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 (1.42.0) (judge verdict: Accepted)

const MOD: usize = 1_000_000_007;

struct Combination {
    fact: Vec<usize>,
    inv_fact: Vec<usize>,
}

impl Combination {
    fn new(n: usize) -> Combination {
        let mut fact = vec![0; n + 1];
        let mut inv_fact = vec![0; n + 1];
        fact[0] = 1;
        for i in 1..=n {
            fact[i] = fact[i - 1] * i % MOD;
        }
        inv_fact[n] = Self::pow(fact[n], MOD - 2);
        for i in (1..=n).rev() {
            inv_fact[i - 1] = inv_fact[i] * i % MOD;
        }

        Combination { fact, inv_fact }
    }

    fn pow(mut a: usize, mut n: usize) -> usize {
        let mut res = 1;
        while n > 0 {
            if n & 1 > 0 {
                res = res * a % MOD;
            }
            a = a * a % MOD;
            n >>= 1;
        }
        res
    }
    
    fn c(&self, n: usize, r: usize) -> usize {
        if n < r { return 0; }
        let tmp = self.inv_fact[n - r] * self.inv_fact[r] % MOD;
        self.fact[n] * tmp % MOD
    }

    fn f(&self, r: usize, c: usize) -> usize {
        self.c(r + c, r)
    }

    fn g(&self, r: usize, c: usize) -> usize {
        self.f(r + 1, c + 1) - 1
    }
}

fn main() {
    let (r1, c1, r2, c2): (usize, usize, usize, usize) = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let mut iter = buf.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
        )
    };

    let comb = Combination::new(r2 + c2 + 2);
    let mut ans = comb.g(r2, c2);
    ans = (ans + MOD - comb.g(r2, c1 - 1)) % MOD;
    ans = (ans + MOD - comb.g(r1 - 1, c2)) % MOD;
    ans = (ans + comb.g(r1 - 1, c1 - 1)) % MOD;
    println!("{}", ans);
}