Problem p02550 (python)

Fixed submission:
import sys

input = sys.stdin.buffer.readline

n, x, mod = map(int, input().split())
ans = 0
temp = x
num = 1
# while temp < mod:
#     temp *= x
#     num += 1


A = [0] * (mod + 1)

kouho = {}
if n < mod:
    A[1] = x % mod
    ans += A[1]
    for i in range(2, n + 1):
        A[i] = A[i - 1] * A[i - 1] % mod
        ans += A[i]
        # print(ans)
else:
    A[1] = x
    ans += A[1]
    kouho[A[1]] = 1
    temp = A[1]
    i = 1
    migi = 1
    for i in range(2, mod + 1):
        A[i] = temp * temp % mod
        if A[i] in kouho:
            migi = i
            break
        kouho[A[i]] = i
        temp = A[i]
    saisho = 0
    hidari = kouho[A[i]]
    saisho = sum(A[1:hidari])
    # for i in range(1, hidari):
    #     saisho += A[i]
    cycle_val = sum(A[hidari:migi])
    # cycle_val = 0
    # for i in range(hidari, migi):
    #     cycle_val += A[i]
    cycle = migi - hidari
    if cycle >= 2:

        kaisu = n // cycle
        amari = n % cycle - (hidari - 1)
        amari %= cycle
        kaisu = (n - (amari + hidari - 1)) // cycle
        amari_val = sum(A[hidari : hidari + amari])
        # amari_val = 0
        # for i in range(hidari, hidari + amari):
        #     amari_val += A[i]
        ans = saisho + cycle_val * kaisu + amari_val
    else:
        ans = 0
        if cycle == 0:
            for j in range(1, i + 1):
                ans += A[j]
        else:
            for j in range(1, i + 1):
                ans += A[j]
            ans += (n - i) * A[j]
print(ans)

Buggy submission (verdict: Runtime Error):
import sys

input = sys.stdin.buffer.readline

n, x, mod = map(int, input().split())
ans = 0
temp = x
num = 1
# while temp < mod:
#     temp *= x
#     num += 1


A = [0] * (mod + 1)

kouho = {}
if n < mod:
    A[1] = x % mod
    ans += A[1]
    for i in range(2, n + 1):
        A[i] = A[i - 1] * A[i - 1] % mod
        ans += A[i]
        # print(ans)
else:
    A[1] = x
    ans += A[1]
    kouho[A[1]] = 1
    temp = A[1]
    for i in range(2, mod + 1):
        A[i] = temp * temp % mod
        if A[i] in kouho:
            migi = i
            break
        kouho[A[i]] = i
        temp = A[i]
    saisho = 0
    hidari = kouho[A[i]]
    saisho = sum(A[1:hidari])
    # for i in range(1, hidari):
    #     saisho += A[i]
    cycle_val = sum(A[hidari:migi])
    # cycle_val = 0
    # for i in range(hidari, migi):
    #     cycle_val += A[i]
    cycle = migi - hidari
    if cycle >= 2:

        kaisu = n // cycle
        amari = n % cycle - (hidari - 1)
        amari %= cycle
        kaisu = (n - (amari + hidari - 1)) // cycle
        amari_val = sum(A[hidari : hidari + amari])
        # amari_val = 0
        # for i in range(hidari, hidari + amari):
        #     amari_val += A[i]
        ans = saisho + cycle_val * kaisu + amari_val
    else:
        ans = 0
        if cycle == 0:
            for j in range(1, i + 1):
                ans += A[j]
        else:
            for j in range(1, i + 1):
                ans += A[j]
            ans += (n - i) * A[j]
print(ans)

Buggy submission (verdict: Runtime Error):
import sys

input = sys.stdin.buffer.readline

n, x, mod = map(int, input().split())
ans = 0
temp = x
num = 1
# while temp < mod:
#     temp *= x
#     num += 1

# from kiriさん
def gcd(a, b):
    while b:
        a, b = b, a % b
    return a


def isPrimeMR(n):
    d = n - 1
    d = d // (d & -d)
    L = [2]
    for a in L:
        t = d
        y = pow(a, t, n)
        if y == 1:
            continue
        while y != n - 1:
            y = (y * y) % n
            if y == 1 or t == n - 1:
                return 0
            t <<= 1
    return 1


