P16285 [Lanqiao Cup 2026 NOI Qualifier Python A Group] Optional Numbers

Given $N$ positive integers $A_1, A_2, \dots, A_N$ and a target integer $K$. If a positive integer $X$ is a common multiple of $A_1, A_2, \dots, A_N$, then we call $X$ an optional number. Now, you need to find the smallest positive integer $P$ such that for any optional number $X$, $\text{lcm}(X, P)$ (the least common multiple of $X$ and $P$) is divisible by $K$.

The first line contains two integers $N$ and $K$. The second line contains $N$ integers $A_1, A_2, \dots, A_N$.

Output one integer, representing the smallest positive integer $P$ that satisfies the condition.

### Constraints For $20\%$ of the testdata, $1 \leq N \leq 20$, $1 \leq K, A_i \leq 10^6$. For all testdata, $1 \leq N \leq 2 \times 10^5$, $1 \leq K, A_i \leq 10^{18}$. Translated by ChatGPT 5