Given an integer sequence $A$ and $q$ queries in the form of $l, r$, find the number of occurrences of the most frequent value in the range $A_l, A_{l+1}, ..., A_r$.
### Input
- The first line consists of two integers $n, q$.
- The second line contains $n$ integers $A_i$.
- The next $q$ lines each contain two integers $x, y$, representing a query. Two integers $l, r$ are calculated as follows:
+ $l = (x + \text{lastans}) \mod n + 1$
+ $r = (y + \text{lastans}) \mod n + 1$
+ $\text{lastans}$ is the answer from the previous query. In the first query, $\text{lastans}$ is conventionally set to $0$. If $l > r$, swap the values of $l$ and $r$.
### Output
- Print $q$ lines, each line containing the corresponding answer for each query.
### Constraints
- $1 \le n, q \le 2 \times 10^5$.
- $1 \le A_i \le 2 \times 10^5$.
- $1 \le x,y \le n$.
### Sample
Input:
```
5 3
1 2 2 3 2
1 3
1 5
4 5
```
Output:
```
2
1
1
```
