#![allow(unused_imports)] use std::io::{ self, Write }; use std::str::FromStr; use std::cmp::{ min, max }; use std::collections::{ BinaryHeap, VecDeque }; #[allow(unused_macros)] macro_rules! trace { ($var:expr) => { let _ = writeln!(&mut std::io::stderr(), ">>> {} = {:?}", stringify!($var), $var); }; ($($args:expr),*) => { trace!(($($args),*)) } } #[allow(unused_macros)] macro_rules! put { ($var:expr) => { let _ = writeln!(&mut std::io::stdout(), "{}", $var); }; ($var:expr, $($args:expr),*) => { let _ = write!(&mut std::io::stdout(), "{} ", $var); put!($($args),*); }; } type Matrix = Vec>; fn kake(a: &Matrix, b: &Matrix) -> Matrix { let n = a.len(); let mut c: Matrix = vec![vec![0.0; n]; n]; for i in 0..n { for j in 0..n { for k in 0..n { c[i][j] += a[i][k] * b[k][j]; } } } c } fn eye(n: usize) -> Matrix { let mut e: Matrix = vec![vec![0.0; n]; n]; for i in 0..n { e[i][i] = 1.0; } e } fn pow(a: &Matrix, n: usize) -> Matrix { if n == 0 { eye(n) } else if n == 1 { a.clone() } else if n % 2 == 0 { let b = kake(a, a); pow(&b, n / 2) } else { let b = kake(a, a); let c = pow(&b, (n - 1) / 2); kake(&c, a) } } fn main() { let mut sc = Scanner::new(); let h: usize = sc.cin(); let w: usize = sc.cin(); let m: usize = sc.cin(); let si: usize = sc.cin(); let sj: usize = sc.cin(); let gi: usize = sc.cin(); let gj: usize = sc.cin(); let mut fs = vec![vec![false; w]; h]; let mut ids = vec![vec![None; w]; h]; let n; { let mut id = 0; for i in 0..h { let cs: Vec = sc.cin::().chars().collect(); for j in 0..w { if cs[j] == '.' { fs[i][j] = true; ids[i][j] = Some(id); id += 1; } } } n = id; } // for i in 0..h { trace!(fs[i]); } // for i in 0..h { trace!(ids[i]); } let mut d = vec![vec![0.0; n]; n]; for i in 0..h { for j in 0..w { if fs[i][j] { let id = ids[i][j].unwrap(); let mut ps = vec![]; if fs[i-1][j] { ps.push((i-1, j)); } if fs[i+1][j] { ps.push((i+1, j)); } if fs[i][j-1] { ps.push((i, j-1)); } if fs[i][j+1] { ps.push((i, j+1)); } if ps.len() == 0 { d[id][id] = 1.0; } else { let q: f64 = 1.0 / (ps.len() as f64); for &p in ps.iter() { let (i2, j2) = p; let id2 = ids[i2][j2].unwrap(); d[id][id2] = q; } } } } } // for i in 0..n { trace!(d[i]); } let dm = pow(&d, m); // for i in 0..n { trace!(dm[i]); } { let s = ids[si][sj].unwrap(); let t = ids[gi][gj].unwrap(); put!(dm[s][t]); } } #[allow(dead_code)] struct Scanner { stdin: io::Stdin, buffer: VecDeque, } #[allow(dead_code)] impl Scanner { fn new() -> Scanner { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } } fn reserve(&mut self) { while self.buffer.len() == 0 { let mut line = String::new(); let _ = self.stdin.read_line(&mut line); for w in line.split_whitespace() { self.buffer.push_back(String::from(w)); } } } fn cin(&mut self) -> T { self.reserve(); match self.buffer.pop_front().unwrap().parse::() { Ok(a) => a, Err(_) => panic!("parse err") } } }