Counting Node Pairs with Two-Pointer and Edge Deduction
Initialize a count array to store the number of edges incident to each node.
Initialize a shared map to store the number of shared edges between each pair of nodes.
Iterate over the edges to populate the count array and shared map.
Sort the count array.
For each query, initialize the result for that query to 0.
Use a two-pointer approach to count the number of pairs where the sum of counts is greater than the query value.
Iterate over the shared map to adjust the result by deducting pairs that are directly connected but do not exceed the query value when the shared edge count is subtracted.
Return the results array containing the answer for each query.