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)

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}

macro_rules! trace {
    ($x:expr) => { dbg!($x); };
    ($($xs:expr),*) => { dbg!(($($xs),*)); }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;


fn ex_gcd(x: i64, y: i64) -> (i64, i64) {
    let mut r0 = x;
    let mut a0 = 1;
    let mut b0 = 0;

    let mut r = y;
    let mut a = 0;
    let mut b = 1;

    while r > 0 {
        let r2 = r0 % r;
        let a2 = a0 - r0 / r * a;
        let b2 = b0 - r0 / r * b;
        r0 = r; r = r2;
        a0 = a; a = a2;
        b0 = b; b = b2;
    }
    (a0, b0)
}

fn mod_inv(x: i64, m: i64) -> i64 {
    let mut a = ex_gcd(x, m).0;
    while a < 0 { a += m; }
    a
}

fn comb(n: i64, k: i64, m: i64) -> i64 {
    if k == 0 { return 1; }
    if k == 1 { return n % m; }
    if n - k < k { return comb(n, n - k, m); }
    let mut c = 1;
    for i in 0..k {
        c *= n - i; c %= m;
        c *= mod_inv(k - i, m); c %= m;
    }
    c
}

fn biF(r: i64, c: i64) -> i64 {
    (comb(r + c + 2, r + 1, M) + M - 1) % M
}

fn main() {
    let mut sc = Scanner::new();
    // for i in 1..6 {
    //     for j in 1..6 {
    //         trace!(i, j, F(i, j), biF(i, j));
    //     }
    // }
    let r1: i64 = sc.cin();
    let c1: i64 = sc.cin();
    let r2: i64 = sc.cin();
    let c2: i64 = sc.cin();

    let mut ans = biF(r2, c2);
    ans %= M;
    ans += biF(r1-1,c1-1);
    ans %= M;
    ans += M - biF(r2, c1-1);
    ans %= M;
    ans += M - biF(r1-1, c2);
    ans %= M;
    put!(ans);
}

use std::io::{self, Write};
use std::str::FromStr;
use std::collections::VecDeque;

struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
impl Scanner {
    fn new() -> Self { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> { self.cin::<String>().chars().collect() }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> { (0..n).map(|_| self.cin()).collect() }
}