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.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
import java.io.IOException;
import java.nio.file.Files;
import java.nio.file.Paths;

public class Main {
	
	static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[1024]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
	
	static class FastScanner {

	    private final BufferedReader bufferedReader;
	    private StringTokenizer stringTokenizer;

	    public FastScanner() {
	        bufferedReader = new BufferedReader(new InputStreamReader(System.in));
	    }

	    public String next() {
	        while (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
	            try {
	                stringTokenizer = new StringTokenizer(bufferedReader.readLine());
	            } catch (IOException e) {
	                throw new RuntimeException("Can't read next value", e);
	            }
	        }
	        return stringTokenizer.nextToken();
	    }

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

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

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

	    public String nextLine(){
	        String str = "";
	        try {
	            str = bufferedReader.readLine();
	        } catch (IOException e) {
	            e.printStackTrace();
	        }
	        return str;
	    }
	}
	
	static void closeall() throws IOException{
		printWriter.close();
		sc.close();
		in.close();
	}
	static Scanner sc = new Scanner(System.in);
	static Reader in = new Reader();
	static FastScanner fastScanner = new FastScanner();
	static PrintWriter printWriter = new PrintWriter(new BufferedOutputStream(System.out));
	static BufferedReader read = new BufferedReader(new InputStreamReader(System.in));
	static long INF = (long)(1e18);
	
	int V,E;
	ArrayList<Integer> adj[];
	Main(int v,int e){
		V=v;
		E=e;
		adj=new ArrayList[v];
		for(int i=0;i<v;i++)
			adj[i] = new ArrayList<>();
	}
	void addEdge(int u,int v){
		adj[u].add(v);
		adj[v].add(u);
	}
	
	static class e implements Comparable<e>{
		double x;
		int index;
		e(double a,int b){
			x=a;
			index=b;
		}
		@Override
		public int compareTo(e item) {
			// TODO Auto-generated method stub
			if (this.x < item.x) {
		        return -1;
		    }
		    else if(this.x > item.x){
		        return 1;
		    }
			return 0;
		}
		
	}
	
	static long power(long a,long k)
	{
		long m = 998244353;
	    long ans=1;
	    long tmp=a%m;
	    while(k>0)
	    {
	        if(k%2==1)
	        	ans=ans*tmp%m;
	        tmp=tmp*tmp%m;
	        k>>=1;
	    }
	    return ans;
	}
	
	static int ans;
	
	public static void main(String args[])throws IOException{
		int n = in.nextInt();
		double p = in.nextDouble();
		int t = in.nextInt();
		double[][] dp = new double[t+1][n+1];
		Arrays.fill(dp[0], 0);
		dp[1][0]=1-p;
		dp[1][1]=p;
		for(int i=2;i<=t;i++){
			dp[i][0]=dp[i-1][0]*(1-p);
			for(int j=1;j<=i && j<=n;j++){
				if(j!=n)
					dp[i][j]=dp[i-1][j-1]*p+dp[i-1][j]*(1-p);
				else
					dp[i][j]=dp[i-1][j-1]*p+dp[i-1][j];
			}
		}
		double ans = 0;
		/*for(int i=0;i<=t;i++){
			for(int j=0;j<=n;j++)
				System.out.print(dp[i][j]+" ");
			System.out.println();
		}*/
		for(int i=0;i<=n;i++)
			ans+=(double)i*(dp[t][i]);
		printWriter.println(ans);
		closeall();
	}
}