#include using namespace std; using vec = vector; using mat = vector; mat mul(mat &a, mat &b) { mat c(a.size(), vec(b[0].size(), 0)); for (int k = 0; k < a[0].size(); k++) { for (int i = 0; i < a.size(); i++) { for (int j = 0; j < b[0].size(); j++) { c[i][j] += a[i][k] * b[k][j]; } } } return c; } mat pow(mat a, int64_t n) { mat r(a.size(), vec(a.size(), 0)); for (int i = 0; i < a.size(); i++) { r[i][i] = 1; } for (; n; n >>= 1) { if (n & 1) { r = mul(r, a); } a = mul(a, a); } return r; } bool inside(int a, int b, int alim, int blim) { return 0 <= a && a < alim && 0 <= b && b < blim; } int main() { int r, c, t, dd[] = {0, 1, 0, -1, 0}; pair st, fin; cin >> r >> c >> t >> st.first >> st.second >> fin.first >> fin.second; string s[r]; for (auto &i : s) { cin >> i; } { int num = 0; for (auto &i : s) { for (auto &j : i) { if (j == '.') { num++; } } } if (num == 1) { cout << fixed << setprecision(10) << double(st == fin) << endl; return 0; } } mat a(r * c, vec(r * c, 0)); for (int i = 0; i < r; i++) { for (int j = 0; j < c; j++) { int num = 0; for (int k = 0; k < 4; k++) { int ni = i + dd[k], nj = j + dd[k + 1]; if (!inside(ni, nj, r, c) || s[ni][nj] == '#') { continue; } num++; } for (int k = 0; k < 4; k++) { int ni = i + dd[k], nj = j + dd[k + 1]; if (!inside(ni, nj, r, c) || s[ni][nj] == '#') { continue; } a[i * c + j][ni * c + nj] = 1.0 / num; } } } a = pow(a, t); cout << fixed << setprecision(10) << a[st.first * c + st.second][fin.first * c + fin.second] << endl; return 0; }