【2020秋招笔试】百信银行：快速计算阶乘+快速幂

$O(logn)$时间复杂度的情况下计算 $t!$ 和 $a^t$。
快速幂计算在笔试中写过好多次了，万万没想到阶乘也可以。

import sys
def power(n, m):
    global number, cn, p_size, mask
    if (m == 1):
        cur = n
    elif(m & 1 != 0):
        cur = n * power(n, m - 1)
    else:
        cur = power(n, m >> 1)
        cur *= cur
        cn[number] = (cur >> ((m >> 1) * p_size)) & mask  
        number += 1
    return cur

def factor(n):
    global number, cn, p_size, mask
    if (n == 1):
        return 1
    elif(n & 1 == 1):
        return n * factor(n - 1)
    else:
        cur = factor(n >> 1)
        pos = number
        number += 1
        return cn[pos] * cur * cur
    
def factorial(n):
    global number, cn, p_size, mask
    x = (1 << n) + 1
    number = 0
    mask = (1 << n) - 1
    p_size = n
    power(x, n)
    number = 0
    return factor(n)
p_size = 0
mask = 0
cn = []
number = 0
N = int(sys.stdin.readline().strip())
for ppp in range(N):
    line = sys.stdin.readline().strip()
    a,t = list(map(int, line.split()))
    cn = [0 for i in range(t+1)]
    p = power(a, t)
    number = 0
    q = factorial(t)
    print(max(p, q))