P15913 [TOPC 2024] In Search of the Lost Array

In a forgotten realm, a group of adventurers stumbles upon a set of mysterious scrolls hidden deep within an ancient library. These scrolls hold the secrets of a powerful numerical array that controls the magic of the realm. However, the scrolls have been damaged over time, and only fragments remain. Specifically, the adventurers discover a sequence of numbers representing the products of adjacent elements of an unknown array $A$. The original array $A$ consists of $n$ integers $a_1, a_2, \dots, a_n$ where $1 \le a_i \le 100$ for $1 \le i \le n$. The only information remaining on the scrolls is a sequence of $n-1$ integers $b_1, b_2, \dots, b_{n-1}$, which are unordered products of adjacent elements from $A$. In other words: $$ \{b_1, b_2, \dots, b_{n-1}\} = \{a_1 \times a_2, a_2 \times a_3, \dots, a_{n-1} \times a_n\} $$ Your task is to help the adventurers reconstruct one possible original array $A$. If there are multiple valid arrays $A$ that could result in the same sequence $b$, you may output any of them.

The first line contains a single integer $n$, representing the length of the array $A$. The second line contains $n-1$ space-separated integers $b_1, b_2, \dots, b_{n-1}$, representing the products of adjacent elements in the array $A$.

If there is no such array $A$, then print **No** on a line. Otherwise, print **Yes** on the first line. Then, output $n$ space-separated integers $a_1, a_2, \dots, a_n$ on the second line, where $\{b_1, b_2, \dots, b_{n-1}\} = \{a_1 \times a_2, a_2 \times a_3, \dots, a_{n-1} \times a_n\}$.

- $1 < n \le 18$. - $1 \le a_i \le 100$ for $i \in \{1, 2, \dots, n\}$ - $1 \le b_i \le 10000$ for $i \in \{1, 2, \dots, n - 1\}$