Gateway Alliances

In a network of N nodes, some nodes are designated as 'Gateways'. A connected component is considered 'Global' if it contains at least TWO different gateway nodes. Given the list of gateways and a sequence of M edges being added, after each edge addition, output the total number of nodes that currently belong to any 'Global' component. Example: Input: 5 2 0 4 3 0 1 1 2 2 4 Output: 0 0 5 (Gateways are 0 and 4. After (0,1) and (1,2), only one gateway (0) is in the component {0,1,2}. After (2,4), gateways 0 and 4 are connected, so all nodes {0,1,2,4} (and 3 is separate) are global? No, component {0,1,2,4} has 4 nodes).