memo.insert(0, HashMap::new());
    memo.get_mut(&0).unwrap().insert(0, 1);
    println!("{}", dfs(n, n, &mut memo));
}