#![allow(unused_imports, unused_macros)] 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),+).unwrap(); }; } macro_rules! outputln { ($($args:expr),+) => { output!($($args),+); outputln!(); }; () => { output!("\n"); if cfg!(debug_assertions) { out.flush().unwrap(); } } } let (m, k): (usize, i64) = kin.input(); let mut a = SquareMatrix::zeros(); for i in 0..m { for j in 0..m { a[(i + j) % m][i] += 1; a[(i * j) % m][i] += 1; } } let b = a.pow(k); outputln!("{}", b[0][0]); } const MOD: i64 = 1e9 as i64 + 7; const N: usize = 50; #[derive(Clone)] struct SquareMatrix(Box<[[i64; N]]>); impl SquareMatrix { fn zeros() -> Self { Self(vec![[0; N]; N].into()) } fn id() -> Self { let mut a = Self::zeros(); for i in 0..N { a[i][i] = 1; } a } fn mul(&self, rhs: &Self) -> Self { let mut a = Self::zeros(); for i in 0..N { for j in 0..N { for k in 0..N { a[i][j] = (a[i][j] + self[i][k] * rhs[k][j]) % MOD; } } } a } fn pow(&self, mut k: i64) -> Self { let mut a = self.clone(); let mut b = Self::id(); while k > 0 { if k & 1 == 1 { b = b.mul(&a); } a = a.mul(&a); k >>= 1; } b } } use std::ops::*; impl> Index for SquareMatrix { type Output = I::Output; fn index(&self, i: I) -> &Self::Output { &self.0[i] } } impl> IndexMut for SquareMatrix { fn index_mut(&mut self, i: I) -> &mut Self::Output { &mut self.0[i] } } // ----------------------------------------------------------------------------- pub mod kyoproio { 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); }