Given an array $A$ of $n$ integers. There are $q$ queries, each consisting of two integers $l, r$. Calculate $A_l + \text{min}(A_l, A_{l+1}) + ... + \text{min}(A_l, A_{l+1}, ..., A_r)$.
### Input
- The first line contains two positive integers $n, q$.
- The second line contains $n$ integers $A_i$.
- The next $q$ lines each contain two integers $l, r$.
### Output
- For each query, print the answer on a separate line.
### Constraints
- $1 \le n, q \le 10^5$.
- $1 \le A_i \le 10^9$.
- $1 \le l \le r \le n$.
### Example
Input:
```
6 3
5 3 7 2 1 4
2 4
3 6
1 3
```
Output:
```
8
11
11
```
