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.io.*;
import java.math.BigInteger;
import java.util.StringTokenizer;

/**
 * Created by Leonti on 2016-03-19.
 */
public class D {

    public static void main(String[] args) {
        InputReader inputReader = new InputReader(System.in);
        PrintWriter printWriter = new PrintWriter(System.out, true);

        int n = inputReader.nextInt();
        double p = inputReader.nextDouble();
        int t = inputReader.nextInt();
        double[][] z = new double[t + 1][n + 1];

        z[1][1] = p;
        z[1][0] = 1 - p;

        for (int i = 1; i < t; i++) {
            for (int j = 0; j <= n ; j++) {
                if (j == n) {
                    z[i + 1][j] += z[i][j];
                } else {
                    z[i + 1][j] += z[i][j] * (1 - p);
                    z[i + 1][j + 1] += z[i][j] * p;
                }
            }
        }

        double res = 0;
        for (int i = 1; i <= n; i++) {
            res += (i * z[t][i]);
        }

        printWriter.print(res);

        printWriter.close();
    }

    private static class InputReader {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public int[] nextIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; ++i) {
                array[i] = nextInt();
            }
            return array;
        }

        public long[] nextLongArray(int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; ++i) {
                array[i] = nextLong();
            }
            return array;
        }

        public double[] nextDoubleArray(int size) {
            double[] array = new double[size];
            for (int i = 0; i < size; ++i) {
                array[i] = nextDouble();
            }
            return array;
        }

        public String[] nextStringArray(int size) {
            String[] array = new String[size];
            for (int i = 0; i < size; ++i) {
                array[i] = next();
            }
            return array;
        }

        public boolean[][] nextBooleanTable(int rows, int columns, char trueCharacter) {
            boolean[][] table = new boolean[rows][columns];
            for (int i = 0; i < rows; ++i) {
                String row = next();
                assert row.length() == columns;
                for (int j = 0; j < columns; ++j) {
                    table[i][j] = (row.charAt(j) == trueCharacter);
                }
            }
            return table;
        }

        public char[][] nextCharTable(int rows, int columns) {
            char[][] table = new char[rows][];
            for (int i = 0; i < rows; ++i) {
                table[i] = next().toCharArray();
                assert table[i].length == columns;
            }
            return table;
        }

        public int[][] nextIntTable(int rows, int columns) {
            int[][] table = new int[rows][columns];
            for (int i = 0; i < rows; i++) {
                for (int j = 0; j < columns; j++) {
                    table[i][j] = nextInt();
                }
            }
            return table;
        }

        public long[][] nextLongTable(int rows, int columns) {
            long[][] table = new long[rows][columns];
            for (int i = 0; i < rows; i++) {
                for (int j = 0; j < columns; j++) {
                    table[i][j] = nextLong();
                }
            }
            return table;
        }

        public double[][] nextDoubleTable(int rows, int columns) {
            double[][] table = new double[rows][columns];
            for (int i = 0; i < rows; i++) {
                for (int j = 0; j < columns; j++) {
                    table[i][j] = nextDouble();
                }
            }
            return table;
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

        public boolean hasNext() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = readLine();
                if (line == null) {
                    return false;
                }
                tokenizer = new StringTokenizer(line);
            }
            return true;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(readLine());
            }
            return tokenizer.nextToken();
        }

        public String readLine() {
            String line;
            try {
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }
    }
}