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)

fn read_stdin() -> String {
    use std::io::Read;
    let mut input = String::new();
    std::io::stdin().read_to_string(&mut input).unwrap();
    input
}

fn scan<'a, I: Iterator<Item = &'a str>, T: std::str::FromStr>(tokens: &mut I) -> T {
    tokens.next().unwrap().parse().ok().unwrap()
}

fn main() {
    let input = read_stdin();
    let tokens = &mut input.split_whitespace();
    let r1: usize = scan(tokens);
    let c1: usize = scan(tokens);
    let r2: usize = scan(tokens);
    let c2: usize = scan(tokens);
    fn f(i: usize, j: usize) -> F {
        let (i, j) = if i < j { (i, j) } else { (j, i) };
        let mut numer = F(1);
        let mut denom = F(1);
        for k in 0..i {
            numer = numer * F(i + j - k);
            denom = denom * F(i - k);
        }
        numer / denom
    }
    fn g(i: usize, j: usize) -> F {
        f(i + 1, j + 1) - F(1)
    }
    println!(
        "{}",
        (g(r2, c2) - g(r2, c1 - 1) - g(r1 - 1, c2) + g(r1 - 1, c1 - 1)).value()
    );
}

const MODULO: usize = 1_000_000_007;

#[derive(Clone, Copy, Debug, Eq, PartialEq)]
struct F(usize);

impl F {
    fn value(self) -> usize {
        self.0
    }
    fn pow(self, e: usize) -> F {
        let mut a = F(1);
        let mut b = self;
        let mut e = e;
        while e != 0 {
            if e & 1 != 0 {
                a = a * b;
            }
            b = b * b;
            e >>= 1;
        }
        a
    }
    fn inverse(self) -> F {
        self.pow(MODULO - 2)
    }
}

impl std::ops::Add for F {
    type Output = F;
    fn add(self, other: F) -> F {
        F((self.value() + other.value()) % MODULO)
    }
}

impl std::ops::Sub for F {
    type Output = F;
    fn sub(self, other: F) -> F {
        F((self.value() + MODULO - other.value()) % MODULO)
    }
}

impl std::ops::Mul for F {
    type Output = F;
    fn mul(self, other: F) -> F {
        F((self.value() * other.value()) % MODULO)
    }
}

impl std::ops::Div for F {
    type Output = F;
    fn div(self, other: F) -> F {
        self * other.inverse()
    }
}