CF763C.Timofey and remoduling

Little Timofey likes integers a lot. Unfortunately, he is very young and can't work with very big integers, so he does all the operations modulo his favorite prime m. Also, Timofey likes to look for arithmetical progressions everywhere.

One of his birthday presents was a sequence of distinct integers _a_1, _a_2, ..., a__n. Timofey wants to know whether he can rearrange the elements of the sequence so that is will be an arithmetical progression modulo m, or not.

Arithmetical progression modulo m of length n with first element x and difference d is sequence of integers x, x + d, x + 2_d_, ..., x + (n - 1)·d, each taken modulo m.

小 Timofey 非常喜欢整数。但不幸的是，他年龄太小，无法处理非常大的整数，因此他所有的运算都在其最喜爱的质数 $ m $ 下取模。此外，Timofey 喜欢到处寻找等差数列。

他生日时收到的一件礼物是一个由互不相同的整数 $ a_1,,a_2,,\dots,,a_n $ 构成的序列。Timofey 想知道：能否重新排列该序列中的元素，使其成为一个模 $ m $ 意义下的等差数列？

模 $ m $ 意义下长度为 $ n $、首项为 $ x $、公差为 $ d $ 的等差数列，是指如下整数序列：

$$x,\;x+d,\;x+2d,\;\dots,\;x+(n-1)\cdot d,$$

其中每一项均对 $ m $ 取模。

The first line contains two integers m and n (2 ≤ m ≤ 109 + 7, 1 ≤ n ≤ 105, m is prime) — Timofey's favorite prime module and the length of the sequence.

The second line contains n distinct integers _a_1, _a_2, ..., a__n (0 ≤ a__i < m) — the elements of the sequence.

第一行包含两个整数 $m$ 和 $n$（$2 \le m \le 10^9 + 7$，$1 \le n \le 10^5$，且 $m$ 为质数）—— Timofey 最喜欢的质数模数和序列长度。

第二行包含 $n$ 个互不相同的整数 $a_1,\,a_2,\,...,\,a_n$（$0 \le a_i < m$）—— 序列的元素。

Print -1 if it is not possible to rearrange the elements of the sequence so that is will be an arithmetical progression modulo m.

Otherwise, print two integers — the first element of the obtained progression x (0 ≤ x < m) and its difference d (0 ≤ d < m).

If there are multiple answers, print any of them.

如果无法重新排列该序列的元素，使其成为模 $m$ 的等差数列，则输出 $-1$。

否则，输出两个整数：所得等差数列的首项 $x$（满足 $0 \le x < m$）及其公差 $d$（满足 $0 \le d < m$）。

若存在多个答案，输出任意一个即可。