#include "bits/stdc++.h"


#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep1(i, n) for (int i = 1; i < (n); ++i)
#define rep1n(i, n) for (int i = 1; i <= (n); ++i)
#define repr(i, n) for (int i = (n) - 1; i >= 0; --i)
#define pb push_back
#define eb emplace_back
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define each(x, a) for (auto &x : a)
#define ar array
#define vec vector
#define range(i, n) rep(i, n)

using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using str = string;
using pi = pair<int, int>;
using pl = pair<ll, ll>;

using vi = vector<int>;
using vl = vector<ll>;
using vpi = vector<pair<int, int>>;
using vvi = vector<vi>;

int Bit(int mask, int b) { return (mask >> b) & 1; }

template<class T>
bool ckmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool ckmax(T &a, const T &b) {
    if (b > a) {
        a = b;
        return true;
    }
    return false;
}

// [l, r)
template<typename T, typename F>
T FindFirstTrue(T l, T r, const F &predicat) {
    --l;
    while (r - l > 1) {
        T mid = l + (r - l) / 2;
        if (predicat(mid)) {
            r = mid;
        } else {
            l = mid;
        }
    }
    return r;
}


template<typename T, typename F>
T FindLastFalse(T l, T r, const F &predicat) {
    return FindFirstTrue(l, r, predicat) - 1;
}

const int INFi = 2e9;
const ll INF = 2e18;

double GetTime() {
    return (double)clock() / CLOCKS_PER_SEC;
}

void solve() {
    double st = GetTime();
    int n, k; cin >> n >> k;
    vector<ld> dp(n + 1);
    ld p; cin >> p;
    rep(i, n) dp[i] = INF;
    vector<ld> pwp(n + 1);
    pwp[0] = 1;
    for(int i = 1; i <= n; ++i) {
        pwp[i] = (pwp[i - 1]) * (1 - p);
    }
    const ld EPS = 1e-9;
    ld mn = (ld)n + (ld)n * p;
    for(int t = 0; t <= k; ++t) {
        if ((GetTime() - st) > 1.4) break;
        vector<ld> ndp(n + 1);
        ndp[n] = 0;
        for(int i = n; i >= 0; --i) {
            if (i < n) {
                ndp[i] = 1 + (1 - p) * ndp[i + 1] + p * dp[i];
            }
            // ndp[0] + 1 = 1 + ndp[i] * (1 - p)^{i} + p * (ndp[0] + 1) * (1 + (1 - p) + .. (1 - p)^{i-1})
            // ndp[0] + 1 = 1 + ndp[i] * (1 - p)^{i} + (ndp[0] + 1) * (1 - (1-p)^{i})
            // (ndp[0] + 1) * (1-p)^{i};
            // (ndp[0] + 1) * c = ndp[i] * pwp[i] + 1
            if (!i) break;
            ld e0 = (ndp[i] + (1 - pwp[i]) / (p * pwp[i]));
            if (e0 <= dp[i - 1] || (t == 0 && i == n)) {
                for(int j = i - 1; j >= 0; --j) {
                    ndp[j] = 1 + (1 - p) * ndp[j + 1] + p * e0;
                }
                break;
            }
        }
        swap(dp, ndp);
        if (abs(dp[0] - mn) <= EPS) {
            cout << mn << '\n';
            return;
        }
//        cerr << dp[0] << endl;
    }
    cout << dp[0] << '\n';
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(12) << fixed;
    int t = 1;
//    cin >> t;
    rep(i, t) {
        solve();
    }
    return 0;
}

/*
 * 100000 10000000
0.0002
 */