Submission #2163433

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/**
 *  _           _                 __                            _   _ _   _                                 _                    _                  _
 * | |         | |               / /                           | | (_) | (_)                               | |                  (_)                | |
 * | |__   __ _| |_ ___   ___   / /__ ___  _ __ ___  _ __   ___| |_ _| |_ ___   _____ ______ _ __ _   _ ___| |_ ______ ___ _ __  _ _ __  _ __   ___| |_ ___
 * | '_ \ / _` | __/ _ \ / _ \ / / __/ _ \| '_ ` _ \| '_ \ / _ \ __| | __| \ \ / / _ \______| '__| | | / __| __|______/ __| '_ \| | '_ \| '_ \ / _ \ __/ __|
 * | | | | (_| | || (_) | (_) / / (_| (_) | | | | | | |_) |  __/ |_| | |_| |\ V /  __/      | |  | |_| \__ \ |_       \__ \ | | | | |_) | |_) |  __/ |_\__ \
 * |_| |_|\__,_|\__\___/ \___/_/ \___\___/|_| |_| |_| .__/ \___|\__|_|\__|_| \_/ \___|      |_|   \__,_|___/\__|      |___/_| |_|_| .__/| .__/ \___|\__|___/
 *                                                  | |                                                                           | |   | |
 *                                                  |_|                                                                           |_|   |_|
 *
 * https://github.com/hatoo/competitive-rust-snippets
 */
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
mod util {
    use std::io::{stdin, stdout, BufWriter, StdoutLock};
    use std::str::FromStr;
    use std::fmt::Debug;
    #[allow(dead_code)]
    pub fn line() -> String {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().to_string()
    }
    #[allow(dead_code)]
    pub fn chars() -> Vec<char> {
        line().chars().collect()
    }
    #[allow(dead_code)]
    pub fn gets<T: FromStr>() -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|t| t.parse().unwrap())
            .collect()
    }
    #[allow(dead_code)]
    pub fn with_bufwriter<F: FnOnce(BufWriter<StdoutLock>) -> ()>(f: F) {
        let out = stdout();
        let writer = BufWriter::new(out.lock());
        f(writer)
    }
}
#[allow(unused_macros)]
macro_rules ! get { ( $ t : ty ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; line . trim ( ) . parse ::<$ t > ( ) . unwrap ( ) } } ; ( $ ( $ t : ty ) ,* ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; let mut iter = line . split_whitespace ( ) ; ( $ ( iter . next ( ) . unwrap ( ) . parse ::<$ t > ( ) . unwrap ( ) , ) * ) } } ; ( $ t : ty ; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ ( $ t : ty ) ,*; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( $ ( $ t ) ,* ) ) . collect ::< Vec < _ >> ( ) } ; ( $ t : ty ;; ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; line . split_whitespace ( ) . map ( | t | t . parse ::<$ t > ( ) . unwrap ( ) ) . collect ::< Vec < _ >> ( ) } } ; ( $ t : ty ;; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( $ t ;; ) ) . collect ::< Vec < _ >> ( ) } ; }
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { println ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }

#[allow(dead_code)]
pub const M: u64 = 1_000_000_007;

#[allow(dead_code)]
pub fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}
#[allow(dead_code)]
pub fn lcm(a: u64, b: u64) -> u64 {
    a / gcd(a, b) * b
}
#[allow(dead_code)]
/// (gcd, x, y)
pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) {
    if b == 0 {
        (a, 1, 0)
    } else {
        let (gcd, x, y) = extgcd(b, a % b);
        (gcd, y, x - (a / b) * y)
    }
}
#[allow(dead_code)]
pub fn mod_pow(x: u64, n: u64, m: u64) -> u64 {
    let mut res = 1;
    let mut x = x;
    let mut n = n;
    while n > 0 {
        if n & 1 == 1 {
            res = (res * x) % m;
        }
        x = (x * x) % m;
        n >>= 1;
    }
    res
}
#[allow(dead_code)]
pub fn mod_inverse(a: u64, m: u64) -> u64 {
    let (_, x, _) = extgcd(a as i64, m as i64);
    ((m as i64 + x) as u64 % m) % m
}
#[allow(dead_code)]
pub fn fact_table(len: usize, m: u64) -> Vec<u64> {
    let mut res = vec![1; len + 1];
    for i in 1..len + 1 {
        res[i] = (i as u64 * res[i - 1]) % m;
    }
    res
}
#[allow(dead_code)]
/// Factorial and Inverse factorial table
pub fn fact_inv_table(size: usize, m: u64) -> (Vec<u64>, Vec<u64>) {
    let mut fact = vec![1; size];
    let mut fact_inv = vec![1; size];
    for i in 2..size {
        fact[i] = fact[i - 1] * i as u64 % m;
        fact_inv[i] = m - ((m / i as u64) * fact_inv[(m % i as u64) as usize] % m);
    }
    for i in 1..size {
        fact_inv[i] = fact_inv[i - 1] * fact_inv[i] % m;
    }
    (fact, fact_inv)
}
#[allow(dead_code)]
/// (a mod p, e when n! = a p\^e)
pub fn mod_fact(n: u64, p: u64, fact: &[u64]) -> (u64, u64) {
    if n == 0 {
        (1, 0)
    } else {
        let (a, b) = mod_fact(n / p, p, fact);
        let pow = b + n / p;
        if n / p % 2 != 0 {
            (a * (p - fact[(n % p) as usize]) % p, pow)
        } else {
            (a * fact[(n % p) as usize] % p, pow)
        }
    }
}
#[allow(dead_code)]
/// C(n, k) % p
pub fn mod_comb(n: u64, k: u64, p: u64, fact: &[u64]) -> u64 {
    if n < k {
        0
    } else {
        let (a1, e1) = mod_fact(n, p, fact);
        let (a2, e2) = mod_fact(k, p, fact);
        let (a3, e3) = mod_fact(n - k, p, fact);
        if e1 > e2 + e3 {
            0
        } else {
            a1 * mod_inverse(a2 * a3 % p, p) % p
        }
    }
}
#[allow(dead_code)]
/// H(n, k) % p
pub fn mod_comb_repetition(n: u64, k: u64, p: u64, fact: &[u64]) -> u64 {
    mod_comb(n - 1 + k, n - 1, p, fact)
}

#[derive(Eq, PartialEq, Clone, Debug)]
/// Equivalent to std::cmp::Reverse
pub struct Rev<T>(pub T);
impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}
impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}

#[allow(dead_code)]
fn main() {
    let n = get!(usize);
    let mut wh = get!(u64, u64; n);

    wh.sort_by_key(|t| Rev(t.1));

    let fact = fact_table(200000, M);
    let mut ans = 0;

    let inv = |x| mod_inverse(x, M);
    let comb = |n, r| mod_comb(n, r, M, &fact);

    let mut p = 0;
    let mut q = 0;

    for ((w, h), i) in wh.into_iter().zip(1..) {
        if i >= 3 {
            let l = (p + M - h * q % M) % M;
            let r = 2 * fact[i] % M * comb(n as u64, i as u64) % M * fact[n - i] % M * w % M;

            ans += l * r % M;
            ans %= M;
        }

        if i > 1 {
            let yy = inv(i as u64 * (i as u64 + 1));
            p += h * yy;
            p %= M;
            q += yy;
            q %= M;
        }
    }

    println!("{}", ans);
}

Submission Info

Judge Result