/*************************************************************************
 *  Compilation:  javac Birthday.java
 *  Execution:    java Birthday T N
 *  
 *  Computes the number of people (by simulation) that must enter a room
 *  until two of them share a birthday. Assumes birthdays a uniform
 *  and independent from 0 to N-1. Repeats the experiment T times and
 *  prints the average
 *  
 *  % java Birthday 100000 365
 *  Average = 24.65394
 *
 *************************************************************************/


public class Birthday { 

    public static void main(String[] args) { 
        int T = Integer.parseInt(args[0]);     // number of trials
        int N = Integer.parseInt(args[1]);     // number of days
        int count = 0;                         // total number of people

        for (int t = 0; t < T; t++) {

            boolean[] days = new boolean[N];          // auto-initialized to false

            while (true) {
                count++;
                int d = (int) (N * Math.random());    // integer between 0 and N-1
                if (days[d]) break;
                days[d] = true;
            }
        }

        System.out.println("Average = " + 1.0 * count / T);
    }
}