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Problems

A fish lunch

A fish lunch

Time limit 1 second
Memory limit 256 MiB

Alex decided to go on a trip. Now he is flying in the airplane, the lunchtime has just started. Lunch can be one of two kinds — meat or fish, and flight attendants ask each of the passengers, what kind of dinner he or she prefers.

But Alex knows that neither lunch of one type will not be enough for all passengers. If one of the types ends, flight attendants stop asking passengers about their preferences and just give them what remains. Alex wants to get a fish lunch. He knows that there are N passengers in the airplane, N_1 meat lunches and N_2 fish lunches. Moreover, he looked in what order does flight attendants distribute lunches, and noticed that he is I. He also has a statistics, from which we learn that fish lunches are prefered by P % of passengers. Now he wants to know, what’s his chance to get a fish dinner?

Input data

The single line contains 5 integers: N, N_1, N_2, I Ри P .

0 ≤ N1 1000

0 ≤ N2 1000

1 ≤ N ≤ N1 + N2

1 ≤ I ≤ N

0 ≤ P ≤ 100

Output data

You should print only one number — Alex’s chance to get fish lunch. Output response should be with an absolute percentage error of no more than 10 ^7.

Examples

Input example #1
10 5 5 10 50
Output example #1
0.500000000
Author Евгений Капун
Source Зимняя школа по программированию 2014, Харьков