Test data generation is not an easy task! Often, generating big random test cases is not enough to ensure thorough testing of solutions for correctness. For example, consider a problem from an old Codeforces round. Its input format looks roughly as follows: The first line contains a single integer n ( 1 ≤ n ≤ max n ) — the size of the set. The second line contains n distinct integers a 1 , a 2 , ..., a n ( 1 ≤ a i ≤ max a ) — the elements of the set in increasing order . If you don't pay attention to the problem solution, it looks fairly easy to generate a good test case for this problem. Let n = max n , take random distinct a i from 1 to max a , sort them... Soon you understand that it's not that easy. Here is the actual problem solution. Let g be the greatest common divisor of a 1 , a 2 , ..., a n . Let x = a n / g - n . Then the correct solution outputs " Alice " if x is odd, and " Bob " if x is even. Consider two wrong solutions to this problem which differ from the correct one only in the formula for calculating x . The first wrong solution calculates x as x = a n / g (without subtracting n ). The second wrong solution calculates x as x = a n - n (without dividing by g ). A test case is interesting if it makes both wrong solutions output an incorrect answer. Given max n , max a and q , find the number of interesting test cases satisfying the constraints, and output it modulo q . The only line contains three integers max n , max a and q ( 1 ≤ max n ≤ 30 000 ; max n ≤ max a ≤ 10 9 ; 10 4 ≤ q ≤ 10 5 + 129 ). Output a single integer — the number of test cases which satisfy the constraints and make both wrong solutions output an incorrect answer, modulo q . In the first example, interesting test cases look as follows: