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)

#[macro_use]
mod input_mcr {
    // ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
    // diff: using Parser
    #[macro_export(local_inner_macros)]
    macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

    use std::io;
    use std::io::BufRead;
    use std::str;

    // ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
    // ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
    // diff: using std::io::BufRead::fill_buf()
    pub struct Parser<R> {
        pub reader: R,
        buf: Vec<u8>,
        pos: usize,
    }

    impl Parser<io::Empty> {
        pub fn from_str(s: &str) -> Parser<io::Empty> {
            Parser {
                reader: io::empty(),
                buf: s.as_bytes().to_vec(),
                pos: 0,
            }
        }
    }

    impl<R: BufRead> Parser<R> {
        pub fn new(reader: R) -> Parser<R> {
            Parser {
                reader: reader,
                buf: vec![],
                pos: 0,
            }
        }
        pub fn update_buf(&mut self) {
            self.buf.clear();
            self.pos = 0;
            loop {
                let (len, complete) = {
                    let buf2 = self.reader.fill_buf().unwrap();
                    self.buf.extend_from_slice(buf2);
                    let len = buf2.len();
                    (len, buf2[len - 1] <= 0x20)
                };
                self.reader.consume(len);
                if complete {
                    break;
                }
            }
        }
        pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                let mut end = begin;
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
                } else {
                    self.update_buf();
                }
            }
        }
        pub fn fast_i64(&mut self) -> i64 {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                if begin == self.buf.len() {
                    self.update_buf();
                    continue;
                }
                let mut res = 0;
                let (is_positive, mut end) = match self.buf[begin] {
                    b'+' => (true, begin + 1),
                    b'-' => (false, begin + 1),
                    _ => (true, begin),
                };
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return if is_positive { res } else { -res };
                } else {
                    self.update_buf();
                }
            }
        }
    }
}

mod modular {
    use std::marker::PhantomData;
    use std::ops::*;

    pub trait ModP {
        fn as_u64() -> u64;
    }

    #[allow(non_camel_case_types)]
    #[derive(Clone, Copy, Debug)]
    pub struct Mod_1_000_000_007();
    impl ModP for Mod_1_000_000_007 {
        fn as_u64() -> u64 {
            1_000_000_007
        }
    }

    #[allow(non_camel_case_types)]
    #[derive(Clone, Copy, Debug)]
    pub struct Mod_998_244_353();
    impl ModP for Mod_998_244_353 {
        fn as_u64() -> u64 {
            998_244_353
        }
    }

    #[derive(Clone, Copy, PartialEq, Debug)]
    pub struct Modular<P: ModP + Copy>(u32, PhantomData<P>);

    impl<P: ModP + Copy> Modular<P> {
        pub fn new(x: u32) -> Modular<P> {
            Modular((x as u64 % P::as_u64()) as u32, PhantomData)
        }
        pub fn pow(self, n: u64) -> Modular<P> {
            if n == 0 {
                return Modular(1, PhantomData);
            }
            let t = self.pow(n / 2);
            if n % 2 == 0 {
                t * t
            } else {
                t * t * self
            }
        }
        pub fn as_u32(self) -> u32 {
            self.0
        }
    }

    impl<P: ModP + Copy> Add for Modular<P> {
        type Output = Self;
        fn add(self, rhs: Self) -> Self::Output {
            let t = (self.0 + rhs.0) as u64;
            let u = if t < P::as_u64() { t } else { t - P::as_u64() };
            Modular(u as u32, PhantomData)
        }
    }

    impl<P: ModP + Copy> AddAssign for Modular<P> {
        fn add_assign(&mut self, rhs: Self) {
            *self = *self + rhs;
        }
    }

    impl<P: ModP + Copy> Sub for Modular<P> {
        type Output = Self;
        fn sub(self, rhs: Self) -> Self::Output {
            let t = if self.0 >= rhs.0 {
                self.0 as u64 - rhs.0 as u64
            } else {
                self.0 as u64 + P::as_u64() - rhs.0 as u64
            };
            assert!(t < P::as_u64());
            Modular(t as u32, PhantomData)
        }
    }

    impl<P: ModP + Copy> SubAssign for Modular<P> {
        fn sub_assign(&mut self, rhs: Self) {
            *self = *self - rhs;
        }
    }

    impl<P: ModP + Copy> Neg for Modular<P> {
        type Output = Modular<P>;
        fn neg(self) -> Modular<P> {
            Modular((P::as_u64() - self.0 as u64) as u32, PhantomData)
        }
    }

    impl<P: ModP + Copy> Mul for Modular<P> {
        type Output = Self;
        fn mul(self, rhs: Self) -> Self::Output {
            Modular(
                ((self.0 as u64 % P::as_u64()) * (rhs.0 as u64 % P::as_u64()) % P::as_u64()) as u32,
                PhantomData,
            )
        }
    }

    impl<P: ModP + Copy> MulAssign for Modular<P> {
        fn mul_assign(&mut self, rhs: Self) {
            *self = *self * rhs;
        }
    }

    impl<P: ModP + Copy> Div for Modular<P> {
        type Output = Self;
        fn div(self, rhs: Self) -> Self::Output {
            if rhs.0 == 0 {
                loop {}
            }
            assert!(rhs.0 != 0);
            self * rhs.pow(P::as_u64() - 2)
        }
    }

    impl<P: ModP + Copy> DivAssign for Modular<P> {
        fn div_assign(&mut self, rhs: Self) {
            *self = *self / rhs;
        }
    }

    pub fn gen_fact_table<P: ModP + Copy>(n: usize) -> Vec<Modular<P>> {
        let mut res = vec![Modular::<P>::new(1); n + 1];
        for i in 0..n {
            res[i + 1] = res[i] * Modular::<P>::new((i + 1) as u32);
        }
        res
    }

    pub fn gen_inv_table<P: ModP + Copy>(n: usize) -> Vec<Modular<P>> {
        let mut res = vec![Modular::<P>::new(0); n + 1];
        res[1] = Modular::<P>::new(1);
        for i in 2..n + 1 {
            res[i] =
                -res[P::as_u64() as usize % i] * Modular::<P>::new((P::as_u64() / i as u64) as u32);
        }
        res
    }

    /*
    #[test]
    fn test_modular_1_000_000_007() {
        type Mod = Modular<Mod_1_000_000_007>;
        assert_eq!(Mod::new(2).pow(1_000_000).as_u32(), 235_042_059)
    }

    #[test]
    fn test_modular_998_244_353() {
        type Mod = Modular<Mod_998_244_353>;
        assert_eq!(Mod::new(2).pow(1_000_000).as_u32(), 421_273_117);
    }
    */
}

use input_mcr::*;
use std::cmp::*;

use modular::*;

type Mod = Modular<Mod_1_000_000_007>;

fn main() {
    input! {
        r1: usize,
        c1: usize,
        r2: usize,
        c2: usize,
    }
    let mut facts = gen_fact_table::<Mod_1_000_000_007>(3_000_000);
    let nCr = |n: usize, r: usize| facts[n] / (facts[n - r] * facts[r]);
    let f = |n: usize, m: usize| nCr(n + m, m);
    let res = f(r2 + 1, c2 + 1) - f(r2 + 1, c1) - f(r1, c2 + 1) + f(r1, c1);
    println!("{}", res.as_u32());
}