Chef and Modular Sequence

You are given an integer $A$. Let's define an infinite sequence $S(A) = A\%P, A^2\%P, A^3\%P, \ldots$, where $P = 10^8+7$ is a prime and $\%$ is the modulo operator. Let's also define a decreasing sum $D(S)$ as the sum of all elements of a sequence $S$ which are strictly smaller than all preceding elements of $S$. When $S$ is a sequence of non-negative integers, the number of such elements is c