For every positive integer $n$ the Fibonacci sequence modulo $n$ is periodic. The period depends on the value of $n$. This period is called the Pisano period for $n$, often shortened to $\pi (n)$.

Define $M(p)$ as the largest integer $n$ such that $\pi (n)=p$, and define $M(p)=1$ if there is no such $n$.
For example, there are three values of $n$ for which $\pi (n)$ equals $18$: $19,38,76$. Therefore $M(18)=76$.

Let the product function $P(n)$ be: $$P(n)=\prod _{p=1}^{n}M(p).$$ You are given: $P(10)=264$.

Find $P(1000000)mod1234567891$.