Lottery
In a certain country, a daily lottery takes place. A sensor sequentially generates N random real numbers, each independently and uniformly distributed over the interval (0, 1). Once all numbers are drawn, they are ranked: the smallest number receives the label 1, the second smallest gets 2, and so forth, with the largest number labeled N.
To win the lottery, a participant must correctly predict all the labels. The challenge is that for each number, the participant must guess its label immediately after it is drawn, without knowledge of the subsequent numbers.
You have decided to enter this lottery, and the sensor has provided you with the first number x. Your task is to choose a label for this number that maximizes your probability of winning, assuming optimal play for the remaining numbers.
Input
The input consists of a single line containing two numbers: an integer N (1 ≤ N ≤ 20) and a real number x (0 < x < 1).
Output
Output the optimal label for the first drawn number x. It is guaranteed that the value of x is at least 10^{-5} away from any value where multiple labels would yield the same maximum probability of winning.