Periodic Strings

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 = v^{n }= 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 nonperiodic 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 spaceseparated integers, N and M .
Output format
A single integer, the number of nonperiodic strings of length N , modulo M .
Test Data
In all subtasks, 2 ≤ M ≤ 10^{8}. 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!
Author:  admin3 
Date Added:  2012016 
Time Limit:  3 sec 
Source Limit:  50000 Bytes 
Languages:  C, C99 strict, CPP 4.3.2, CPP 4.9.2, CPP14, JAVA, PYTH, PYTH 3.4 
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