Primes and moduli P45675

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 $i \in \left[ a, b \right]$.