[Solution] KBG and GN-Theory CodeChef Solution

[Solution] KBG and GN-Theory CodeChef Solution

After solving some Graph Theory related problems KBG challenged Sameer to solve the following problem.

There is an undirected graph consisting of N$N$ vertices numbered from 1$1$ to N$N$.

For every pair of vertices u$u$ and v$v$ (u≠v)$(u\ne v)$ in the graph, there is a undirected weighted edge between u$u$ and v$v$ if and only if u$u$ divides v$v$, with weight vu$\frac{v}{u}$. Note that such a graph will not have self loops or multiple edges.

You must answer Q$Q$ queries. In each query you are given two vertices u$u$ and v$v$. You must find the

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 minimum distance from vertex u$u$ to vertex v$v$.

Input Format

• The first line contains a single integer T$T$ — the number of test cases. Then the test cases follow.
• The first line of each test case contains two integers N$N$ and Q$Q$ — the number of vertices and the number of queries.

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• The next Q$Q$ lines contain two space-separated integers u$u$ and v$v$ — vertices corresponding to the query.

Output Format

For each test case, print Q$Q$ lines — the answers to the Q$Q$ queries.

Constraints

• 1≤T≤105$1\le T\le {10}^5$
• 1≤N≤105$1\le N\le {10}^5$
• 1≤Q≤105$1\le Q\le {10}^5$
• 1≤u,v≤N$1\le u,v\le N$
• The sum of N$N$ over all test cases does not exceed 105${10}^5$.
• The sum of Q$Q$ over all test cases does not exceed 105