# Freshman's Product (noch nicht übersetzt)

Problem 778

If $a,b$ are two nonnegative integers with decimal representations $a=(\dots a_2a_1a_0)$ and $b=(\dots b_2b_1b_0)$ respectively, then the freshman's product of $a$ and $b$, denoted $a\boxtimes b$, is the integer $c$ with decimal representation $c=(\dots c_2c_1c_0)$ such that $c_i$ is the last digit of $a_i\cdot b_i$.
For example, $234 \boxtimes 765 = 480$.

Let $F(R,M)$ be the sum of $x_1 \boxtimes \dots \boxtimes x_R$ for all sequences of integers $(x_1,\dots,x_R)$ with $0\leq x_i \leq M$.
For example, $F(2, 7) = 204$, and $F(23, 76) \equiv 5870548 \pmod{ 1\,000\,000\,009}$.

Find $F(234567,765432)$, give your answer modulo $1\,000\,000\,009$