You are in a book shop which sells $n$ different books. You know the price and number of pages of each book.

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 each book at most once.

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

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

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

• $1 \le n \le 1000$
• $1 \le x \le 10^5$
• $1 \le h_i, s_i \le 1000$

Print one integer: the maximum number of pages.