Modulo Fermat's Theorem
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## Math, Number Theory, Number theory

Problem
Editorial
Analytics

It is well-known that the equation: $x^k + y^k = z^k$ has no positive solution for $k \ge 3$. But what if we consider solution over a finite field. Now, the task you are given is related to that:

Given a prime $P$, you are asked to count the number of positive integers $k$ doesn't exceed $L$ s.t. modulo equation $x^k + y^k = z^k\ (modulo\ P)$ has solution $0 < x, y, z < P$.

Input Format

A line contains two space-separated integers $P, L$ as described above.

Output Format

Output answer in a single line.

Constraints

• $1 \le P \le 10^6$
• $1 \le L \le 10^{18}$

SAMPLE INPUT
5 4

SAMPLE OUTPUT
2

Explanation

Let's enumerate all possible values of $k$:

• $k = 1:$ there is a solution $(x, y, z) = (1, 1, 2)$.
• $k = 2:$ there is no solution.
• $k = 3:$ this is a solution $(x, y, z) = (1, 3, 2)$.
• $k = 4:$ there is no solution.

So, answer is $2$.

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

## This Problem was Asked in

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