Problem:
Score: 1000 points

Problem Statement

Find the number of sequences of N non-negative integers A_1, A_2, ..., A_N that satisfy the following conditions:

L \leq A_1 + A_2 + ... + A_N \leq R

When the N elements are sorted in non-increasing order, the M-th and (M+1)-th elements are equal.

Since the answer can be enormous, print it modulo 10^9+7.

Constraints

All values in input are integers.

1 \leq M < N \leq 3 \times 10^5

1 \leq L \leq R \leq 3 \times 10^5

Input

Input is given from Standard Input in the following format:

N M L R

Output

Print the number of sequences of N non-negative integers, modulo 10^9+7.

Sample Input 1

4 2 3 7

Sample Output 1

105

The sequences of non-negative integers that satisfy the conditions are:

\begin{eqnarray} &(1, 1, 1, 0), (1, 1, 1, 1), (2, 1, 1, 0), (2, 1, 1, 1), (2, 2, 2, 0), (2, 2, 2, 1), \\ &(3, 0, 0, 0), (3, 1, 1, 0), (3, 1, 1, 1), (3, 2, 2, 0), (4, 0, 0, 0), (4, 1, 1, 0), \\ &(4, 1, 1, 1), (5, 0, 0, 0), (5, 1, 1, 0), (6, 0, 0, 0), (7, 0, 0, 0)\end{eqnarray}

and their permutations, for a total of 105 sequences.

Sample Input 2

2 1 4 8

Sample Output 2

3

The three sequences that satisfy the conditions are (2, 2), (3, 3), and (4, 4).

Sample Input 3

141592 6535 89793 238462

Sample Output 3

933832916

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

// ${url}
//
#![allow(unused_imports)]
use std::io::*;
use std::io::Write;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

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

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

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

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

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

    ($iter:expr, switch) => {
        {
            let ty = read_value!($iter, i32);
            if ty == 1 {
                vec![ty, read_value!($iter, i32), read_value!($iter, i32)]
            } else if ty == 2 {
                vec![ty, read_value!($iter, i32)]
            } else {
                vec![ty, read_value!($iter, i32)]
            }
        }
    };

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

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

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

#[allow(unused_macros)]
macro_rules! dvec {
    ($t:expr ; $len:expr) => {
        vec![$t; $len]
    };

    ($t:expr ; $len:expr, $($rest:expr),*) => {
        vec![dvec!($t; $($rest),*); $len]
    };
}

#[allow(unused_macros)]
macro_rules! ifv {
    ($t:expr, $a:expr, $b: expr) => {
        if $t { $a } else { $b }
    }
}

#[allow(unused_macros)]
macro_rules! fill {
    ($t:expr, $v:expr) => {
        for i in 0..$t.len() {
            $t[i] = $v;
        }
    };
}

#[allow(unused_macros)]
macro_rules! join {
    ($t:expr, $glue:expr) => {
        $t.into_iter().map(|w| w.to_string()).collect::<Vec<_>>().join($glue)
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

// ===

struct Combination {
    fact: Vec<i64>,
    invfact: Vec<i64>,
}

impl Combination {
    fn inv(a: i64) -> i64 {
        Combination::pow(a, MOD - 2)
    }

    fn pow(a: i64, p: i64) -> i64 {
        let mut p = p;
        let mut aa = a;
        let mut ret = 1;
        while p >= 1 {
            if p & 1 == 1 {
                ret *= aa;
                ret %= MOD;
            }
            p >>= 1;
            aa = aa * aa % MOD;
        }
        ret
    }

    fn new(upto: usize) -> Self {
        let mut fact = vec![0; upto];
        let mut invfact = vec![0; upto];

        fact[0] = 1;
        for i in 1..upto {
            fact[i] = fact[i - 1] * (i as i64) % MOD;
        }

        invfact[upto - 1] = Combination::inv(fact[upto - 1]);
        invfact[0] = 1;
        for i in (1..upto - 1).rev() {
            invfact[i] = invfact[i + 1] * ((i + 1) as i64) % MOD;
        }

        Combination {
            fact: fact,
            invfact: invfact,
        }
    }

    fn comb(&self, n: usize, r: usize) -> i64 {
        if r < 0 || r > n {
            return 0;
        }
        self.fact[n] * self.invfact[r] % MOD * self.invfact[n - r] % MOD
    }
}

//===

const MOD: i64 = 1e9 as i64 + 7;

fn solve(n: usize, m: usize, h: usize) -> i64 {
    let comb = Combination::new(h+n+10);
    let more = m;
    let less = n - m;
    let mut total = 0;
    for l in 0..h {
        let least_use = (l+1) * more;
        if least_use > h {
            break;
        }
        let mut w = 0;
        let left = h - least_use;
        for z in 0..less+1 {
            let f = (l+1)*z;
            if left < f {
                break;
            }
            let add = comb.comb(less, z) * comb.comb(left-f+n, n) % MOD;
            if z % 2 == 0 {
                w += add;
            } else {
                w += MOD-add;
            }
        }
        for z in 0..less+1 {
            let f = l*z;
            if left < f {
                break;
            }
            let add = comb.comb(less, z) * comb.comb(left-f+n, n) % MOD;
            if z % 2 == 1 {
                w += add;
            } else {
                w += MOD-add;
            }
        }
        total += w % MOD;
        total %= MOD;
    }
    total *= comb.comb(n, m);
    total %= MOD;
    (comb.comb(h+n, n) + MOD - total) % MOD
}

fn main() {
    input! {
        n: usize, m: usize, low: usize, high: usize
    };
    println!("{}", (solve(n, m, high) + MOD - solve(n, m, low-1)) % MOD);
}