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)

const MODULO: u64 = 1_000_000_007;

#[derive(Clone, Copy, Debug)]
struct F(u64);

impl std::ops::Neg for F {
    type Output = Self;
    fn neg(self) -> Self {
        F((MODULO - self.0) % MODULO)
    }
}

impl std::ops::Add for F {
    type Output = Self;
    fn add(self, rhs: Self) -> Self {
        F((self.0 + rhs.0) % MODULO)
    }
}

impl std::ops::Sub for F {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self {
        F((self.0 + MODULO - rhs.0) % MODULO)
    }
}

impl std::ops::Mul for F {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self {
        F((self.0 * rhs.0) % MODULO)
    }
}

impl std::ops::Div for F {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        let mut out = self;
        let mut base = rhs;
        let mut exponent = MODULO - 2;
        while exponent != 0 {
            if exponent & 1 != 0 {
                out = out * base;
            }
            base = base * base;
            exponent >>= 1;
        }
        out
    }
}

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

struct Scanner<'a> {
    iter: std::str::SplitWhitespace<'a>,
}

impl<'a> Scanner<'a> {
    fn new(text: &'a str) -> Self {
        Scanner {
            iter: text.split_whitespace(),
        }
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.iter.next().unwrap().parse().ok().unwrap()
    }
}

// ABC154 F - Many Many Paths
pub fn main() {
    let stdin = read_stdin();
    let mut sc = Scanner::new(&stdin);
    let r1: u64 = sc.read();
    let c1: u64 = sc.read();
    let r2: u64 = sc.read();
    let c2: u64 = sc.read();
    fn binom(m: u64, n: u64) -> F {
        let (m, n) = if m < n { (m, n) } else { (n, m) };
        let mut numer = F(1);
        let mut denom = F(1);
        for i in 0..m {
            numer = numer * F(n + m - i);
            denom = denom * F(m - i);
        }
        numer / denom
    }
    let ans = binom(r2 + 1, c2 + 1) - binom(r2 + 1, c1) - binom(r1, c2 + 1) + binom(r1, c1);
    println!("{}", ans.0);
}