// ---------- begin ModInt ---------- const MOD: u32 = 1_000_000_007; #[derive(Clone, Copy)] struct ModInt(u32); impl std::ops::Add for ModInt { type Output = ModInt; fn add(self, rhs: ModInt) -> Self::Output { let mut d = self.0 + rhs.0; if d >= MOD { d -= MOD; } ModInt(d) } } impl std::ops::AddAssign for ModInt { fn add_assign(&mut self, rhs: ModInt) { *self = *self + rhs; } } impl std::ops::Sub for ModInt { type Output = ModInt; fn sub(self, rhs: ModInt) -> Self::Output { let mut d = self.0 + MOD - rhs.0; if d >= MOD { d -= MOD; } ModInt(d) } } impl std::ops::SubAssign for ModInt { fn sub_assign(&mut self, rhs: ModInt) { *self = *self - rhs; } } impl std::ops::Mul for ModInt { type Output = ModInt; fn mul(self, rhs: ModInt) -> Self::Output { ModInt((self.0 as u64 * rhs.0 as u64 % MOD as u64) as u32) } } impl std::ops::MulAssign for ModInt { fn mul_assign(&mut self, rhs: ModInt) { *self = *self * rhs; } } impl std::ops::Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { ModInt(if self.0 == 0 {0} else {MOD - self.0}) } } impl std::fmt::Display for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::str::FromStr for ModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } impl From for ModInt { fn from(val: usize) -> ModInt { ModInt((val % MOD as usize) as u32) } } #[allow(dead_code)] impl ModInt { pub fn new(n: u32) -> ModInt { ModInt(n % MOD) } pub fn zero() -> ModInt { ModInt(0) } pub fn one() -> ModInt { ModInt(1) } pub fn pow(self, mut n: u32) -> ModInt { let mut t = ModInt::one(); let mut s = self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(self) -> ModInt { assert!(self.0 > 0); self.pow(MOD - 2) } } // ---------- end ModInt ---------- // ---------- begin Precalc ---------- #[allow(dead_code)] struct Precalc { inv: Vec, fact: Vec, ifact: Vec, } #[allow(dead_code)] impl Precalc { pub fn new(n: usize) -> Precalc { let mut inv = vec![ModInt::one(); n + 1]; let mut fact = vec![ModInt::one(); n + 1]; let mut ifact = vec![ModInt::one(); n + 1]; for i in 2..(n + 1) { fact[i] = fact[i - 1] * ModInt(i as u32); } ifact[n] = fact[n].inv(); if n > 0 { inv[n] = ifact[n] * fact[n - 1]; } for i in (1..n).rev() { ifact[i] = ifact[i + 1] * ModInt((i + 1) as u32); inv[i] = ifact[i] * fact[i - 1]; } Precalc { inv: inv, fact: fact, ifact: ifact, } } pub fn inv(&self, n: usize) -> ModInt { assert!(n > 0); self.inv[n] } pub fn fact(&self, n: usize) -> ModInt { self.fact[n] } pub fn ifact(&self, n: usize) -> ModInt { self.ifact[n] } pub fn comb(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[k] * self.ifact[n - k] } } // ---------- end Precalc ---------- // ---------- begin Matrix ---------- mod matrix { use std::ops::*; pub trait SemiRing: Add + Mul + Copy { fn zero() -> Self; fn one() -> Self; } #[derive(Clone)] pub struct SquareMatrix { size: usize, buf: Box<[R]>, } #[allow(dead_code)] impl SquareMatrix { pub fn zero(size: usize) -> Self { SquareMatrix { size: size, buf: vec![R::zero(); size * size].into_boxed_slice(), } } pub fn identity(size: usize) -> Self { let mut e = Self::zero(size); for i in 0..size { e.buf[i * size + i] = R::one(); } e } pub fn set_at(&mut self, x: usize, y: usize, val: R) { assert!(x < self.size && y < self.size); self.buf[x * self.size + y] = val; } pub fn get_at(&self, x: usize, y: usize) -> R { assert!(x < self.size && y < self.size); self.buf[x * self.size + y] } pub fn matadd(&self, rhs: &Self) -> Self { assert!(self.size == rhs.size); let buf: Vec = self .buf .iter() .zip(rhs.buf.iter()) .map(|p| *p.0 + *p.1) .collect(); SquareMatrix { size: self.size, buf: buf.into_boxed_slice(), } } pub fn matmul(&self, rhs: &Self) -> Self { let size = self.size; assert!(size == rhs.size); let mut res = Self::zero(size); for (x, a) in res.buf.chunks_mut(size).zip(self.buf.chunks(size)) { for (a, b) in a.iter().zip(rhs.buf.chunks(size)) { for (x, b) in x.iter_mut().zip(b.iter()) { *x = *x + *a * *b; } } } res } pub fn mat_pow(&self, mut n: usize) -> Self { let size = self.size; let mut t = Self::identity(size); let mut s = self.clone(); while n > 0 { if n & 1 == 1 { t = t.matmul(&s); } s = s.matmul(&s); n >>= 1; } t } } #[allow(dead_code)] impl> SquareMatrix { pub fn matsub(&self, rhs: &Self) -> Self { assert!(self.size == rhs.size); let buf: Vec = self .buf .iter() .zip(rhs.buf.iter()) .map(|p| *p.0 - *p.1) .collect(); SquareMatrix { size: self.size, buf: buf.into_boxed_slice(), } } } } // ---------- end Matrix ---------- use matrix::*; impl SemiRing for ModInt { fn zero() -> Self { ModInt::zero() } fn one() -> Self { ModInt::one() } } type M = SquareMatrix; fn run() { let mut s = String::new(); std::io::stdin().read_line(&mut s).unwrap(); let mut n: u64 = s.trim().parse().unwrap(); let mut t = M::identity(6); let mut s = M::zero(6); for i in 1..6 { s.set_at(i, i - 1, ModInt::one()); } for i in 0..6 { s.set_at(i, 5, ModInt(6).inv()); } while n > 0 { if n & 1 == 1 { t = t.matmul(&s); } s = s.matmul(&s); n >>= 1; } let ans = t.get_at(5, 5); println!("{}", ans); } fn main() { run(); }