Indian National Olympiad in Informatics 2015
A string is any nonempty sequence of 0s and 1s. Examples of strings are 00, 101, 111000, 1, 0, 01. The length of a string is the number of symbols in it. For example, the length of 111000 is 6. If u and v are strings, then uv is the string obtained by concatenating u and v. For example if u = 110 and v = 0010 then uv = 1100010.
A string w is periodic if there exists a string v such that w = vn = vv · · · v (n times), for some n ≥ 2. Note that in this case the length of v is strictly less than that of w. For example, 110110 is periodic, because it is vv for v = 110.
Given a positive integer N , find the number of strings of length N which are not periodic. Report the answer modulo M . The non-periodic strings of length 2 are 10 and 01. The non- periodic strings of length 3 are 001, 010, 011, 100, 101, and 110.

-----Input format-----
A single line, with two space-separated integers, N and M .

-----Output format-----
A single integer, the number of non-periodic strings of length N , modulo M .

-----Test Data-----
In all subtasks, 2 ≤ M ≤ 108. The testdata is grouped into 4 subtasks.
Subtask 1 (10 marks) 1 ≤ N ≤ 4000. N is the product of two distinct prime numbers.
Subtask 2 (20 marks) 1 ≤ N ≤ 4000. N is a power of a prime number.
Subtask 3 (35 marks) 1 ≤ N ≤ 4000.
Subtask 4 (35 marks) 1 ≤ N ≤ 150000.

-----Example-----
Here is the sample input and output corresponding to the example above:

-----Sample input-----
3 176

-----Sample output-----
6

Note: Your program should not print anything other than what is specified in the output format. Please remove all diagnostic print statements before making your final submission. A program with extraneous output will be treated as incorrect!

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# cook your dish here\r\ndef offset(l, flag):\r\n    x = 0\r\n    # print(l)\r\n    for i in range(1, len(l)):\r\n        temp = []\r\n        for j in range(i):\r\n            v = getbig(l[i], l[j], fs)\r\n            if v > 1:\r\n                temp.append(v)\r\n                if flag:\r\n                    x += 2**v - 2\r\n                else:\r\n                    x -= 2**v - 2\r\n        x += offset(temp, not flag)\r\n    return x\r\n    \r\ndef getbig(v1, v2, factors):\r\n    x = 1\r\n    for f in factors:\r\n        while v1%f == 0 and v2%f == 0:\r\n            v1//=f\r\n            v2//=f\r\n            x*=f\r\n    return x\r\n    \r\ndef prime_factors(n):\r\n    i = 2\r\n    factors = set()\r\n    while i * i <= n:\r\n        if n % i:\r\n            i += 1\r\n        else:\r\n            n //= i\r\n            factors.add(i)\r\n    if n > 1:\r\n        factors.add(n)\r\n    return factors\r\n    \r\nn,m = map(int, input().split())\r\nif n == 1:\r\n    print(1)\r\nelse:\r\n    fs = prime_factors(n)\r\n    fs.discard(n)\r\n    ans = 2**n-2\r\n    temp = []\r\n    for v in fs:\r\n        v = n//v\r\n        temp.append(v)\r\n        ans -= 2**v - 2\r\n        # print(ans)\r\n    ans += offset(temp, True)\r\n    # print(fs)\r\n    print(ans%m)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13535