Random Numbers

Yuuka has $n$ integers $a\_1, a\_2, \dots, a\_n$, each generated uniformly and independently between $1$ and $10^{18}$, inclusive.

Yuuka chooses an integer $m$. Next, an integer $k$ is generated uniformly between $0$ and $(m - 1)$, inclusive. Then Yuuka changes every $a\_i$ to $(a\_i + k) \bmod m$. Finally, she shuffles the integers randomly. The resulting integers are $b\_1, b\_2, \ldots, b\_n$.

Given $a\_1, \dots, a\_n$ and $b\_1, \dots, b\_n$, find the values of $m$ and $k$.

The first line contains $n$ ($10^5 \le n \le 2 \cdot 10^5$).

The second line contains $n$ integers $a\_1, \dots, a\_n$, randomly generated with $1 \le a\_i \le 10^{18}$.

The third line contains $n$ integers $b\_1, \dots, b\_n$ with $0 \le b\_i < 10^{10}$.

It is guaranteed that a solution exists with $0 \le k < m \le 10^{10}$.

Print $m$ and $k$ on a single line. If several answers are possible, print any one of them.

The example in the statement only shows the format. The system tests do not include it (test 1 is a different test), because it violates the constraints.