Problem p02550 (python)

Fixed submission:
"""MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMWO:,'..'xXWWMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMO. .:kOo.,kNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMO. .lNWWo..lXMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MNOxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxMMMMWKxoloxKWNc  .:xxd;  ,dxxxkXMXkxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxMM
MKc''''''''''''''''.  ..'''''.   .''''.  .''MMMWx..,:. .xXo''.  .''.  ..'';kMk;'''''.  .'.''.  .''''''.  ..''.   .''MM
MWNXNNNNNNNNNNNNNNNO' ;KNNNNNKo. cKNNNd. lXNMMMK; ,0Wx. :NWXXl .dNNO' ;KNNNWMWNNNNNXc .kNNNNx. cXNNNNNO' ;KNN0; 'ONNMM
MMMMMMMMMMMMMMMMMWM0' :NMMMMWMX: .OMWWx. oWMMMMWx. ';. .dNMWWo .xMM0' :NWWMMMMMMMMWWl .OMMMWk. lWWMMWM0' ;XMMX: ,KMMMM
MMMMMMWMWkccccccccc;. :NMWNNNKd. :XMMWx. oWMMMWKo. .',. .,ldx; .dMM0' :NMMMMMMMNNWMWl .OMMMWk. lWMMMMM0' ;XMMX: ,0MMMM
MMWXKNWMWxcc,. .;cc;. :XMk,''..'lKWMMWx. oWMNx:. .lONNKxl.     .xMM0' :NMMMMMM0:,oKO' ,KMMMMk. lWWNkoc,. .;::;. ,KMMMM
MMXc.lXMMWWWNd..xWM0' :NM0;  ;kXWMMMWNl  oWMK:.;xXWWMWXx:. ,c' .dMM0' :NMMMMMMKc. ...;kWMMMMk. lWWc .:;. .clc:. ,KMMMM
MWWx. lXMWMMMK, lWM0' :NMMNx'.,ldxxoc'   oWMWNKNWWWN0o' .:kNWo .dMM0' :NMMMMMMMNO;  ,OWWWMMMk. lWM' lXx. lNMMX: ,KMMMM
MMMWk'.,xKNX0c..kWM0' :NMMMMNkl;,'',:l:  oWMMMMMWMWO' 'l0WMWWo .xMM0' :NMMMMMMMMMNd. .oXWMMMk. lWMd.....;0WMMX: ,KMMMM
MMMMWKo'...'..:kWMM0' :NMMMMMMMWWNNWWWx. oWMMMMMMMMWOxXWMWMWWo .xMM0' :NMMMMMMMMMMMKl. ,kNMMk. lWMWKkxx0NMWMMX: ,KMMMM
MMMMMMMN0kxk0XNWMMWKl;xNMMMMMMMMMMMMWM0c;kWMMMMMMMMMMMWWMMMMWk;:OMMXl,dNMMMMMMMMMMMMWO; .dNM0c;kWWMMMMMMMMMMMNd,oXMMMM
MMMMMMMMWWMWMMMMMMMMMWWMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMWWMMWWMMWMMMMMMMMMMMMMMNkxKWMMWWMMMMMMMMMMMMMMWMMWMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM"""


#				 Author: Udit "luctivud" Gupta @ https://www.linkedin.com/in/udit-gupta-1b7863135/					 #


import math;   		from collections import *
import sys;   		from functools import reduce
import time;   		from itertools import groupby

# sys.setrecursionlimit(10**6)

# def input()         : return sys.stdin.readline()
def get_ints()      : return map(int, input().strip().split())
def get_list()      : return list(get_ints())
def get_string()    : return list(input().strip().split())
def printxsp(*args) : return print(*args, end="")
def printsp(*args)  : return print(*args, end=" ")


DIRECTIONS = [(+0, +1), (+0, -1), (+1, +0), (+1, -1)] 
NEIGHBOURS = [(-1, -1), (-1, +0), (-1, +1), (+0, -1),\
              (+1, +1), (+1, +0), (+1, -1), (+0, +1)]



# MAIN >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

# se = set()
# n = 16; x = 2; m = 1001
# for i in range(n):
# 	print(x % m, i)
# 	if (x % m) in se:
# 		print(x % m, i)
# 	else:
# 		se.add(x % m)
# 	x **= 2;
# 	x %= m


n, x, m = get_ints()
prefix_sum = [0]
found = set()
d = dict()
ind = 0; doneInd = 1;
for i in range(n):
	if (x % m) not in found:
		found.add(x % m)
		d[x % m] = i
		prefix_sum.append(prefix_sum[-1] + (x % m))
	else:
		ind = d[x % m]
		doneInd = i
		break
	x **= 2
	x %= m
# print(ind, doneInd, prefix_sum[ind])
# print(prefix_sum)
# print(prefix_sum)

try:
	lastset = prefix_sum[-1] - prefix_sum[ind];
	offset = prefix_sum[ind]

	sz = len(prefix_sum) - ind - 1

	rem = n - ind
	ans = offset
	ans += lastset * (rem // sz)
	ans += prefix_sum[ind + (rem % sz)] - offset
# print(sz, lastset, rem)
except:
	ans = 1

print(ans)

