using System; using static System.Console; using System.Linq; using System.Collections.Generic; class Program { static int NN => int.Parse(ReadLine()); static int[] NList => ReadLine().Split().Select(int.Parse).ToArray(); static string[] SList(long n) => Enumerable.Repeat(0, (int)n).Select(_ => ReadLine()).ToArray(); public static void Main() { Solve(); } static void Solve() { var c = NList; var (h, w, t) = (c[0], c[1], c[2]); c = NList; var (sy, sx) = (c[0], c[1]); c = NList; var (gy, gx) = (c[0], c[1]); var s = SList(h); var a = new double[1][]; a[0] = new double[h * w]; a[0][sy * w + sx] = 1; var x = new double[h * w][]; for (var i = 0; i < h * w; ++i) x[i] = new double[h * w]; var mx = new int[] { 0, 0, -1, 1 }; var my = new int[] { -1, 1, 0, 0 }; for (var i = 0; i < h; ++i) for (var j = 0; j < w; ++j) { if (s[i][j] == '.') { var mc = 0; for (var k = 0; k < 4; ++k) { var nx = i + mx[k]; var ny = j + my[k]; if (s[nx][ny] == '.') ++mc; } for (var k = 0; k < 4; ++k) { var nx = i + mx[k]; var ny = j + my[k]; if (s[nx][ny] == '.') x[i * w + j][nx * w + ny] = 1.0 / mc; } if (mc == 0) x[i * w + j][i * w + j] = 1; } } var b = Matrix.Mul(a, Matrix.Pow(x, t)); WriteLine(b[0][gy * w + gx].ToString("0.0000000000")); } class Matrix { static int mod = 17; // 行列の累乗 public static double[][] Pow(double[][] m, long k) { var multi = m; var r = new double[m.Length][]; for (var i = 0; i < m.Length; ++i) { r[i] = new double[m.Length]; r[i][i] = 1; } while (k > 0) { if ((k & 1) == 1) r = Mul(r, multi); multi = Mul(multi, multi); k >>= 1; } return r; } // 行列の積 public static double[][] Mul(double[][] x, double[][] y) { var r = new double[x.Length][]; for (var i = 0; i < x.Length; ++i) r[i] = new double[y[0].Length]; for (var i = 0; i < x.Length; ++i) for (var k = 0; k < x[0].Length; ++k) { for (var j = 0; j < y[0].Length; ++j) r[i][j] = (r[i][j] + x[i][k] * y[k][j]) % mod; } return r; } } }