Given an array A of n integers, there are q queries, each falling into one of two types:
- 1lrk: Find the k-th smallest number in the subarray Al...r.
- 2lrx: For every l≤i≤r, increment Ai by x.
Find the answers for each query of type 1.
### Input
- The first line contains two integers n,q.
- The second line contains n integers Ai.
- The next q lines each contain a query in the specified format.
### Output
- Print an integer as the answer for each query of type 1.
### Constraints
- 1≤n,q≤105.
- 0≤|Ai|,|x|≤2×104.
- 1≤k≤r−l+1.
### Example
Input:
1111111
Output:
1