Given a tree of $n$ vertices. Vertex $i$ has number $A_i$ on it.
You are also given $q$ queries of the form $u, x$, find the distance of the nearest vertex having value $x$ on it to $u$.
### Input
- The first line contains two integers $n, q$.
- The second line contains $n$ integers $A_i$.
- The next $n-1$ lines, each line contains two integers $u, v$, there is an edge between $u$ and $v$.
- The next $q$ lines, each line contains two integers $u, x$, a query.
### Output
- Print the answer for each query, print `-1` if no solution exists.
### Constraints
- $1 \le n, q \le 5 \times 10^4$.
- $1 \le A_i, x \le n$.
### Example
Input:
```
3 2
1 2 3
1 2
1 3
2 2
1 3
```
Output:
```
0
1
```
