#include <bits/stdc++.h>

using real = long double;
constexpr int MAXK = 100;

struct Poly {
    real fi, fn, c;
    Poly next(real p) const {
        Poly res;
        res.fi = fi * (1 - p);
        res.fn = fn * (1 - p) + p;
        res.c = c * (1 - p) + 1;
        return res;
    }
};

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int n, k;
    std::cin >> n >> k;

    k = std::min(k, MAXK);

    real p;
    std::cin >> p;

    std::vector<Poly> suf(n + 1);
    suf[0].fi = 1;
    for (int i = 1; i <= n; ++i) suf[i] = suf[i - 1].next(p);

    std::vector<real> f(n + 1);
    // suf[n].fn * fn + suf[n].c = fn
    f[n] = suf[n].c / (1 - suf[n].fn);
    for (int i = 1; i < n; ++i) {
        f[i] = (1 - p) * f[i - 1] + p * f[n] + 1;
    }

    for (int _ = 0; _ < k; ++_) {
        std::vector<real> g(f);

        std::vector<real> pre(n + 1);
        for (int i = 1; i <= n; ++i) {
            pre[i] = (1 - p) * pre[i - 1] + p * g[i] + 1;
        }

        auto check = [&](int x) -> real {
            // suf[n - x].fi * pre[x] + suf[n - x].fn + suf[n - x].c = fn
            auto s = suf[n - x];
            real fn = (s.fi * pre[x] + s.c) / (1 - s.fn);
            return fn;
        };

        int l = 0, r = n;
        while (l < r) {
            int mid1 = (l + r) / 2;
            int mid2 = mid1 + 1;
            if (check(mid1) < check(mid2)) r = mid1;
            else l = mid2;
        }

        std::copy(pre.begin(), pre.begin() + l + 1, f.begin());
        real fn = check(l);
        for (int i = l + 1; i <= n; ++i) {
            f[i] = (1 - p) * f[i - 1] + p * fn + 1;
        }
    }

    std::cout << std::fixed << std::setprecision(12);
    std::cout << f[n] << '\n';
}