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)

#[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)*}
    };

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

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

#[allow(dead_code)]
type Graph = Vec<Vec<usize>>;

fn main() {
    input! {
        l: usize,
        r: usize,
    }
    const N: usize = 60;
    let mut dp = vec![vec![vec![vec![0; 2]; 2]; 2]; N + 1];
    dp[N][0][0][0] = 1;

    for bit in (0..N).rev() {
        let lb = (l >> bit) & 1;
        let rb = (r >> bit) & 1;
        for start in 0..2 {
            for ismore in 0..2 {
                for isless in 0..2 {
                    let pre = dp[bit + 1][start][ismore][isless];
                    for nr in 0..2 {
                        for nl in 0..2 {
                            if nr == 0 && nl == 1 {
                                continue;
                            }
                            if start == 0 && nr != nl {
                                continue;
                            }
                            if isless == 0 && rb == 0 && nr == 1 {
                                continue;
                            }
                            if ismore == 0 && lb == 1 && nl == 0 {
                                continue;
                            }

                            let nismore = if ismore == 0 && lb == nl { 0 } else { 1 };
                            let nisless = if isless == 0 && rb == nr { 0 } else { 1 };
                            let nstart = if start == 1 || nr == 1 && nl == 1 {
                                1
                            } else {
                                0
                            };
                            dp[bit][nstart][nismore][nisless] += pre;
                            dp[bit][nstart][nismore][nisless] %= 1_000_000_007;
                        }
                    }
                }
            }
        }
    }

    let mut ans = 0;
    for j in 0..2 {
        for k in 0..2 {
            ans += dp[0][1][j][k];
            ans %= 1_000_000_007;
        }
    }
    println!("{}", ans);
}