Strengthen It

You are given an undirected graph having A nodes and |B| edges, i^th edge connecting nodes B[i][1] and B[i][2].

Strength of a connected component is defined as the number of edges existing in that component.

Given an integer C, you have to tell the maximum strength that a connected component in the given graph can have, if we are allowed to add exactly C edges to the graph.

1 <= A <= 10⁵

1 <= |B| <= 2 * 10⁵

1 <= B[i][0], B[i][1] <= A

0 <= C <= 10⁹

First argument is an integer A

Second argument is a 2D matrix B having size |B| X 2

Third argument is an integer C

Return an integer denoting the maximum strength achievable in the graph.

Input 1:

 A = 7 
 B = [
       [1, 2]
       [2, 3]
       [3, 1]
       [4, 5]
       [5, 6]
       [6, 1]
     ]
 C = 1

Input 2:

 A = 3
 B = [
       [1, 2]
       [2, 2]
       [2, 3]
       [3, 1]
     ]
 C = 2

Output 1:

 7

Output 2:

 6

Explanation 1:

 Initially there are 3 components in the graph.
 We can add an edge between node 1 and node 4.
 Now the resultant graph will have 2 components with strengths 7 and 0.
 Maximum achievable strength after adding one edge = 7.

Explanation 2:

 The graph contains only a single component.
 If we add 2 edges in the component, the strength becomes 6.