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: Accepted)

use std::cmp::*;
use std::io::*;
const MOD: u64 = 1_000_000_007;

mod enumeration {
    pub struct Enumeration {
        fact: Vec<u64>,
        finv: Vec<u64>,
        modulo: u64,
    }
    impl Enumeration {
        pub fn new(n: usize, modulo: u64) -> Enumeration {
            let mut fact: Vec<u64> = vec![1; n];
            let mut inv: Vec<u64> = vec![1; n];
            let mut finv: Vec<u64> = vec![1; n];
            for i in 2..n {
                fact[i] = fact[i - 1] * (i as u64) % modulo;
                inv[i] = modulo - (modulo / (i as u64)) * inv[(modulo as usize % i)] % modulo;
                finv[i] = inv[i] * finv[i - 1] % modulo;
            }
            Enumeration {
                fact: fact,
                finv: finv,
                modulo: modulo,
            }
        }
        pub fn c(&self, n: usize, k: usize) -> u64 {
            if n < k {
                return 0;
            }
            self.fact[n] * self.finv[n - k] % self.modulo * self.finv[k] % self.modulo
        }
    }
}

fn main() {
    let mut s: String = String::new();
    stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let r1: usize = itr.next().unwrap().parse().unwrap();
    let c1: usize = itr.next().unwrap().parse().unwrap();
    let r2: usize = itr.next().unwrap().parse().unwrap();
    let c2: usize = itr.next().unwrap().parse().unwrap();
    let en = enumeration::Enumeration::new(2000020, MOD);
    let area1 = en.c(r2 + 1 + c2 + 1, c2 + 1) - 1;
    let area2 = en.c(r1 + c2 + 1, c2 + 1) - 1;
    let area3 = en.c(r2 + 1 + c1, c1) - 1;
    let area4 = en.c(r1 + c1, c1) - 1;
    println!("{}", (area1 + MOD - area2 + MOD - area3 + area4) % MOD);
}