Buggy submission (verdict: Runtime Error):
"""MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMWO:,'..'xXWWMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMO. .:kOo.,kNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMO. .lNWWo..lXMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MNOxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxMMMMWKxoloxKWNc  .:xxd;  ,dxxxkXMXkxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxMM
MKc''''''''''''''''.  ..'''''.   .''''.  .''MMMWx..,:. .xXo''.  .''.  ..'';kMk;'''''.  .'.''.  .''''''.  ..''.   .''MM
MWNXNNNNNNNNNNNNNNNO' ;KNNNNNKo. cKNNNd. lXNMMMK; ,0Wx. :NWXXl .dNNO' ;KNNNWMWNNNNNXc .kNNNNx. cXNNNNNO' ;KNN0; 'ONNMM
MMMMMMMMMMMMMMMMMWM0' :NMMMMWMX: .OMWWx. oWMMMMWx. ';. .dNMWWo .xMM0' :NWWMMMMMMMMWWl .OMMMWk. lWWMMWM0' ;XMMX: ,KMMMM
MMMMMMWMWkccccccccc;. :NMWNNNKd. :XMMWx. oWMMMWKo. .',. .,ldx; .dMM0' :NMMMMMMMNNWMWl .OMMMWk. lWMMMMM0' ;XMMX: ,0MMMM
MMWXKNWMWxcc,. .;cc;. :XMk,''..'lKWMMWx. oWMNx:. .lONNKxl.     .xMM0' :NMMMMMM0:,oKO' ,KMMMMk. lWWNkoc,. .;::;. ,KMMMM
MMXc.lXMMWWWNd..xWM0' :NM0;  ;kXWMMMWNl  oWMK:.;xXWWMWXx:. ,c' .dMM0' :NMMMMMMKc. ...;kWMMMMk. lWWc .:;. .clc:. ,KMMMM
MWWx. lXMWMMMK, lWM0' :NMMNx'.,ldxxoc'   oWMWNKNWWWN0o' .:kNWo .dMM0' :NMMMMMMMNO;  ,OWWWMMMk. lWM' lXx. lNMMX: ,KMMMM
MMMWk'.,xKNX0c..kWM0' :NMMMMNkl;,'',:l:  oWMMMMMWMWO' 'l0WMWWo .xMM0' :NMMMMMMMMMNd. .oXWMMMk. lWMd.....;0WMMX: ,KMMMM
MMMMWKo'...'..:kWMM0' :NMMMMMMMWWNNWWWx. oWMMMMMMMMWOxXWMWMWWo .xMM0' :NMMMMMMMMMMMKl. ,kNMMk. lWMWKkxx0NMWMMX: ,KMMMM
MMMMMMMN0kxk0XNWMMWKl;xNMMMMMMMMMMMMWM0c;kWMMMMMMMMMMMWWMMMMWk;:OMMXl,dNMMMMMMMMMMMMWO; .dNM0c;kWWMMMMMMMMMMMNd,oXMMMM
MMMMMMMMWWMWMMMMMMMMMWWMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMWWMMWWMMWMMMMMMMMMMMMMMNkxKWMMWWMMMMMMMMMMMMMMWMMWMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM"""


#				 Author: Udit "luctivud" Gupta @ https://www.linkedin.com/in/udit-gupta-1b7863135/					 #


import math;   		from collections import *
import sys;   		from functools import reduce
import time;   		from itertools import groupby

# sys.setrecursionlimit(10**6)

# def input()         : return sys.stdin.readline()
def get_ints()      : return map(int, input().strip().split())
def get_list()      : return list(get_ints())
def get_string()    : return list(input().strip().split())
def printxsp(*args) : return print(*args, end="")
def printsp(*args)  : return print(*args, end=" ")


DIRECTIONS = [(+0, +1), (+0, -1), (+1, +0), (+1, -1)] 
NEIGHBOURS = [(-1, -1), (-1, +0), (-1, +1), (+0, -1),\
              (+1, +1), (+1, +0), (+1, -1), (+0, +1)]



# MAIN >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

# se = set()
# n = 16; x = 2; m = 1001
# for i in range(n):
# 	print(x % m, i)
# 	if (x % m) in se:
# 		print(x % m, i)
# 	else:
# 		se.add(x % m)
# 	x **= 2;
# 	x %= m


n, x, m = get_ints()
prefix_sum = [0]
found = set()
d = dict()
ind = 1; doneInd = 1;
for i in range(n):
	if (x % m) not in found:
		found.add(x % m)
		d[x % m] = i
		prefix_sum.append(prefix_sum[-1] + (x % m))
	else:
		ind = d[x % m]
		doneInd = i
		break
	x **= 2
	x %= m
# print(ind, doneInd, prefix_sum[ind])
# print(prefix_sum)
# print(prefix_sum)

lastset = prefix_sum[-1] - prefix_sum[ind];
offset = prefix_sum[ind]

sz = len(prefix_sum) - ind - 1

rem = n - ind
ans = offset
ans += lastset * (rem // sz)
ans += prefix_sum[ind + rem % sz] - offset
# print(sz, lastset, rem)

print(ans)