Given a list of n integers, you are asked to remove one of the integers in a way that the sum of the resulting sequence modulo m is equal to s. More formally, if the index of the removed element is r:
The program should find the index of that number or print Impossible if that kind of number does not exist.
Input
The first line of the input contains 3 integers n (1 β€ n β€ ), m (1 β€ m β€ ), and s (0 β€ s < m).
The second line contains n space-separated integers ( β€ β€ ).
Output
In case such a number does not exist, the program should print Impossible, otherwise, the program should print the smallest index of such a number in the given sequence. The indexing starts from 1.