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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.StringTokenizer;
public class Main{
public interface SpaceCharFilter {
public boolean isSpaceChar(int ch);
}
class InputReader {
 
 
private InputStream stream;
 
private byte[] buf = new byte[1024];
 
private int curChar;
 
private int numChars;
 
private SpaceCharFilter filter;
 
public InputReader(InputStream stream) {
 
this.stream = stream;
 
}
 
 
public int read() {
 
if (numChars == -1)
 
throw new InputMismatchException();
 
if (curChar >= numChars) {
 
curChar = 0;
 
try {
 
numChars = stream.read(buf);
 
} catch (IOException e) {
 
throw new InputMismatchException();
 
}
 
if (numChars <= 0)
 
return -1;
 
}
 
return buf[curChar++];
 
}
 
 
public int readInt() {
 
int c = read();
 
while (isSpaceChar(c))
 
c = read();
 
int sgn = 1;
 
if (c == '-') {
 
sgn = -1;
 
c = read();
 
}
 
int res = 0;
 
do {
 
if (c < '0' || c > '9')
 
throw new InputMismatchException();
 
res *= 10;
 
res += c - '0';
 
c = read();
 
} while (!isSpaceChar(c));
 
return res * sgn;
 
}
 
 
public String readString() {
 
int c = read();
 
while (isSpaceChar(c))
 
c = read();
 
StringBuilder res = new StringBuilder();
 
do {
 
res.appendCodePoint(c);
 
c = read();
 
} while (!isSpaceChar(c));
 
return res.toString();
 
}
 
 
public boolean isSpaceChar(int c) {
 
if (filter != null)
 
return filter.isSpaceChar(c);
 
return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
 
}
 
 
public String next() {
 
return readString();
 
}
 
 
 
}
 
 
class OutputWriter {
 
private final PrintWriter writer;
 
 
public OutputWriter(OutputStream outputStream) {
 
writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
 
}
 
 
public OutputWriter(Writer writer) {
 
this.writer = new PrintWriter(writer);
 
}
 
 
public void print(Object...objects) {
 
for (int i = 0; i < objects.length; i++) {
 
if (i != 0)
 
writer.print(' ');
 
writer.print(objects[i]);
 
}
 
}
 
 
public void printLine(Object...objects) {
 
print(objects);
 
writer.println();
 
}
 
 
public void close() {
 
writer.close();
 
}
 
 
public void flush() {
 
writer.flush();
 
}
 
 
}
 
/**
* @param args
*/
 
InputReader in= new InputReader(System.in);
OutputWriter out = new OutputWriter(System.out);
StringTokenizer tok;
public static void main(String[] args) throws IOException
{
new Main().run();
}

void run() throws IOException
{
solve();
out.flush();
tok=null;
}
void solve() throws IOException{
    int n=in.readInt();
    double p=Double.parseDouble(in.readString());
    int t=in.readInt();
    
    double[][] E=new double[n+1][t+1];
    E[0][0]=1;
    for (int i=1;i<=t;++i){
        E[0][i]=E[0][i-1]*(1-p);
    }
    for (int i=1;i<=n;++i){
        for (int j=1;j<=t;++j){
            if (i==n){
            E[i][j]=E[i-1][j-1]*p + E[i][j-1];  
            }else{
            E[i][j]=E[i-1][j-1]*p + E[i][j-1]*(1-p);
            }
            }
    }
    int mn=Math.min(t,n);
    double ans=0;
    for (int i=0;i<=mn;++i){
        ans+=E[i][t]*i;
    }
    DecimalFormat df=new DecimalFormat("0.000000");
    out.printLine(df.format(ans));
}
}