#![allow(unused)] use kyoproio::*; use std::{ collections::*, io::{self, prelude::*}, iter, mem::{replace, swap}, }; fn main() -> io::Result<()> { std::thread::Builder::new() .stack_size(64 * 1024 * 1024) .spawn(solve)? .join() .unwrap(); Ok(()) } fn solve() { let stdin = io::stdin(); let mut kin = KInput::new(stdin.lock()); let stdout = io::stdout(); let mut out = io::BufWriter::new(stdout.lock()); macro_rules! output { ($($args:expr),+) => { write!(&mut out, $($args),+) }; } macro_rules! outputln { ($($args:expr),+) => { output!($($args),+); outputln!(); }; () => { output!("\n"); if cfg!(debug_assertions) { out.flush(); } } } const MOD: i64 = 1e9 as i64 + 7; let (n, m): (i64, i64) = kin.input(); let c = Combination::new(100001, MOD); let mut ans = 0; let mut sign = 1; for i in (1..=m).rev() { ans += MOD + sign * (c.comb(m, i) * c.pow(i, n) % MOD); ans %= MOD; sign = -sign; } outputln!("{}", ans); } pub fn mod_pow(mut a: i64, mut b: i64, m: i64) -> i64 { let mut y = 1; while b > 0 { if b & 1 == 1 { y = y * a % m; } a = a * a % m; b >>= 1; } y } pub fn mod_inv(x: i64, m: i64) -> i64 { mod_pow(x, m - 2, m) } pub struct Combination { m: i64, fact: Vec, } impl Combination { pub fn new(size: usize, m: i64) -> Self { let mut comb = Self { m, fact: Vec::new(), }; comb.resize(size); comb } pub fn resize(&mut self, size: usize) { let old_len = self.fact.len(); self.fact.resize(size + 1, 0); for i in old_len..=size { self.fact[i] = if i == 0 { 1 } else { i as i64 * self.fact[i - 1] % self.m }; } } pub fn fact(&self, x: i64) -> i64 { self.fact[x as usize] } pub fn perm(&self, a: i64, b: i64) -> i64 { if a >= b { self.fact(a) * self.inv(self.fact(a - b)) % self.m } else { 0 } } pub fn comb(&self, a: i64, b: i64) -> i64 { if a >= b { self.fact(a) * self.inv(self.fact(b) * self.fact(a - b) % self.m) % self.m } else { 0 } } pub fn pow(&self, a: i64, b: i64) -> i64 { mod_pow(a, b, self.m) } pub fn inv(&self, x: i64) -> i64 { self.pow(x, self.m - 2) } } // ----------------------------------------------------------------------------- pub mod kyoproio { #![warn(unused)] use std::io::prelude::*; pub trait Input { fn str(&mut self) -> &str; fn input(&mut self) -> T { T::input(self) } fn iter(&mut self) -> Iter { Iter(self, std::marker::PhantomData) } fn seq>(&mut self, n: usize) -> B { self.iter().take(n).collect() } } pub struct KInput { src: R, buf: String, pos: usize, } impl KInput { pub fn new(src: R) -> Self { Self { src, buf: String::with_capacity(1024), pos: 0, } } } impl Input for KInput { fn str(&mut self) -> &str { loop { if self.pos >= self.buf.len() { self.pos = 0; self.buf.clear(); if self.src.read_line(&mut self.buf).expect("io error") == 0 { return &self.buf; } } let range = self.pos ..self.buf[self.pos..] .find(|c: char| c.is_ascii_whitespace()) .map(|i| i + self.pos) .unwrap_or_else(|| self.buf.len()); self.pos = range.end + 1; if range.end > range.start { return &self.buf[range]; } } } } pub struct Iter<'a, T, I: ?Sized>(&'a mut I, std::marker::PhantomData<*const T>); impl<'a, T: InputParse, I: Input + ?Sized> Iterator for Iter<'a, T, I> { type Item = T; fn next(&mut self) -> Option { Some(self.0.input()) } } pub trait InputParse: Sized { fn input(src: &mut I) -> Self; } impl InputParse for Vec { fn input(src: &mut I) -> Self { src.str().as_bytes().to_owned() } } macro_rules! from_str_impl { { $($T:ty)* } => { $(impl InputParse for $T { fn input(src: &mut I) -> Self { src.str().parse::<$T>().expect("parse error") } })* } } from_str_impl! { String char bool f32 f64 isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128 } macro_rules! tuple_impl { ($H:ident $($T:ident)*) => { impl<$H: InputParse, $($T: InputParse),*> InputParse for ($H, $($T),*) { fn input(src: &mut I) -> Self { ($H::input(src), $($T::input(src)),*) } } tuple_impl!($($T)*); }; () => {} } tuple_impl!(A B C D E F G); }