Given an array $A$ consisting of $n$ integers and $q$ queries, each represented as a tuple $(l, r)$. The task is to determine the index of the smallest value within the subarray $A_l, A_{l+1}, \ldots, A_r$ for each query.
### Input
- The first line contains two integers $n, q$.
- The second line contains $n$ integers $A_i$.
- The next $q$ lines, each line contains two integers $l, r$, a query.
### Output
- Print the answer for each query. If there multiple indices with the same minimum value, print the smallest one.
### Constraints
- $1 \le n, q \le 10^5$.
- $1 \le A_i \le 10^9$.
- $1 \le l \le r \le n$.
### Example
Input:
```
4 2
1 4 3 1
1 4
2 3
```
Output:
```
1
3
```
