[UCSD白板题] Huge Fibonacci Number modulo m

Problem Introduction

The Fibonacci numbers are defined as follows: \(F_0=0\), \(F_1=1\),and \(F_i=F_{i-1}+F_{i-2}\) for $ i \geq 2$.

Problem Description

Task.Given two integers \(n\) and \(m\), output \(F_n \ mod \ m\)(that is, the remainder of \(F_n\) when divided by \(m\)).

Input Format.The input consists of two integers \(n\) and \(m\) given on the same line(separated by a space).

Constraints. \(1 \leq n \leq 10^{18}, 2 \leq m \leq 10^5\).

Output Format.Output \(F_n \ mod \ m\)

Sample 1.
Input:

281621358815590 30524

Output:

11963

Solution

# Uses python3
import sys

def get_fibonaccihuge(n, m):
    x, y = 0, 1
    pisano = []
    while True:
        pisano.append(x)
        x, y = y % m, (x+y) % m
        if x == 0 and y == 1:
            break
    return pisano[n % len(pisano)]

if __name__ == '__main__':
    input = sys.stdin.read()
    n, m = map(int, input.split())
    print(get_fibonaccihuge(n, m))