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CSES Problem Set

Distance Queries


Task | Statistics


CSES - Distance Queries

Time limit:1.00 s Memory limit:512 MB

You are given a tree that consists of $n$ nodes.

Your task is to process $q$ queries of the form: what is the distance between nodes $a$ and $b$?

Input

The first input line contains two integers $n$ and $q$: the number of nodes and queries. The nodes are numbered $1,2,\ldots,n$.

Then there are $n-1$ lines that describe the edges. Each line contains two integers $a$ and $b$: there is an edge between nodes $a$ and $b$.

Finally, there are $q$ lines that describe the queries. Each line contains two integer $a$ and $b$: what is the distance between nodes $a$ and $b$?

Output

Print $q$ integers: the answer to each query.

Constraints
Example

Input:
5 3
1 2
1 3
3 4
3 5
1 3
2 5
1 4


Output:
1
3
2