Area

A square field has been divided into $N^2$ rectangular plots by drawing $(N-1)$ vertical and $(N-1)$ horizontal lines. The rows of plots are numbered $1 \ldots N$ from bottom to top, and the columns are numbered $1 \ldots N$ from left to right, as shown in the figures below. The figures are not to scale.

The plots at the intersection of the $i$-th column and the $i$-th row ($1 \le i \le N$) form the long diagonal. The plots at the intersection of the $(i+1)$-st column and the $i$-th row ($1 \le i \le N-1$) form the short diagonal.

You know the areas of the plots on both diagonals. Find the area of the plot at the intersection of the $X$-th column and the $Y$-th row.

The first line contains an integer $N$ ($2 \le N \le 1\,000$).

The second line contains $N$ integers $A_1, A_2, \dots, A_N$ ($1 \le A_i \le 10^9$), the areas of the plots on the long diagonal.

The third line contains $N-1$ integers $B_1, B_2, \dots, B_{N-1}$ ($1 \le B_i \le 10^9$), the areas of the plots on the short diagonal.

The fourth line contains two integers $X$ and $Y$ ($1 \le X, Y \le N$), the coordinates of the plot whose area you need.

Let $S$ be the area of the plot. Print $S$ as a list of lines, each with two integers $P_i$ and $S_i$. Each $P_i$ is a distinct prime, and each $S_i$ is a non-zero integer, such that $S = P_1^{S_1} \cdot P_2^{S_2} \cdot \ldots \cdot P_k^{S_k}$, where $k$ is the number of lines. List the lines in increasing order of $P_i$.

If $S = 1$, print a single line "1 1".