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.*;
 
 
public class Myclass {
    //static ArrayList a[]=new ArrayList[3000001];
     public static void main(String[]args)
    {
        InputReader in=new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        String s[]=in.nextLine().split(" ");
        int n=Integer.parseInt(s[0]);
        double d=Double.parseDouble(s[1]);
        int t=Integer.parseInt(s[2]);
        double p[]=new double[20001];
        double _p[]=new double[2001];
        p[0]=_p[0]=1F;
        for(int i=1;i<=2000;i++) {
        	p[i]=(p[i-1]*d);
        	_p[i]=(_p[i-1]*(1F-d));
        }
        if(d==1) {
        	pw.println(Math.min(n, t));
        	pw.flush();
        	pw.close();
        	System.exit(0);
        }
        double dp[][]=new double[2001][2001];
        dp[0][0]=1F;
        for(int i=1;i<=2000;i++) {
        	for(int j=0;j<=i;j++) {
        		if(j==0) {
        			dp[i][j]=_p[i];
        		}
        		else if(j==1) {
        			dp[i][j]=(double)i*(p[1])*(_p[i-1]);
        		}
        		else
        		{
        			dp[i][j]=((dp[i-1][j-1])*(d/(1F-d))+dp[i-1][j])*(1F-d);
        		}
        	}
        }
        double ans=0F;
        for(double i=1;i<n;i++) {
        	if(i>t)
        		break;
        	ans+=dp[t][(int) i]*i;
        }
        if(n>=t) {
        	ans+=dp[t][(int) n]*n;
        }
        else
        {
        	double tmp=0F;
        	for(int i=n;i<=t;i++) {
        		tmp+=dp[i-1][n-1]*d;
        	}
        	
        	ans+=(tmp)*(double)n;
        }
        pw.printf("%.15f",ans);
        pw.flush();
        pw.close();
 
    }
    private static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
   static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        { 
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
        static class tri implements Comparable<tri> {
            int p, c, l;
 
            tri(int p, int c, int l) {
                this.p = p;
                this.c = c;
                this.l = l;
            }
 
            public int compareTo(tri o) {
                return Integer.compare(l, o.l);
            }
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(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;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
   public static long modularExponentiation(long x,long n,long M)
   {
       long result=1;
       while(n>0)
       {
           if(n % 2 ==1)
               result=(result%M * x%M)%M;
           x=(x%M * x%M)%M;
           n=n/2;
       }
       return result;
   }
   
   public static long modInverse(int A,int M)
   {
       return modularExponentiation(A,M-2,M);
   }
   
   public static long modInverse(long A,long M)
   {
       return modularExponentiation(A,M-2,M);
   }
    static class pair implements Comparable<pair>{
        Integer x;
        Integer y;

        pair(int x,int w){
            this.x=x;
            this.y=w;
        }
        
        public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
            return result;
            }  
         public String toString(){
            return (x+" "+y);
        }
  }
    public static long GCD(long a,long b)
    {
        if(b==0)
            return a;
        else
            return GCD(b,a%b);
    }
  static class query{
      Long x;
      Long y;
      Integer z;
      query(long x,long y,int z){
          this.x=x;
          this.y=y;
          this.z=z;
      }
  }
    
}