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)

pub fn main() {
    let (r1, c1, r2, c2): (i64, i64, i64, i64) = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let words: Vec<i64> = buf.split_whitespace().map(|w| w.parse().unwrap()).collect();
        (words[0], words[1], words[2], words[3])
    };
    let p: i64 = 1_000_000_007;
    fn inverse(x: i64, p: i64) -> i64 {
        if x == 1 {
            1
        } else {
            let q = p / x;
            let y = p % x;
            q * (p - inverse(y, p)) % p
        }
    }
    fn binom(m: i64, n: i64, p: i64) -> i64 {
        let (m, n) = if m < n { (m, n) } else { (n, m) };
        let mut c = 1;
        for i in 0..m {
            c = c * (n + m - i) % p;
            c = c * inverse(m - i, p) % p;
        }
        c
    }
    let mut ans = binom(r2 + 1, c2 + 1, p);
    ans = (ans - binom(r2 + 1, c1, p) + p) % p;
    ans = (ans - binom(r1, c2 + 1, p) + p) % p;
    ans = (ans + binom(r1, c1, p)) % p;
    println!("{}", ans);
}