// ---------- begin Matrix ---------- #[allow(dead_code)] mod matrix { use std::ops::{Add, Mul}; pub trait SemiRing: Add + Mul + Copy { fn zero() -> Self; fn one() -> Self; } pub const SIZE: usize = 2; #[derive(Clone)] pub struct SquareMatrix { buf: [[T; SIZE]; SIZE], } impl SquareMatrix { pub fn zero() -> Self { let z = T::zero(); SquareMatrix { buf: [[z; SIZE]; SIZE], } } pub fn identity() -> Self { let mut m = Self::zero(); for i in 0..SIZE { m.buf[i][i] = T::one(); } m } pub fn set_at(&mut self, i: usize, j: usize, v: T) { self.buf[i][j] = v; } pub fn get_at(&self, i: usize, j: usize) -> T { self.buf[i][j] } pub fn matmul(&self, rhs: &Self) -> Self { let mut res = Self::zero(); for (x, a) in res.buf.iter_mut().zip(self.buf.iter()) { for (a, b) in a.iter().zip(rhs.buf.iter()) { for (x, b) in x.iter_mut().zip(b.iter()) { *x = *x + *a * *b; } } } res } pub fn matadd(&self, rhs: &Self) -> Self { let mut c = Self::zero(); for (c, (a, b)) in c.buf.iter_mut().zip(self.buf.iter().zip(rhs.buf.iter())) { for (c, (a, b)) in c.iter_mut().zip(a.iter().zip(b.iter())) { *c = *a + *b; } } c } pub fn matpow(&self, mut n: usize) -> Self { let mut t = Self::identity(); let mut s = self.clone(); while n > 0 { if n & 1 == 1 { t = t.matmul(&s); } s = s.matmul(&s); n >>= 1; } t } } } // ---------- end Matrix ---------- // ---------- begin ModInt ---------- mod modint { #[allow(dead_code)] pub struct Mod; impl ConstantModulo for Mod { const MOD: u32 = 1_000_000_007; } #[allow(dead_code)] pub struct StaticMod; static mut STATIC_MOD: u32 = 0; impl Modulo for StaticMod { fn modulo() -> u32 { unsafe { STATIC_MOD } } } #[allow(dead_code)] impl StaticMod { pub fn set_modulo(p: u32) { unsafe { STATIC_MOD = p; } } } use std::marker::*; use std::ops::*; pub trait Modulo { fn modulo() -> u32; } pub trait ConstantModulo { const MOD: u32; } impl Modulo for T where T: ConstantModulo, { fn modulo() -> u32 { T::MOD } } pub struct ModInt(pub u32, PhantomData); impl Clone for ModInt { fn clone(&self) -> Self { ModInt::new_unchecked(self.0) } } impl Copy for ModInt {} impl Add for ModInt { type Output = ModInt; fn add(self, rhs: Self) -> Self::Output { let mut d = self.0 + rhs.0; if d >= T::modulo() { d -= T::modulo(); } ModInt::new_unchecked(d) } } impl AddAssign for ModInt { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs; } } impl Sub for ModInt { type Output = ModInt; fn sub(self, rhs: Self) -> Self::Output { let mut d = T::modulo() + self.0 - rhs.0; if d >= T::modulo() { d -= T::modulo(); } ModInt::new_unchecked(d) } } impl SubAssign for ModInt { fn sub_assign(&mut self, rhs: Self) { *self = *self - rhs; } } impl Mul for ModInt { type Output = ModInt; fn mul(self, rhs: Self) -> Self::Output { let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64; ModInt::new_unchecked(v as u32) } } impl MulAssign for ModInt { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { if self.0 == 0 { Self::zero() } else { Self::new_unchecked(T::modulo() - 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::new_unchecked((val % T::modulo() as usize) as u32) } } impl From for ModInt { fn from(val: u64) -> ModInt { ModInt::new_unchecked((val % T::modulo() as u64) as u32) } } impl From for ModInt { fn from(val: i64) -> ModInt { let m = T::modulo() as i64; ModInt::new((val % m + m) as u32) } } #[allow(dead_code)] impl ModInt { pub fn new_unchecked(d: u32) -> Self { ModInt(d, PhantomData) } pub fn zero() -> Self { ModInt::new_unchecked(0) } pub fn one() -> Self { ModInt::new_unchecked(1) } pub fn is_zero(&self) -> bool { self.0 == 0 } } #[allow(dead_code)] impl ModInt { pub fn new(d: u32) -> Self { ModInt::new_unchecked(d % T::modulo()) } pub fn pow(&self, mut n: u64) -> Self { let mut t = Self::one(); let mut s = *self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(&self) -> Self { assert!(self.0 != 0); self.pow(T::modulo() as u64 - 2) } } #[allow(dead_code)] pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 { let mut t = 1 % m; let mut s = r % m; while n > 0 { if n & 1 == 1 { t = t * s % m; } s = s * s % m; n >>= 1; } t } } // ---------- end ModInt ---------- // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- use modint::*; type M = ModInt; use matrix::*; type Mat = SquareMatrix; impl SemiRing for M { fn zero() -> Self { M::zero() } fn one() -> Self { M::one() } } fn run() { input! { a: M, b: M, n: usize, } let mut mat = Mat::zero(); mat.set_at(0, 0, a * M::new(2)); mat.set_at(0, 1, -(a * a - b)); mat.set_at(1, 0, M::one()); let pow = mat.matpow(n); let ans = pow.get_at(1, 0) * M::new(2) * a + pow.get_at(1, 1) * M::new(2); println!("{}", ans); } fn main() { run(); }