#include <iostream>
#include <queue>
#include <set>
using namespace std;


class RectangularIsland {
	
	static const int N = 4, dx[N], dy[N];
	long long** table, out, fav;
	int steps, width, height;
	queue<pair<int, int> > cells;
	
	void back()
	{
		set<pair<int, int> > toAdd;
		while (steps-- > 0) { // for each step
			for (set<pair<int, int> >::iterator it = toAdd.begin(); it != toAdd.end(); ++it) {
				cells.push(*it); // update queue
			}
			toAdd.clear();
			while (!cells.empty()) { // retrieve all positions in this state
				pair<int, int> cell = cells.front();
				cells.pop();
				for (int i = 0; i < N; ++i) {
					long long& tmp = table[cell.first + dx[i]][cell.second + dy[i]];
					if (tmp == -1) {
						out += table[cell.first][cell.second];
					} else {
						tmp += table[cell.first][cell.second]; // update number of steps
						toAdd.insert(make_pair(cell.first + dx[i], cell.second + dy[i]));
					}
				}
				table[cell.first][cell.second] = 0;
			}
		}
	}
	
	void print_table()
	{
		for (int i = 0; i <= height + 1; ++i) {
			for (int j = 0; j <= width + 1; ++j) {
				cout << table[i][j] << " ";
			}
			cout << endl;
		} 
	}
	
	public:
	double theProbablity(int width, int height, int y, int x, int steps)
	{
		this->width = width;
		this->height = height;
		this->steps = steps;
		out = fav = 0;
		table = new (nothrow) long long*[height + 2];
		int i, j; // memory allocation
		for (i = 0; i <= height + 1; ++i) table[i] = new (nothrow) long long[width + 2];
		for (i = 0; i <= width + 1; ++i) {
			table[0][i] = -1;
			table[height + 1][i] = -1;
		} // create the margin [/\]_[\/]
		for (i = 0; i <= height + 1; ++i) {
			table[i][0] = -1;
			table[i][width + 1] = -1;
		}
		for (i = 1; i <= height; ++i) {
			for (j = 1; j <= width; ++j) {
				table[i][j] = 0; // fill the rest
			}
		}
		x = height - x;
		y = y + 1; // mark the start cell
		table[x][y] = 1;
		cells.push(make_pair(x, y));
		back();
		//print_table();
		for (i = 1; i <= height; ++i) {
			for (j = 1; j <= width; ++j) {
				fav += table[i][j]; // fill the rest
			}
		}
		//cout << fav << " " << out;
		return (double)fav / (fav + out);
	}
};

const int RectangularIsland::dx[] = {0, 0, -1, 1};
const int RectangularIsland::dy[] = {1, -1, 0, 0};