| int modular_power(int base, int exponent, int modulus) |
| ; |
|
|
| int binomial_digit_mod_prime(int upper, int lower, int prime) |
|
|
| { |
| if (lower > upper) { |
| return 0; |
| } |
|
|
| if (lower > upper - lower) { |
| lower = upper - lower; |
| } |
|
|
| int numerator = 1; |
| int denominator = 1; |
|
|
| for (int i = 1; i <= lower; ++i) { |
| int factor = upper - lower + i; |
| long long numerator_product = (long long)numerator * factor; |
| long long denominator_product = (long long)denominator * i; |
|
|
| numerator = (int)(numerator_product % prime); |
| denominator = (int)(denominator_product % prime); |
| } |
|
|
| int inverse = modular_power(denominator, prime - 2, prime); |
| long long answer = (long long)numerator * inverse; |
| return (int)(answer % prime); |
| } |
|
|
| int lucas_theorem(int n, int m, int prime) |
|
|
| { |
| int upper = n + m; |
| int lower = n; |
| int result = 1; |
|
|
| while (upper > 0 || lower > 0) { |
| int upper_digit = upper % prime; |
| int lower_digit = lower % prime; |
|
|
| if (lower_digit > upper_digit) { |
| return 0; |
| } |
|
|
| int digit_binomial = |
| binomial_digit_mod_prime(upper_digit, lower_digit, prime); |
| long long product = (long long)result * digit_binomial; |
| result = (int)(product % prime); |
|
|
| upper /= prime; |
| lower /= prime; |
| } |
|
|
| return result; |
| } |
|
|
