6 - Product of Minimums

The *beauty* of an array $A_1,A_2,\ldots,A_N$ is defined by the following formula: $$\prod\limits_{i = 1}^{N}\prod\limits_{j = i}^{N}\min(A_i,A_{i+1},\ldots,A_j).$$ You are given two integers $X$ and $P$ where $P$ is prime. You have to find an array $A$ such that - $1 \leq N \leq 2000$ - $0 \leq A_i \leq 100$ for each $i$ from $1$ to $N$ - The *beauty* of $A$ is equivalent to $X$ modulo $