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.

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.

Constraints

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

Sample Input 1

2 3
8 10
4 3 8

Sample Output 1

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.

Sample Input 2

1 1
1000000000000
0

Sample Output 2

0

Sample Input 3

10 12
59 168 130 414 187 236 330 422 31 407
495 218 351 105 351 414 198 230 345 297 489 212

Sample Output 3

2270

见题面 Input 部分

见题面 Output 部分