Today Marisa wants to make a potion bottle out of $m$ type of mushrooms.
There are $n$ mushrooms placed in a row. The $i^{th}$ mushroom is of the type $A_i$.
But there are some restrictions: Marisa can't put more than $B_i$ mushrooms of type $i$ in the same bottle, because that would make the potion unstable and explode.
She will choose a consecutive segment of mushrooms. Help her find the maximum number of mushrooms she can put in her potion.
### Input
- The first line contains 2 integers $n, m$.
- The second line contains $n$ integers $A_i$.
- The third line contains $m$ integers $B$.
### Output
- The maximum number of mushrooms Marisa can use.
### Constraints
- $1 \le n, m \le 10^5$.
- $1 \le A_i \le m$.
- $0 \le B_i \le 10^5$.
### Example
Input:
```
5 3
1 2 3 2 1
1 2 1
```
Output:
```
4
```
