Calculate nCr mod p.

general
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How to compute nCr % p for large data Efficiently?

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Read here @rashedcs - Best known algos for calculating nCr % M

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Precompute the factorial till n. Then you can find n!,r! and (n-r)! (all mod p) in order 1.

The property further useful is (ab)mod p = ((a mod p)(b mod p))mod p.

Then using inverse modulo find the result.To read more about inverse modulo refer link : Modular Inverse -- from Wolfram MathWorld

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You can check this out for the various implementations of cominations when mod is prime or any general number.