Given a tree of $n$ vertices rooted at $1$, vertex $i$ has color $A_i$.
Given $q$ queries, each of the form $(u, x)$, count the number of colors appear at least $x$ times in the subtree rooted at $u$.
### 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.
### Constraints
- $1 \le n,q\le 10^5$.
- $1 \le A_i \le 10^9$.
- $1 \le u, v,x \le n$.
### Example
Input:
```
4 3
1 2 2 2
1 2
2 3
2 4
1 2
1 1
2 3
```
Output:
```
1
2
1
```
