НОД на множестве чисел. Оптимизация

def nod(a, b):
  if b == 0:
    return a
  return nod(b, a%b)
 
n, k = map(int, input().split())
data = list(map(int, input().split()))
maxi = 1
for i in range(len(data)-k+1):
  nod1 = 0
  for j in range(i, i+k):
    if nod1 == 0:
      nod1 = data[j]
    nod1 = nod(data[j], nod1)
  maxi = max(nod1, maxi)
print(maxi)

from math import gcd
n, k = map(int, input().split())
*a, = map(int, input().split())
print(max(gcd(*a[i:i + k]) for i in range(n - k + 1)))

from math import gcd
n, k = map(int, input('n, k->').split())
*a, = map(int, input('arr->').split())
for i in range(k-1):
    a = [gcd(a[i],a[i+1]) for i in range(len(a)-1)]
print(max(a))

from math import gcd
 
 
def query(lo, hi):
    res = 0
    lo += n
    hi += n
    while lo <= hi:
        res = gcd(res, t[lo], t[hi])
        lo = (lo + 1) // 2
        hi = (hi - 1) // 2
    return res
 
 
n, k = map(int, input().split())
*a, = map(int, input().split())
# print(max(gcd(*a[i:i + k]) for i in range(n - k + 1)))
 
t = [0] * (n + 1) + a
 
for i in range(n - 1, 0, -1):
    t[i] = gcd(t[2 * i], t[2 * i + 1])
 
print(max(query(i + 1, i + k) for i in range(n - k + 1)))