# ZeroJudge - g015: 老鼠愛反悔
### 題目連結：https://zerojudge.tw/ShowProblem?problemid=g015
###### tags: `ZeroJudge` `數學` `機率`

#include <iostream>
#include <iomanip>
#include <cmath>
using namespace std;
#define ERROR 1e-5

static const auto Initialize = [] {
	cin.sync_with_stdio(false); cin.tie(nullptr);
	return nullptr;
}();

double FastTransitionMatrix(unsigned long long time, double success2Fail, double fail2Success) {
	double answer[2][2] = { { 1, 0 }, { 0, 1 } }, power[2][2] = { { 1 - success2Fail, fail2Success }, { success2Fail, 1 - fail2Success } }, buffer[2][2];
	while (time) {
		if (time & 1) {
			for (int i = 0; i < 2; ++i)
				for (int j = 0; j < 2; ++j) {
					buffer[i][j] = 0;
					for (int k = 0; k < 2; ++k)
						buffer[i][j] += answer[i][k] * power[k][j];
				}
			for (int i = 0; i < 2; ++i)
				for (int j = 0; j < 2; ++j)
					if (abs(answer[i][j] - buffer[i][j]) >= ERROR)
						answer[i][j] = buffer[i][j];
		}
		for (int i = 0; i < 2; ++i)
			for (int j = 0; j < 2; ++j) {
				buffer[i][j] = 0;
				for (int k = 0; k < 2; ++k)
					buffer[i][j] += power[i][k] * power[k][j];
			}
		for (int i = 0; i < 2; ++i)
			for (int j = 0; j < 2; ++j)
				if (abs(power[i][j] - buffer[i][j]) >= ERROR)
					power[i][j] = buffer[i][j];
		time >>= 1;
	}
	return answer[0][0] - ERROR;
}

int main() {
	unsigned long long time;
	double success2Fail, fail2Success;
	while (cin >> time >> success2Fail >> fail2Success)
		cout << fixed << setprecision(2) << FastTransitionMatrix(time, success2Fail, fail2Success) << '\n';
}