Problem Statement

There are several balls. Each ball is one of the colors $1$, $2$, $\ldots$, $N$, and for each $i = 1, 2, \ldots, N$, there are $A_i$ balls of color $i$.

Additionally, there are $M$ boxes. For each $j = 1, 2, \ldots, M$, the $j$-th box can hold up to $B_j$ balls in total.

Here, for all pairs of integers $(i, j)$ satisfying $1 \leq i \leq N$ and $1 \leq j \leq M$, the $j$-th box may hold at most $(i \times j)$ balls of color $i$.

Print the maximum total number of balls that the $M$ boxes can hold.

Constraints

• All input values are integers.
• $1 \leq N \leq 500$
• $1 \leq M \leq 5 \times 10^5$
• $0 \leq A_i, B_i \leq 10^{12}$

Input

The input is given from Standard Input in the following format:

N M
A_1 A_2 \ldots A_N
B_1 B_2 \ldots B_M

Output

Print the answer.