Primes and moduli

Let $p_n$ be the $n$ th prime number (starting at 0): $p_0 = 2, p_1 = 3, p_2 = 5, p_3 = 7, \dots$ Define $r_n$ as the remainder of $\left(p_n + 1 \right) ^n + \left(p_n - 1 \right)^n$ modulo $({p_n})^2$ . For instance, $r_3 = 42$ , because $\begin{equation*} (7+1)^3 + (7-1)^3 \enspace = \enspace 512 + 216 \enspace = \enspace 728 \enspace = \enspace 14 \cdot 49 + 42 \enspace . \end{equation*}$

Given two integer numbers $a$ and $b$ , find the largest $r_i$ such that $i \in \left[ a, b \right]$ .

Input

Input consists of several cases, each one with two integer numbers $a$ and $b$ , where $0 \le a \le b$ and $p_b \le 10^7$ .

Output

For every case, print the largest $r_i$ such that $i \in \left[ a, b \right]$ .

Problem information

Author: Albert Graells

Generation: 2026-01-25T11:19:12.426Z