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 P518D {
	static final long LARGE_LONG = 1000000000000000000L;
	static final int LARGE_INT = 1000000007;
	
	public static void main(String[] args) throws IOException {
		FastReader in = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		
		int N = in.nextInt();
		double P = in.nextDouble();
		int T = in.nextInt();
		double[][] dp = new double[N+1][T+1];	// dp[i][j] = Prob that at time j, i person left
		dp[N][0] = 1.0;
		double ev = 0.0;   // expected value
		for (int j = 1; j <= T; j++) {
			dp[N][j] = dp[N][j-1] * (1 - P);
			for (int i=N-1; i>0; i--) {
				dp[i][j] = dp[i+1][j-1] * P + dp[i][j-1] * (1 - P);
			}
			dp[0][j] = dp[0][j-1] + dp[1][j-1] * P;
			ev += (1 - dp[0][j-1]) * P;		// probability that at time  j-1 at least one person remains
		}
		//out.println(Arrays.deepToString(dp));
		out.println(ev);
		out.close();
	}
	
	/* FastReader code from  https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/ 
	   nextLine modified, and added next(), and hasNext()
	*/
	static class FastReader { 
        final private int BUFFER_SIZE = 1 << 16; 
        final private int MAX_LINE_SIZE = 1 << 20; 
        private DataInputStream din; 
        private byte[] buffer, lineBuf; 
        private int bufferPointer, bytesRead; 
  
        public FastReader() { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
        public FastReader(String file_name) throws IOException { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
		public boolean hasNext() throws IOException { 
            byte c; 
            while ((c = read()) != -1) { 
				if (c > ' ') {
					bufferPointer--;
					return true;
				}
			}
			return false;
		}
        public String nextLine() throws IOException { 
			if (lineBuf == null)	lineBuf = new byte[MAX_LINE_SIZE];
			int ctr = 0;
            byte c; 
            while ((c = read()) != -1) { 
                if (c == '\r')        continue; 
                if (c == '\n')        break; 
                lineBuf[ctr++] = c; 
            } 
            return new String(lineBuf, 0, ctr); 
        }
		public String next() throws IOException { 
			if (lineBuf == null)	lineBuf = new byte[MAX_LINE_SIZE];
			int ctr = 0;
            byte c = read(); 
            while (c <= ' ')  	c = read(); 
			while (c > ' ') {
				lineBuf[ctr++] = c;
				c = read();
			}
			return new String(lineBuf, 0, ctr);
		}
        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(); 
        } 
    } 
}