The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 114 (Div. 1) |
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Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

dp

math

probabilities

*1800

No tag edit access

The problem statement has recently been changed. View the changes.

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B. Wizards and Huge Prize

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOne must train much to do well on wizardry contests. So, there are numerous wizardry schools and magic fees.

One of such magic schools consists of *n* tours. A winner of each tour gets a huge prize. The school is organised quite far away, so one will have to take all the prizes home in one go. And the bags that you've brought with you have space for no more than *k* huge prizes.

Besides the fact that you want to take all the prizes home, you also want to perform well. You will consider your performance good if you win at least *l* tours.

In fact, years of organizing contests proved to the organizers that transporting huge prizes is an issue for the participants. Alas, no one has ever invented a spell that would shrink the prizes... So, here's the solution: for some tours the winner gets a bag instead of a huge prize. Each bag is characterized by number *a*_{i} — the number of huge prizes that will fit into it.

You already know the subject of all tours, so you can estimate the probability *p*_{i} of winning the *i*-th tour. You cannot skip the tour under any circumstances.

Find the probability that you will perform well on the contest and will be able to take all won prizes home (that is, that you will be able to fit all the huge prizes that you won into the bags that you either won or brought from home).

Input

The first line contains three integers *n*, *l*, *k* (1 ≤ *n* ≤ 200, 0 ≤ *l*, *k* ≤ 200) — the number of tours, the minimum number of tours to win, and the number of prizes that you can fit in the bags brought from home, correspondingly.

The second line contains *n* space-separated integers, *p*_{i} (0 ≤ *p*_{i} ≤ 100) — the probability to win the *i*-th tour, in percents.

The third line contains *n* space-separated integers, *a*_{i} (1 ≤ *a*_{i} ≤ 200) — the capacity of the bag that will be awarded to you for winning the *i*-th tour, or else -1, if the prize for the *i*-th tour is a huge prize and not a bag.

Output

Print a single real number — the answer to the problem. The answer will be accepted if the absolute or relative error does not exceed 10^{ - 6}.

Examples

Input

3 1 0

10 20 30

-1 -1 2

Output

0.300000000000

Input

1 1 1

100

123

Output

1.000000000000

Note

In the first sample we need either win no tour or win the third one. If we win nothing we wouldn't perform well. So, we must to win the third tour. Other conditions will be satisfied in this case. Probability of wining the third tour is 0.3.

In the second sample we win the only tour with probability 1.0, and go back home with bag for it.

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