[Codechef] Help with selection

Author            : Dipu Kumar Mohanto 
                    CSE, Batch - 6
                    BRUR.
Problem Statement : Help with selection 
Source            : Codechef
Category          : Combinatorics
Algorithm         : Lucas Theorem
Verdict           : Accepted

import math
 
def read():
    return map(int, input().split())
 
def readAll():
    return (int(i) for i in input().split())
 
fact = [0 for _ in range(1000000+5)]
 
def bigMod(a, p, m):
    if p == 0:
        return 1 % m
    if p == 1:
        return a % m
    if p % 2 == 1:
        return (a % m * bigMod(a, p - 1, m) % m) % m
    ret = bigMod(a, p // 2, m)
    return (ret %m * ret % m) % m
 
def modInverse(a, m):
    return bigMod(a, m-2, m)
 
def nCr(n, r, mod):
 if n < r:
  return 0
    temp = (fact[r] * fact[n-r]) % mod
    temp = modInverse(temp, mod)
    return (fact[n] * temp) % mod
 
def lucas(n, r, p):
    if n == 0 and r == 0:
        return 1
    ni = n % p
    ri = r % p
    return (nCr(ni, ri, p) * lucas(n // p, r // p, p)) % p
 
def getAns(n, r, p):
    fact[0] = 1
    for i in range(1, p):
        fact[i] = (i * fact[i-1]) % p
    return lucas(n, r, p)
 
if __name__ == '__main__':
    tc = int(input())
    for tcase in range(1, tc+1):
        n, r, p = readAll()
        print(getAns(n, r, p))