Kiwi Juice

There are $N$ bottles, and every bottle has the same maximum capacity of $C$ liters. Bottle $i$ holds $B_i$ liters of kiwi juice.

Dotori sells this juice to buy a new laptop. The price of one bottle is set only by how much juice is in it. A price is fixed for every amount from 0 liters up to $C$ liters, and a fuller bottle is not always worth more. One bottle holding 0 liters can be worth more than one bottle filled to $C$ liters.

Instead of selling the bottles as they are, Dotori pours juice between them to push the total higher. The pouring rule is this. Pick two different bottles $A$ and $B$, then pour from $A$ into $B$ without stopping until $A$ is empty or $B$ is full. For example, if $C = 10$, bottle $A$ holds 5 liters and bottle $B$ holds 7 liters, then after the pour $A$ holds 3 liters and $B$ holds 10 liters. Under the same capacity, if $A$ holds 3 liters and $B$ holds 4 liters, then after the pour $A$ holds 0 liters and $B$ holds 7 liters.

Dotori may pour as many times as he wants. He is sure every bottle sells, so the money he receives is the sum of the prices of all $N$ bottles. Find the largest amount he can receive.

The first line contains the number of bottles $N$ and the maximum capacity $C$. ($1 \le N \le 15$, $1 \le C \le 49$)

The second line contains $B_1, B_2, \dots, B_N$, the amount of juice in each bottle. ($0 \le B_i \le C$)

The third line contains $P_0, P_1, \dots, P_C$, the price for each amount, in order from 0 liters up to $C$ liters. ($0 \le P_i \le 10^6$)

Print the maximum amount of money Dotori can receive, on one line.