The tanks are coming!
Once upon a time, our familiar student Vasya discovered that Katya, the girl he likes, is interested in military computer games featuring tank battles. Inspired, Vasya decided to create such a game himself and gift it to Katya. He devised the game concept, but the programming work was extensive, so he chose to delegate some tasks to his friends. You have been assigned the task related to minefields.
Consider a field that is N units wide, where 1 < N ≤ 10^9. A tank, which is M units wide (1 < M ≤ N), needs to cross this field. Mines, each occupying 1 unit, are placed in a straight line across the field, meaning there are exactly N possible positions for these mines. The total number of mines, K, does not exceed 10^6. The tank sustains minor damage if it rolls over one mine, but it catches fire if it crosses over at least two mines. The tank moves perpendicular to the line of mines and always crosses exactly M potential mine positions. Your task is to determine the probability that the tank catches fire, given the arrangement of mines.
Input
The first line contains three positive integers N, K, and M, separated by spaces. The following K lines each contain one positive integer, representing the positions of the mines (positions are numbered from 1 to N).
Output
Output the probability of the tank catching fire as an irreducible fraction. If the probability is 0 or 1, output 0/1 or 1/1, respectively.