Hello Codeforces!

Recently I have solved some problem with Articulation Bridge. Then I have come up with a problem that can be solved using Bridge but till now I can't figure out an appropriate solution.

Problem Description

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You are given a connected undirected graph of n nodes and m edges and an integer k.

Now the question is, What is the maximum number of connected components you can create by deleting exactly k edges (k <= m)?

Addition: How to solve the problem if there are Q queries of k?

time limit: 1s for a single case, 2s for the query. memory limit: 512 MB.

Note: if k <= number_of_bridges in the graph, then it is easy to prove that the answer will be k + 1.

Please give me some hints/resources that how can I come up with an efficient solution...