In this task, you need to add to the segment tree the operation of finding for the given $x$ and $l$ the minimum index $j$ such that $j≥l$ and $a[j]≥x$.

The first line contains two integers $n,m\ (1≤n,m≤100,000)$, the size of the array and the number of operations. 
The next line contains $n$ numbers $a_i$, the initial state of the array $(0≤a_i≤10^9)$. 
The following lines contain the description of the operations. The description of each operation is as follows:

• $\text{1 i v}$: change the item with index $i$ to $v\ (0≤i<n,\ 0≤v≤10^9)$.
• $\text{2 x l}$: find the minimum index $j$ such that $j≥l$ and $a[j]≥x\ (0≤x≤10^9,\ 0≤l<n)$. If there is no such element, print −1. Indices start from 0.

For each operation of the second type, print the answer for the query.