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_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};
 
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
 
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
 
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
 
    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
 
use std::cmp::Ordering;
 
use std::cmp;
use std::cmp::min;
use std::collections::BTreeMap;
use std::process;
use std::cmp::Ord;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::VecDeque;
use std::collections::BTreeSet;
use std::mem;
 
use std::ops::{Deref, DerefMut, Index, IndexMut};
use std::any::{Any, TypeId};

fn main(){
    input!{
        n:usize,
    }
    let mut dp = vec![vec![vec![-1;5];5];77];
    let MOD = 1000000007;
    fn dfs(d:i64, xm:usize, am:usize, dp:&mut Vec<Vec<Vec<i64>>>, n:usize, MOD:i64)->i64{
        if d<0{return 1;}
        if dp[d as usize][xm][am] != -1{return dp[d as usize][xm][am];}
        let mut res = 0;
        if n>>d&1 == 1{
            res += dfs(d-1, 1, cmp::min(2, am*2+1), dp, n, MOD);
        }
        else{
            res += dfs(d-1, xm,cmp::min(2, am*2), dp, n, MOD);
        }
        if n>>d&1 == 1{
            res += dfs(d-1, xm, cmp::min(2, am*2), dp, n, MOD);
        }
        else{
            if am != 0 && xm != 0{
                res += dfs(d-1, xm,cmp::min(2, am*2 - 1), dp, n, MOD);
            }
        }
        if am!=0{
            if n>>d&1==1{
                res += dfs(d-1, 1, cmp::min(2, am*2 -1), dp, n, MOD);
            }
            else{
                res += dfs(d-1, xm, cmp::min(2, am*2 - 2), dp, n, MOD);
            }
        }
        dp[d as usize][xm][am] = res%MOD;
        dp[d as usize][xm][am]

    }
    println!("{}", dfs(60, 0, 0, &mut dp, n, MOD));

}