#[allow(unused_imports)] use std::cmp::{max, min}; #[allow(unused_imports)] use std::collections::{HashMap, HashSet}; mod util { use std::io::stdin; 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 get() -> T where ::Err: Debug, { let mut line: String = String::new(); stdin().read_line(&mut line).unwrap(); line.trim().parse().unwrap() } #[allow(dead_code)] pub fn gets() -> Vec where ::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 get2() -> (T, U) where ::Err: Debug, ::Err: Debug, { let mut line: String = String::new(); stdin().read_line(&mut line).unwrap(); let mut iter = line.split_whitespace(); ( iter.next().unwrap().parse().unwrap(), iter.next().unwrap().parse().unwrap(), ) } #[allow(dead_code)] pub fn get3() -> (S, T, U) where ::Err: Debug, ::Err: Debug, ::Err: Debug, { let mut line: String = String::new(); stdin().read_line(&mut line).unwrap(); let mut iter = line.split_whitespace(); ( iter.next().unwrap().parse().unwrap(), iter.next().unwrap().parse().unwrap(), iter.next().unwrap().parse().unwrap(), ) } } #[allow(unused_macros)] macro_rules! debug { ($x: expr) => { println!("{}: {:?}", stringify!($x), $x) } } // (gcd, x, y) 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) } } 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 = n >> 1; } res } 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 } fn fact_table(len: usize, m: u64) -> Vec { let mut res = vec![1; len]; for i in 1..len { res[i] = (i as u64 * res[i - 1]) % m; } res } // (a mod p, e when n! = a p^e) fn mod_fact(n: u64, p: u64, fact: &Vec) -> (u64, u64) { if n == 0 { (1, 0) } else { let (a, b) = mod_fact(n / p, p, fact); let e = b + n / p; if n / p % 2 != 0 { (a * (p - fact[(n % p) as usize]) % p, e) } else { (a * fact[(n % p) as usize] % p, e) } } } fn mod_comb(n: u64, k: u64, p: u64, fact: &Vec) -> 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 } } } const M: u64 = 1000000007; fn main() { let n: u64 = util::get(); let fact = fact_table(200000, M); let mut a = 0; for i in 1..n + 1 { let p = mod_comb(n, i, M, &fact) * mod_pow(i, n - i, M) % M; a = (a + p) % M; } println!("{}", a); }