Statement

You want to organize a chess tournament in your town! Given the recent developments in the chess world, you want to use some extra measures to make sure that everyone there is playing fairly. Towards this aim, you came up with a system to decide the strength of each move played by each player. In order to decide whether a player cheated or not, you compute the average move strength, concluding that a player cheated if it exceeds the player's initial chess rating by a certain threshold. More formally, you are given the data from K chess players. For each chess player you know the number of moves N they made during the contest, the strength S_i (i < N) of each of them, and the rating R and threshold T you are going to use. Decide whether each player cheated or not!