Problem Statement

There are N roulette wheels.
The $i-th (1\leq i\leq N) wheel has P _ i integers S _ {i,1},S _ {i,2},\ldots,S _ {i,P _ i}$ written on it, and you can play it once by paying C _ i yen.
When you play the i-th wheel once, an integer j between 1 and P _ i, inclusive, is chosen uniformly at random, and you earn S _ {i,j} points.
The points you earn from the wheels are determined independently of past results.
Takahashi wants to earn at least M points.
Takahashi will act to minimize the amount of money he pays before he earns at least M points.
After each play, he can choose which wheel to play next based on the previous results.
Find the expected amount of money Takahashi will pay before he earns at least M points.
More formal definition
Here is a more formal statement.
For a strategy that Takahashi can adopt in choosing which wheel to play, the expected amount of money E that he pays before he earns at least M points with that strategy is defined as follows.

• For a natural number X, let f(X) be the expected amount of money Takahashi pays before he earns at least M points or plays the wheels X times in total according to that strategy. Let $E=\displaystyle\lim _ {X\to+\infty}f(X)$.

Under the conditions of this problem, it can be proved that $\displaystyle\lim _ {X\to+\infty}f(X)$ is finite no matter what strategy Takahashi adopts.
Find the value of E when he adopts a strategy that minimizes E.

Input

The input is given from Standard Input in the following format:
N M
$C _ 1 P _ 1 S _ {1,1} S _ {1,2} \ldots S _ {1,P _ 1}$
$C _ 2 P _ 2 S _ {2,1} S _ {2,2} \ldots S _ {2,P _ 2}$
$\vdots$
$C _ N P _ N S _ {N,1} S _ {N,2} \ldots S _ {N,P _ N}$

Output

Print the expected amount of money Takahashi will pay until he earns at least M points in a single line.
Your output will be considered correct when the relative or absolute error from the true value is at most 10 ^ {-5}.

Constraints

• $1\leq N\leq 100$
• $1\leq M\leq 100$
• $1\leq C _ i\leq 10 ^ 4$\ $(1\leq i\leq N)$
• $1\leq P _ i\leq 100$\ $(1\leq i\leq N)$
• $0\leq S _ {i,j}\leq M$\ $(1\leq i\leq N,1\leq j\leq P _ i)$
• $\displaystyle\sum _ {j=1}^{P _ i}S _ {i,j}\gt0$\ $(1\leq i\leq N)$
• All input values are integers.

Sample Input 1

3 14
100 2 5 9
50 4 1 2 4 8
70 5 2 4 2 8 8

Sample Output 1

215.913355350494384765625

For instance, Takahashi can play the wheels as follows.

• Pay 50 yen to play roulette 2 and earn S _ {2,4}=8 points.
• Pay 50 yen to play roulette 2 and earn S _ {2,1}=1 point.
• Pay 100 yen to play roulette 1 and earn S _ {1,1}=5 points. He has earned a total of $8+1+5\geq14$ points, so he quits playing.

In this case, he pays 200 yen before earning 14 points.
Your output will be considered correct when the relative or absolute error from the true value is at most 10 ^ {-5}, so outputs such as 215.9112 and 215.9155 would also be considered correct.

Sample Input 2

2 100
1 2 1 2
10 6 0 0 0 0 0 100

Sample Output 2

60

It is optimal to keep spinning roulette 2 until you get 100 points.

Sample Input 3

20 90
3252 9 0 4 2 7 3 2 3 2 4
2147 1 1
4033 8 0 4 1 7 5 2 5 0
3795 6 6 6 2 3 2 2
3941 7 2 4 4 7 2 0 5
2815 6 2 1 0 5 2 2
3020 2 3 6
3858 9 4 2 7 3 0 4 4 6 5
4533 10 3 6 4 0 6 4 4 2 7 7
4198 8 6 7 0 6 3 6 5 6
3739 8 2 7 1 5 1 4 4 7
2465 4 1 4 0 1
4418 9 7 6 2 4 6 1 5 0 7
5450 12 0 4 4 7 7 4 4 5 4 5 3 7
4196 9 1 6 5 5 7 2 3 6 3
4776 9 2 2 7 3 6 6 1 6 6
2286 3 3 5 6
3152 3 4 1 5
3509 7 0 6 7 0 1 0 3
2913 6 0 1 5 0 5 6

Sample Output 3

45037.072314895291126319493887599716

见题面 Input 部分

见题面 Output 部分