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Best known algos for calculating nCr % M

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I have often encountered calculating nCr problems the last one being one of the IIIT-M problems but it probably had weak test cases that got easy solutions AC. The other one https://cs3.interviewstreet.com/challenges/dashboard/#problem/50877a587c389 of codesprint was completey out of my minds and hands , I tried the inverse euler , power of p in n! ( I would also like if someone could explain me the theory of this method ) but all went in vain . Anyone who could suggest probably the best algos for cases when nCr is to be calculated with large n and r with and without % M where M is prime/not prime + the above method which I coded but couldn't understand how it was so.


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