#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
using i128 = __int128_t;

bool Memory_begin;

template <int mod>
unsigned int down(unsigned int x)
{
    return x >= mod ? x - mod : x;
}
template <int mod>
struct Modint
{
    unsigned int x;
    Modint() = default;
    Modint(unsigned int x) : x(x) {}
    friend istream &operator>>(istream &in, Modint &a) { return in >> a.x; }
    friend ostream &operator<<(ostream &out, Modint a) { return out << a.x; }
    friend Modint operator+(Modint a, Modint b) { return down<mod>(a.x + b.x); }
    friend Modint operator-(Modint a, Modint b) { return down<mod>(a.x - b.x + mod); }
    friend Modint operator*(Modint a, Modint b) { return 1ULL * a.x * b.x % mod; }
    friend Modint operator/(Modint a, Modint b) { return a * ~b; }
    friend Modint operator^(Modint a, i64 b)
    {
        Modint ans = 1;
        for (; b; b >>= 1, a *= a)
            if (b & 1)
                ans *= a;
        return ans;
    }
    friend Modint operator~(Modint a) { return a ^ (mod - 2); }
    friend Modint operator-(Modint a) { return down<mod>(mod - a.x); }
    friend Modint &operator+=(Modint &a, Modint b) { return a = a + b; }
    friend Modint &operator-=(Modint &a, Modint b) { return a = a - b; }
    friend Modint &operator*=(Modint &a, Modint b) { return a = a * b; }
    friend Modint &operator/=(Modint &a, Modint b) { return a = a / b; }
    friend Modint &operator^=(Modint &a, i64 b) { return a = a ^ b; }
    friend Modint &operator++(Modint &a) { return a += 1; }
    friend Modint operator++(Modint &a, int)
    {
        Modint x = a;
        a += 1;
        return x;
    }
    friend Modint &operator--(Modint &a) { return a -= 1; }
    friend Modint operator--(Modint &a, int)
    {
        Modint x = a;
        a -= 1;
        return x;
    }
    friend bool operator==(Modint a, Modint b) { return a.x == b.x; }
    friend bool operator!=(Modint a, Modint b) { return !(a == b); }
};
const int mod = 998244353;
typedef Modint<mod> mint;

__float128 read()
{
    long double ret;
    cin >> ret;
    return (__float128)ret;
}
void print(__float128 res)
{
    long double ret = res;
    cout << fixed << setprecision(10) << ret << '\n';
}

bool Memory_end;

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    cerr << (&Memory_end - &Memory_begin) / 1048576.0 << "MB" << '\n';

    int n, k;
    cin >> n >> k;
    const __float128 e = 1.0;
    __float128 p = read();

    clock_t cur = clock();
    vector<__float128> dp(n + 2), a = dp, b = a;
    for (int i = n; i >= 1; i--)
    {
        a[i] = p, b[i] = e;
        a[i] += (e - p) * a[i + 1];
        b[i] += (e - p) * b[i + 1];
    }
    dp[1] = b[1] / (e - a[1]);
    for (int i = n; i >= 2; i--)
        dp[i] = e + p * dp[1] + (e - p) * dp[i + 1];
    int idx = 0;
    for (int _ = 1; _ <= 300 and k; _++, k--)
    {
        dp[i] = e + p * dp[i] + (e - p) * dp[i + 1];
        auto cal = [&](int c) -> __float128
        {
            if (c == n)
                return dp[1];

            __float128 d = (e - powl(e - p, n - c)) / p;
            __float128 b = powl(e - p, n - c) * dp[n - c + 1] + d;
            __float128 a = d * p;
            return b / (e - a);
            // vector<long double> ret(n + 2);
            // for (int i = n; i >= n - c + 1; i--)
            // {
            //     ret[i] = e + p * dp[i] + (e - p) * ret[i + 1];
            //     a[i] = 0, b[i] = ret[i];
            // }
            // for (int i = n - c; i >= 1; i--)
            // {
            //     a[i] = p, b[i] = e;
            //     a[i] += (e - p) * a[i + 1];
            //     b[i] += (e - p) * b[i + 1];
            // }
            // ret[1] = b[1] / (e - a[1]);
            // for (int i = n - c; i >= 2; i--)
            //     ret[i] = e + p * ret[1] + (e - p) * ret[i + 1];
            // return ret;
        };
        while (idx < n)
        {
            auto dp1 = cal(idx), dp2 = cal(idx + 1);
            if (dp1 > dp2)
                idx++;
            else
                break;
        }
        dp[1] = cal(idx);
        for (int i = n - idx; i >= 2; i--)
            dp[i] = e + p * dp[1] + (e - p) * dp[i + 1];
    }
    print(dp[1]);
}
/*
 */

answer.code: In function ‘int main()’:
answer.code:100:12: error: ‘i’ was not declared in this scope
  100 |         dp[i] = e + p * dp[i] + (e - p) * dp[i + 1];
      |            ^