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Problems

A game

A game

Time limit 1 second
Memory limit 256 MiB

Alex met a friend who invited him to play for the collectible card. The game divided on a rounds, and Bob has calculated that in every round he can win with probability P %. If he wins the round, the friend gives him N_1 collectible cards, otherwise Bob gives his friend N_2 collectible cards. When the loser can have not enough card, the game ends, and the one who has run out of cards is considered to be defeated. Alex has M_1 collectible cards, and he knows that his friend has M_2 collectible cards. To decide whether or not to play, Bob wants to calculate the probability of his winnings in such circumstances, but he can not do it on his own. You need to help him.

Limit

1 ≤ N1, N2, M1, M2 50

0 ≤ P ≤ 100

Input data

The single line contains 5 integers: N_1, N_2, M_1, M_2 and P .

Output data

You should print one number — chances of Alex to win a whole game. Output response should be with an absolute percentage error of no more than 10 ^7.

Examples

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