Problem: Ilya got tired of sports programming, left university and got a job in the subway. He was given the task to determine the escalator load factor. 

Let's assume that n people stand in the queue for the escalator. At each second one of the two following possibilities takes place: either the first person in the queue enters the escalator with probability p, or the first person in the queue doesn't move with probability (1 - p), paralyzed by his fear of escalators and making the whole queue wait behind him.

Formally speaking, the i-th person in the queue cannot enter the escalator until people with indices from 1 to i - 1 inclusive enter it. In one second only one person can enter the escalator. The escalator is infinite, so if a person enters it, he never leaves it, that is he will be standing on the escalator at any following second. Ilya needs to count the expected value of the number of people standing on the escalator after t seconds. 

Your task is to help him solve this complicated task.

Input

The first line of the input contains three numbers n, p, t (1 ≤ n, t ≤ 2000, 0 ≤ p ≤ 1). Numbers n and t are integers, number p is real, given with exactly two digits after the decimal point.

Output

Print a single real number — the expected number of people who will be standing on the escalator after t seconds. The absolute or relative error mustn't exceed 10 - 6.

Examples

Input

1 0.50 1


Output

0.5


Input

1 0.50 4


Output

0.9375


Input

4 0.20 2


Output

0.4

Solution (in JAVA):

Solution:
import java.awt.Container;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;
import java.util.concurrent.LinkedBlockingDeque;

import javax.swing.border.Border;

public class a {

	public static long mod = (long) Math.pow(10, 9) + 7;

	private static class node implements Comparable<node> {
		String ans;

		node(String an) {
			ans = an;
		}

		@Override
		public int compareTo(node o) {
			if (o.ans.length() > ans.length())
				return -1;
			while (o.ans.length() < ans.length())
				return 1;
			for (int i = 0; i < o.ans.length(); i++) {
				if (o.ans.charAt(i) > ans.charAt(i))
					return -1;
				else if (o.ans.charAt(i) < ans.charAt(i))
					return 1;
			}

			return 1;

		}

	}

	public static class point implements Comparable<point> {
		int x;
		int y;

		point(int x, int y) {
			this.x = x;
			this.y = y;

		}

		@Override
		public int compareTo(point o) {
			if (o.x < x)
				return 1;
			else if (o.x > x) {
				return -1;
			} else if (o.y < y)
				return 1;
			else
				return -1;
		}
	}

	public static int ch(long y) {
		int r = Long.bitCount(y);
		return r;
	}

	public static long gcd(long x, long y) {
		if (y == 0)
			return x;

		return gcd(y, x % y);
	}

	public static boolean ch[] = new boolean[10000005];
	public static ArrayList<Integer> prime = new ArrayList();

	// public static Queue<Integer> pp;

	public static void sieve(int k) {
		ch[0] = ch[1] = true;

		for (int i = 2; i <= k; i++) {
			if (!ch[i]) {
				prime.add(i);
				// pp.add(i);
				for (long j = (long) i * (long) i; j <= k; j += i) {
					ch[(int) j] = true;
				}
			}
		}

	}

	public static long pw(int x, int power, int mod) {
		if (power == 1)
			return x % mod;
		else if (power % 2 == 0)
			return pw((x % mod * x % mod) % mod, power / 2, mod);
		else
			return (pw(x, power - 1, mod) % mod * x % mod) % mod;

	}

	public static String addToString(String a, int index, char b) {
		String ans = "";
		for (int i = 0; i < a.length(); i++) {
			if (i == index) {
				ans += b;
				index = -1;
				i--;
				continue;
			}
			ans += a.charAt(i);
		}
		return ans;
	}

	public static int bit[];

	public static void add(int idx, int cost) {
		while (idx < bit.length) {
			bit[idx] += cost;
			idx += (idx & -idx);
		}

	}

	public static int get(int idx) {
		int res = 0;
		while (idx > 0) {
			res += bit[idx];
			idx -= (idx & -idx);
		}
		return res;
	}

	public static int dx[] = { 0, 1, 0, -1 };
	public static int dy[] = { 1, 0, -1, 0 };

	public static int n;
	public static double p;
	public static int t;

	public static double dp[][];

	public static double solve(int t, int pers) {
		if (pers == 0)
			return n;
		if (t == 0)
			return (double) n - (double) pers;

		if (dp[t][pers] != -1)
			return dp[t][pers];
		double a = 0;
		double b = 0;
		if (pers > 0)
			a = solve(t - 1, pers - 1) * p;
		b = solve(t - 1, pers) * (1.0 - p);
		return dp[t][pers] = a + b;
	}

	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		// BufferedReader in = new BufferedReader(new FileReader(
		// "corporate_gifting.txt"));
		StringBuilder qq = new StringBuilder();
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		// PrintWriter out = new PrintWriter(new FileWriter("out.txt"));
		String y[] = in.readLine().split(" ");

		n = Integer.parseInt(y[0]);
		p = Double.parseDouble(y[1]);
		t = Integer.parseInt(y[2]);
		dp = new double[t + 1][n + 1];
		for (int i = 0; i < t + 1; i++)
			for (int j = 0; j < n + 1; j++)
				dp[i][j] = -1;
		System.out.printf("%.9f\n",solve(t, n));

		out.close();

	}
}