Picking Balls

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

Description

Balls of N different colors are put inside a box. There are Mi balls of color i. What is the possibility of taking K balls out of the box and exactly Pj of them are of color j for each j = 1, 2, ..., N.


Input

Input contains several cases, each of which occupies 3 lines. The first line contains two non-negative integers N and K. The next line has N positive integers M1, M2, .... Mn, followed by a line with N non-negative integers P1, P2, .... Pn. It is guaranteed that K = P1 + P2 + ... + Pn. You may also assume that the total number of balls in any of the cases does not exceed 50.

Subsequent test cases are separated with a single blank line. The input is terminated with two -1's. This case is not to be processed.


Output

One number on a single line for each case - the possibility. Round to 5 digits after the decimal point.

Sample Input

3 3
2 2 2
1 1 1

2 1
2 1
0 1

-1 -1

Sample Output

0.40000
0.33333

Hint

None

Source

Zhejiang University Local Contest 2004

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