Maximum Language Charm

In order to help everyone quickly familiarize themselves with a new programming language, Small A collected statistics on the languages used by n residents in the country. There are m language sets (numbered from 1 to m), and the i-th language set has a_i syntaxes. Each resident uses exactly one language, denoted by b_1, b_2, \ldots, b_n.

The charm of a language is defined as:

\[ charm = a_i \times \text{(number of residents using language } i\text{)} \]

Your task is to determine the maximum charm value among all languages.

inputFormat

The first line contains two integers m and n, representing the number of languages and the number of residents, respectively.

The second line contains m integers: a_1, a_2, \ldots, a_m representing the number of syntaxes for each language.

The third line contains n integers: b_1, b_2, \ldots, b_n denoting the language used by each resident.

outputFormat

Output a single integer: the maximum charm value among all languages.

sample

3 5
3 2 1
1 2 1 3 1

9