#[allow(unused_macros)] macro_rules! input { ( $($t:ty),* ) => {{ let mut s = String::new(); std::io::stdin().read_line(&mut s); let mut splits = s.trim().split_whitespace(); ($( { splits.next().unwrap().parse::<$t>().unwrap() },)*) }} } #[allow(dead_code)] mod mat { use std::fmt::{Debug, Display, Formatter, Result}; use std::iter::Sum; use std::ops::Add; use std::ops::Index; use std::ops::Mul; #[derive(Eq, Clone)] pub struct Mat { inside_vec: Vec>, pub row: usize, pub col: usize, } impl Index for Mat { type Output = Vec; fn index(&self, i: usize) -> &Self::Output { &self.inside_vec[i] } } impl Mat { pub fn new(v: Vec>) -> Self { if let Some((row, col)) = Mat::row_col(&v) { Mat { inside_vec: v, row: row, col: col, } } else { panic!("passed vector's length is not valid."); } } pub fn from_vec(v: Vec) -> Self { let col = v.len(); Mat { inside_vec: vec![v], row: 1, col: col, } } fn row_col(v: &Vec>) -> Option<(usize, usize)> { let col = v[0].len(); for line in v.iter() { if line.len() != col { return None; } } return Some((v.len(), col)); } } impl Mat { pub fn transpose(self) -> Self { let row = self.col; let col = self.row; let mut inside: Vec> = Vec::with_capacity(row); for i in 0..row { let cols = (0..col).map(|k| self[k][i]); inside.push(cols.collect()); } Mat { inside_vec: inside, row: row, col: col, } } } impl PartialEq for Mat { fn eq(&self, other: &Self) -> bool { if self.row == other.row && self.col == other.col { for row in 0..self.row { for col in 0..self.col { if self[row][col] != other[row][col] { return false; } } } return true; } return false; } } impl Debug for Mat { fn fmt(&self, f: &mut Formatter) -> Result { let mut s = "".to_string(); for line in &self.inside_vec { s += "|"; for val in line { s += &format!(" {:^3}", val); } s += " |\n"; } write!(f, "{}", s) } } impl Display for Mat { fn fmt(&self, f: &mut Formatter) -> Result { let mut s = "".to_string(); for line in &self.inside_vec { s += "|"; for val in line { s += &format!(" {:^3}", val); } s += " |\n"; } write!(f, "{}", s) } } impl Mul for Mat where T: Mul + Add + Sum + Copy + PartialEq + Eq + Debug + Display, { type Output = Self; fn mul(self, rhs: Self) -> Self { if self.col != rhs.row { panic ! ( "length of column of left hand side doesn't equal to length of row of right hand side." ); } let mut product: Vec> = Vec::with_capacity(rhs.row); for _ in 0..rhs.row { product.push(Vec::::with_capacity(self.col)); } for i in 0..self.row { for j in 0..rhs.col { let row = self[i].iter(); let col = (0..rhs.row).map(|k| rhs[k][j]); product[i].push(row.zip(col).map(|(s, r)| *s * r).sum()); } } Mat::new(product) } } impl Mul for &'_ Mat where T: Mul + Add + Sum + Copy + PartialEq + Eq + Debug + Display, { type Output = Mat; fn mul(self, rhs: Self) -> Mat { if self.col != rhs.row { panic ! ( "length of column of left hand side doesn't equal to length of row of right hand side." ); } let mut product: Vec> = Vec::with_capacity(rhs.row); for _ in 0..rhs.row { product.push(Vec::::with_capacity(self.col)); } for i in 0..self.row { for j in 0..rhs.col { let row = self[i].iter(); let col = (0..rhs.row).map(|k| rhs[k][j]); product[i].push(row.zip(col).map(|(s, r)| *s * r).sum()); } } Mat::new(product) } } impl Add for Mat where T: Add + Copy + PartialEq + Eq + Debug + Display, { type Output = Self; fn add(self, rhs: Self) -> Self { if self.row != rhs.row { panic!("length of row is not currespond."); } if self.col != rhs.col { panic!("length of column is not currespond."); } let mut sum: Vec> = Vec::with_capacity(self.row); for _ in 0..self.row { sum.push(Vec::::with_capacity(self.col)); } for i in 0..self.row { for j in 0..self.col { sum[i].push(self[i][j] + rhs[i][j]); } } Mat::new(sum) } } impl Mat where T: Add + Mul + Sum + Copy + PartialEq + Eq + Debug + Display, { pub fn pow T + Copy>(self, n: u32, f: F) -> Self { let mut current = self.clone(); let base = self.clone(); for b in format!("{:b}", n).chars().skip(1) { current = (current.clone() * current).map(f); match b { '1' => current = (base.clone() * current.clone()).map(f), _ => (), } } current } pub fn map(self, f: F) -> Mat where F: Fn(T) -> T, { let mut newvec = Vec::with_capacity(self.row); for row in 0..self.row { newvec.push(Vec::with_capacity(self.col)); for col in 0..self.col { newvec[row].push(f(self.inside_vec[row][col])); } } Mat::new(newvec) } } } const MOD: u64 = 1_000_000_007; #[allow(unused_must_use)] #[allow(unused_variables)] fn solve() { use mat::Mat; let (a, b, n) = input!(u64, u64, u32); if n == 0 { println!("0"); return; } let m = Mat::new(vec![vec![a, b], vec![1, 0]]); println!("{}", m.pow(n, |x| x % MOD)[1][0]); } fn main() { solve(); }