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We are going to consider subsets of a given set . We are interested in subsets such that for a given natural number and for any natural number at least one of the numbers , doesn't belong to . We would like to calculate the number of such subsets, that have exactly elements. It is possible that the number of such subsets is huge - therefore it is sufficient to calculate the remainder of the division of the result by .
Write a program which:
In the first and only line of the standard input there are four integers , , and (, , , ), separated by single spaces.
The first and only line should contain one integer - the reminder of the division by of the number of -element subsets of set that fulfill the specified requirements.
For the input data:
6 1234 3 2
the correct result is:
Considered subsets are: , , , , , , , and .
Task author: Jakub Radoszewski.