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.

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

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

Print the answer.

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

14

You can do as follows to put a total of 14 balls into the boxes while satisfying the conditions in the problem statement.

• For balls of color 1, put one into the first box, one into the second box, and three into the third box.
• For balls of color 2, put two into the first box, two into the second box, and five into the third box.