Problem #345
Team Up
There are 50000 teams each containing 30 players with experience points 1,2....30 and there are 1500 teams containing 30 players each with 0 experience points. One mega team has to be formed from these players. The mega team can have any number of players.
Suppose the mega team have n players and the experience point of i^{th} player is a_i. Then the score of the mega team is defined as \sum_{i=0}^{n} 2^{a_i}.
Find the distinct number of mega teams with score 474288\ mod\ 1000000007.
Two Mega teams are considered different, if there is a particular player present in one team and not in another team.