def findFactorRho(n):
    m = 1 << n.bit_length() // 8
    for c in range(1, 99):
        f = lambda x: (x * x + c) % n
        y, r, q, g = 2, 1, 1, 1
        while g == 1:
            x = y
            for i in range(r):
                y = f(y)
            k = 0
            while k < r and g == 1:
                ys = y
                for i in range(min(m, r - k)):
                    y = f(y)
                    q = q * abs(x - y) % n
                g = gcd(q, n)
                k += m
            r <<= 1
        if g == n:
            g = 1
            while g == 1:
                ys = f(ys)
                g = gcd(abs(x - ys), n)
        if g < n:
            if isPrimeMR(g):
                return g
            elif isPrimeMR(n // g):
                return n // g
            return findFactorRho(g)


def primeFactor(n):
    i = 2
    ret = {}
    rhoFlg = 0
    while i * i <= n:
        k = 0
        while n % i == 0:
            n //= i
            k += 1
        if k:
            ret[i] = k
        i += 1 + i % 2
        if i == 101 and n >= 2 ** 20:
            while n > 1:
                if isPrimeMR(n):
                    ret[n], n = 1, 1
                else:
                    rhoFlg = 1
                    j = findFactorRho(n)
                    k = 0
                    while n % j == 0:
                        n //= j
                        k += 1
                    ret[j] = k

    if n > 1:
        ret[n] = 1
    if rhoFlg:
        ret = {x: ret[x] for x in sorted(ret)}
    return ret


A = [0] * (mod + 1)
jisho = primeFactor(mod)
if x * primeFactor(mod)[x] == mod:
    A[1] = x % mod
    ans += A[1]
    for i in range(2, num + 1):
        A[i] = A[i - 1] * A[i - 1] % mod
        ans += A[i]
        # print(ans)
    print(ans)
    exit()

kouho = {}
if n < mod:
    A[1] = x % mod
    ans += A[1]
    for i in range(2, n + 1):
        A[i] = A[i - 1] * A[i - 1] % mod
        ans += A[i]
        # print(ans)
else:
    A[1] = x
    ans += A[1]
    kouho[A[1]] = 1
    temp = A[1]
    for i in range(2, mod + 1):
        A[i] = temp * temp % mod
        if A[i] in kouho:
            migi = i
            break
        kouho[A[i]] = i
        temp = A[i]
    saisho = 0
    hidari = kouho[A[i]]
    saisho = sum(A[1:hidari])
    # for i in range(1, hidari):
    #     saisho += A[i]
    cycle_val = sum(A[hidari:migi])
    # cycle_val = 0
    # for i in range(hidari, migi):
    #     cycle_val += A[i]
    cycle = migi - hidari
    kaisu = n // cycle
    amari = n % cycle - (hidari - 1)
    amari %= cycle
    kaisu = (n - (amari + hidari - 1)) // cycle
    amari_val = sum(A[hidari : hidari + amari])
    # amari_val = 0
    # for i in range(hidari, hidari + amari):
    #     amari_val += A[i]
    ans = saisho + cycle_val * kaisu + amari_val
print(ans)

Buggy submission (verdict: Runtime Error):
import sys

input = sys.stdin.buffer.readline

n, x, mod = map(int, input().split())
ans = 0
temp = x
num = 1
# while temp < mod:
#     temp *= x
#     num += 1


A = [0] * (mod + 1)

# if temp == mod:
#     A[1] = x % mod
#     ans += A[1]
#     for i in range(2, num + 1):
#         A[i] = A[i - 1] * A[i - 1] % mod
#         ans += A[i]
#         # print(ans)
#     print(ans)
#     exit()

kouho = {}
if n < mod:
    A[1] = x % mod
    ans += A[1]
    for i in range(2, n + 1):
        A[i] = A[i - 1] * A[i - 1] % mod
        ans += A[i]
        # print(ans)
else:
    A[1] = x
    ans += A[1]
    kouho[A[1]] = 1
    temp = A[1]
    for i in range(2, mod + 1):
        A[i] = temp * temp % mod
        if A[i] in kouho:
            migi = i
            break
        kouho[A[i]] = i
        temp = A[i]
    saisho = 0
    hidari = kouho[A[i]]
    saisho = sum(A[1:hidari])
    # for i in range(1, hidari):
    #     saisho += A[i]
    cycle_val = sum(A[hidari:migi])
    # cycle_val = 0
    # for i in range(hidari, migi):
    #     cycle_val += A[i]

    cycle = migi - hidari
    kaisu = n // cycle
    amari = n % cycle - (hidari - 1)
    amari %= cycle
    kaisu = (n - (amari + hidari - 1)) // cycle
    amari_val = sum(A[hidari : hidari + amari])
    # amari_val = 0
    # for i in range(hidari, hidari + amari):
    #     amari_val += A[i]
    ans = saisho + cycle_val * kaisu + amari_val
print(ans)