406986: GYM102646 D Team Selection

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

D. Team Selectiontime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

Timmy is creating a basketball team. In front of him are $$$n$$$ players, lined up. Each one has a skill level $$$a_i$$$, and he must select $$$k$$$ of them in the order that they're lined up in. The $$$j$$$-th player he takes will contribute $$$a_i \cdot b_j$$$ value to the team. Find the maximum possible value.

Input

The first line contains two space-separated integers: $$$n$$$ $$$(1 \leq n \leq 10^3)$$$ and $$$k$$$ $$$(1 \leq k \leq n)$$$. The second line contains $$$n$$$ space-separated integers $$$a_1, a_2, \dots, a_n$$$ $$$(1 \leq a_i \leq 10^5)$$$: the players' skill levels, in the order that they're lined up in.. The third line contains $$$k$$$ space-separated integers $$$b_1, b_2, \dots, b_k$$$ $$$(1 \leq b_i \leq 10^5)$$$.

Output

Print the maximum possible value of the team you can make.

ExamplesInput
3 2
1 2 3
2 1
Output
7
Input
5 4
5 9 10 3 2
10 10 5 5
Output
215
Input
7 4
1 9 3 8 19 3 2
50 1 9 3
Output
638
Note

In sample 1, Timmy can take players $$$2$$$ and $$$3$$$ to obtain a value of $$$2 \cdot 2 + 3 \cdot 1 = 7$$$.

In sample 2, Timmy can take players $$$2, 3, 4, $$$ and $$$5$$$ to obtain a value of $$$9 \cdot 10 + 10 \cdot 10 + 3 \cdot 5 + 2 \cdot 5 = 215$$$.

In sample 3, Timmy can take players $$$2, 4, 5, $$$ and $$$6$$$.

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