Given an odd prime $p$, put the numbers $1,...,p-1$ into $\frac{p-1}{2}$ pairs such that each number appears exactly once. Each pair $(a,b)$ has a cost of $abmodp$. For example, if $p=5$ the pair $(3,4)$ has a cost of $12mod5=2$.

The total cost of a pairing is the sum of the costs of its pairs. We say that such pairing is optimal if its total cost is minimal for that $p$.

For example, if $p=5$, then there is a unique optimal pairing: $(1,2),(3,4)$, with total cost of $2+2=4$.

The cost product of a pairing is the product of the costs of its pairs. For example, the cost product of the optimal pairing for $p=5$ is $2\cdot 2=4$.

It turns out that all optimal pairings for $p=2000000011$ have the same cost product.

Find the value of this product.