Cheddar
By Flávio Zavan, UFPR 
Brazil
By Flávio Zavan, UFPR Brazil
Poor Petya is hungry.
– Mom! Mom! Mooooom! - yells the boy at the basement.
– What’s up, son? - The lady answers.
– I want cheddar!
CHEDDAR! The boy is hungry and wants cheddar. You, Petya’s neighbor and an excellent programmer, heard it and wants to help. Since the cheese police does not allow cheddar to be sold to everyone, you will write a program to facilitate the lady’s purchase.
Everyone who tries to buy cheddar must pass a luck test. They receive N die (honest ones, with 6 faces valued from 1 to 6) and a number V. All N die are rolled and S is calculated, where S is the sum of the results of all die. If S is greater than or equal to V, cheddar can be purchased. Otherwise, the buyer goes home with empty hands.
Your program must calculate, given N and V, the probability that Petya’s mom successfully buys cheddar to his son.
The input contains several test cases. Each test case contains a single line with two integers, N (0 < N ≤ 1000) and V (0 ≤ V ≤ 6000).
The input ends with end-of-file (EOF).
For each test case, print a single line with a number with four decimal places, the probability Petya’s mom buys cheddar.
| Input Sample | Output Sample |
|
1 6 |
0.1667 |