**Time limit:**1.00 s**Memory limit:**512 MB

You have decided that the total price of your purchases will be at most $x$. What is the maximum number of pages you can buy? You can buy several copies of the same book.

**Input**

The first input line contains two integers $n$ and $x$: the number of book and the maximum total price.

The next line contains $n$ integers $h_1,h_2,\ldots,h_n$: the price of each book.

The next line contains $n$ integers $s_1,s_2,\ldots,s_n$: the number of pages of each book.

The last line contains $n$ integers $k_1,k_2,\ldots,k_n$: the number of copies of each book.

**Output**

Print one integer: the maximum number of pages.

**Constraints**

- $1 \le n \le 100$

- $1 \le x \le 10^5$

- $1 \le h_i, s_i, k_i \le 1000$

**Example**

Input:

`3 10`

2 6 3

8 5 4

3 5 2

Output:

`28`

Explanation: You can buy three copies of book 1 and one copy of book 3. The price is $3 \cdot 2 + 3 = 9$ and the number of pages is $3 \cdot 8 + 4 = 28$.