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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {

		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;

		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);

		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}

}


class TaskA {

	public void solve(int testNumber, InputReader in, PrintWriter out) {
		String s = in.next();
		String t = in.next();
		
		char[] n = new char[s.length()];
		for(int i=0;i<s.length();++i){
			n[i] = s.charAt(i);
		}
		
		boolean modified = false;
		for(int i=s.length()-1;i>=0;--i){
			if(n[i]<'z'){
				modified = true;				
				n[i]++;
				for(int j=i+1;j<s.length();++j){
					n[j]='a';
				}
				break;
			}			
		}
		
		if(modified&&t.compareTo(new String(n))>0){
			out.println(new String(n));
		}else{
			out.println("No such string");
		}
	}

}

class TaskB {

	public void solve(int testNumber, InputReader in, PrintWriter out)
			throws IOException {
		
		String s = in.next();
		String t = in.next();
		
		int ura = 0;
		int opa = 0;
		
		int[] m = new int['z'+1];
				
		for(int i=0;i<t.length();++i){
			m[t.charAt(i)]++;
		}
		
		boolean[] processed = new boolean[s.length()];
		
		for(int i=0;i<s.length();++i){
			if(!processed[i]&&m[s.charAt(i)]>0){
				m[s.charAt(i)]--;
				ura++;
				processed[i] = true;
			}
		}
		
		for(int i=0;i<s.length();++i){
			if(!processed[i]&&m[neibh(s.charAt(i))]>0){
				m[neibh(s.charAt(i))]--;
				opa++;
				processed[i] = true;
			}
		}
		
		out.println(ura+" "+opa);
		
	}

	private int neibh(char ch) {
		if(ch>='a'&&ch<='z'){
			return ch - 32;
		}else{
			return ch+32;
		}
	}

}

class TaskC {

	public void solve(int testNumber, InputReader in, PrintWriter out) {
		
		int n = in.nextInt();
		int m = in.nextInt();
		int k = in.nextInt();
		
		int[] pos = new int[n];
		int[] programs = new int[n];
		
		for(int i=0;i<n;++i){
			int program = in.nextInt()-1;
			pos[program] = i;
			programs[i] = program;
		}
		
		int touches = 0;
		
		int menuPosition = 0;
		
		for(int i=0;i<m;++i){
			int program = in.nextInt()-1; 
			int position = pos[program];	
//			out.println("touches "+calculate(position,k));
			touches+=calculate(position,k,menuPosition);
			if(position!=0){
				pos[program]--;
				int incProgram = programs[pos[program]];				
//				out.println("Inc "+(incProgram+1));
				pos[incProgram]++;
				swap(programs, pos[program], pos[incProgram]);
			}
		}
		
		out.println(touches);
		
	}

	private void swap(int[] p, int p1, int p2) {
		int tmp = p[p1];
		p[p1] = p[p2];
		p[p2] = tmp;
	}

	private int calculate(int position, int k, int menuPosition) {
		if(position==0){
			return 1;
		}else{
			return 1 + Math.abs((position)/k-(menuPosition)/k);
		}
	}
	
}

class TaskD {

	public void solve(int testNumber, InputReader in, PrintWriter out) {
		
		
		int n = Integer.parseInt(in.next());
		double p = Double.parseDouble(in.next());
		int t = Integer.parseInt(in.next());
		
		double[][] pm = new double[2100][2100];
		
		pm[1][0] = 1-p;
		pm[1][1] = p;
		
		for(int i=2;i<=t;++i){			
			for(int j=0;j<=n;++j){				
				if(j>0){
					pm[i][j] += pm[i-1][j-1]*(p);
				}
				if(j<n){
					pm[i][j] += pm[i-1][j]*(1-p);
				}else{
					pm[i][j] += pm[i-1][j];
				}
			}
		}		
		
		double result = 0;
		
		for(int i=0;i<=n;++i){
			result+= (pm[t][i])*((double)i);
		}
		out.println(result);
	}

}


class InputReader {
	public BufferedReader reader;
	public StringTokenizer tokenizer;

	public InputReader(InputStream stream) {
		reader = new BufferedReader(new InputStreamReader(stream), 32768);
		tokenizer = null;
	}

	public String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

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

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

}