Given a directed graph of $n$ vertices and $n$ edges. Each vertex has exactlyy one outgoing edge.
Given $q$ queries of the form $(u, x)$. Each query represents a scenario where we start at vertex $u$ and need to determine the vertex we will reach after traversing through $x$ consecutive vertices.
### Input
- The first line contains two integers $n,q$.
- The next lines contains $n$ intergers $V_i$, there is a directed edge from $i$ to $V_i$.
- The next $q$ lines, each line contains two integers $u, x$, a query.
### Output
- Print the answer for each query.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le u,V_i \le n$.
- $1 \le x \le 10^9$.
### Example
Input:
```
3 2
2 3 1
1 3
2 2
```
Output:
```
1
1
```
