You are given an array $A$ of $n$ integers.
There are $q$ queries of either form:
- `1 l r x`: Add $x$ to $A_l, A_{l + 1},...,A_r$.
- `2 l r`: Find the minimum value in subarray $A_l,A_{l+1},...,A_r$.
### Input
- The first line contains 2 integers $n, q$.
- The second line contains $n$ integers $A_i$.
- The next $q$ lines, each line contains either 3 (for type $2$) or 4 (for type $1$) integers, a query.
### Output
- Print the answer for each query of type $2$.
### Constraints
- $1 \le n,q \le 10^5$.
- $1 \le i \le n$.
- $1 \le l \le r \le n$.
- $0 \le |A_i|, |x| \le 10^6$.
### Example
Input:
```
5 3
1 2 3 3 2
2 2 4
1 1 4 2
2 3 5
```
Output:
```
2
2
```
