Problem:
Score : 600 points

Problem Statement

Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L \leq x \leq y \leq R) such that the remainder when y is divided by x is equal to y \mbox{ XOR } x.

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.

For example, 3 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ XOR } 101 = 110.)

Constraints

1 \leq L \leq R \leq 10^{18}

Input

Input is given from Standard Input in the following format:

L R

Output

Print the number of pairs of integers (x, y) (L \leq x \leq y \leq R) satisfying the condition, modulo 10^9 + 7.

Sample Input 1

2 3

Sample Output 1

3

Three pairs satisfy the condition: (2, 2), (2, 3), and (3, 3).

Sample Input 2

10 100

Sample Output 2

604

Sample Input 3

1 1000000000000000000

Sample Output 3

68038601

Be sure to compute the number modulo 10^9 + 7.

Solution in Rust (1.15.1) (judge verdict: Accepted)

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)*}
    };
}

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)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

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, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{min, max};

fn main() {
    input!{
        l: usize,
        r: usize
    }
    let mut tab = vec![vec![vec![vec![None; 2]; 2]; 2]; 61];
    for i in 0..2 {
        for j in 0..2 {
            for k in 0..2 {
                tab[0][i][j][k] = Some(1);
            }
        }
    }
    println!("{}", solve(60, 0, 0, 0, l, r, &mut tab));
}

fn solve(n: usize, fl: usize, fr: usize, fmsb: usize, l: usize, r: usize, tab: &mut Vec<Vec<Vec<Vec<Option<usize>>>>>) -> usize {
    if n == 0 {
        return 1;
    }
    if let Some(ret) = tab[n][fl][fr][fmsb]  {
        return ret;
    }
    let d = 1000000007;
    let lb = l & 1 << n - 1;
    let rb = r & 1 << n - 1;
    let mut ret = 0;
    if fl == 1 || lb == 0 {
        if rb > 0 {
            ret += solve(n - 1, fl, 1, fmsb, l, r, tab);
        } else {
            ret += solve(n - 1, fl, fr, fmsb, l, r, tab);
        }
    }
    if (fl == 1 || lb == 0) && (fr == 1 || rb > 0) && fmsb == 1 {
        ret += solve(n - 1, fl, fr, fmsb, l, r, tab);
    }
    if fr == 1 || rb > 0 {
        if lb > 0 {
            ret += solve(n - 1, fl, fr, 1, l, r, tab);
        } else {
            ret += solve(n - 1, 1, fr, 1, l, r, tab);
        }
    }
    ret %= d;
    tab[n][fl][fr][fmsb] = Some(ret);
    ret
}