The problem involves a tree with $n$ vertices, where each vertex $i$ has a value $A_i$. There are $q$ queries of two types:
- `1 u k`: Calculate the sum of values of vertices with a shortest path to vertex u not exceeding $k$.
- `2 u v`: Change the value at vertex $u$ to $v$.
### Input
- The first line contains two integers $n$ and $q$.
- The second line contains $n$ integers $A_i$, representing the values at each vertex.
- The next $q$ lines contain queries in the specified format.
### Output
- For each query of type 1, output an integer representing the answer.
### Constraints
- $1 \le n,q \le 10^5$.
- $1 \le A_i,x \le 10^4$.
- $1 \le u,k \le n$.
### Sample test
Input
```
7 7
8 3 6 5 6 10 6
1 2
2 3
1 4
2 5
2 6
3 7
2 7 9
2 2 2
2 4 10
1 2 2
2 7 10
1 7 1
1 2 3
```
Output:
```
51
16
52
```
