Problem:
Score : 600 points

Problem Statement

Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.

Let us define a function f(r, c) as follows:

f(r,c) := (The number of paths from the point (0, 0) to the point (r, c) that Snuke can trace by repeating the operation above)

Given are integers r_1, r_2, c_1, and c_2.
Find the sum of f(i, j) over all pair of integers (i, j) such that r_1 ≤ i ≤ r_2 and c_1 ≤ j ≤ c_2, and compute this value modulo (10^9+7).

Constraints

1 ≤ r_1 ≤ r_2 ≤ 10^6

1 ≤ c_1 ≤ c_2 ≤ 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

r_1 c_1 r_2 c_2

Output

Print the sum of f(i, j) modulo (10^9+7).

Sample Input 1

1 1 2 2

Sample Output 1

14

For example, there are two paths from the point (0, 0) to the point (1, 1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.

Similarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.

Sample Input 2

314 159 2653 589

Sample Output 2

602215194

Solution in Rust (1.15.1) (judge verdict: Runtime Error)

use std::io::{stdin, Read};
const MOD: u64 = 1000000007;

fn gcd(a: u64, b: u64) -> u64 {
    match b {
        0 => a,
        _ => gcd(b, a % b),
    }
}

fn powmod(base: u64, exp: u64, m: u64) -> u64 {
    let b: Vec<bool> = format!("{:b}", exp)
        .chars()
        .map(|x| x.to_digit(10).unwrap() != 0)
        .collect();
    let mut v = 1;
    for bi in b {
        v *= v;
        v %= m;
        if bi {
            v *= base;
            v %= m
        }
    }
    return v % m;
}

fn invmod(x: u64, m: u64) -> u64 {
    powmod(x, m - 2, m)
}

fn prime_factors(x: u64) -> Vec<u64> {
    let mut res = vec![];
    let mut y = x;
    let mut p = 2;
    let upper = (y as f64).sqrt() as u64;
    while y > 1 && p <= upper {
        match y % p {
            0 => {
                res.push(p);
                y /= p;
            }
            _ => {
                p += 1;
            }
        }
    }
    if y > 1 {
        res.push(y)
    }
    return res;
}

fn get_factorials(n: u64, m: u64) -> Vec<u64> {
    let mut res = vec![0; n as usize];
    res[0] = 1;
    let mut cur = 1;
    for i in 1..n {
        cur *= i;
        cur %= m;
        res[i as usize] = cur;
    }
    res
}

fn get_facinvs(n: u64, m: u64) -> Vec<u64> {
    let mut res = vec![0; n as usize];
    res[0] = 1;
    let mut cur = 1;
    for i in 1..n {
        cur *= invmod(i, m);
        cur %= m;
        res[i as usize] = cur;
    }
    res
}

fn combmod(a: u64, b: u64, m: u64, facts: &Vec<u64>, invs: &Vec<u64>) -> u64 {
    if a < b {
        0
    } else {
        (((facts[a as usize] * invs[b as usize]) % m) * invs[(a - b) as usize]) % m
    }
}

macro_rules! parse {
    ($iter: ident) => {
        $iter.next().unwrap().parse().unwrap()
    };
    ($iter: ident,2) => {
        (parse!($iter), parse!($iter))
    };
    ($iter: ident,3) => {
        (parse!($iter), parse!($iter), parse!($iter))
    };
    ($iter: ident,4) => {
        (parse!($iter), parse!($iter), parse!($iter), parse!($iter))
    };
    ($iter: ident, $n: ident) => {
        $iter.take($n).map(|e| e.parse().unwrap()).collect();
    };
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    let mut iter = s.split_whitespace();
    let (r1, c1, r2, c2): (u64, u64, u64, u64) = parse!(iter, 4);
    let facts = get_factorials(2000001, MOD);
    let facinvs = get_facinvs(2000001, MOD);
    let g = |a: u64, b: u64| combmod(a + b + 2, b + 1, MOD, &facts, &facinvs) - 1;
    println!(
        "{}",
        g(r2, c2) + g(r1 - 1, c1 - 1) - g(r1 - 1, c2) - g(r2, c1 - 1)
    );
}