CF818B.Permutation Game

n children are standing in a circle and playing a game. Children's numbers in clockwise order form a permutation _a_1, _a_2, ..., a__n of length n. It is an integer sequence such that each integer from 1 to n appears exactly once in it.

The game consists of m steps. On each step the current leader with index i counts out a__i people in clockwise order, starting from the next person. The last one to be pointed at by the leader becomes the new leader.

You are given numbers _l_1, _l_2, ..., l__m — indices of leaders in the beginning of each step. Child with number _l_1 is the first leader in the game.

Write a program which will restore a possible permutation _a_1, _a_2, ..., a__n. If there are multiple solutions then print any of them. If there is no solution then print -1.

有 $n$ 个孩子围成一个圆圈进行游戏。孩子们按顺时针方向编号，构成一个长度为 $n$ 的排列 $a_1,\,a_2,\,\dots,\,a_n$。这是一个整数序列，其中 $1$ 到 $n$ 中的每个整数恰好出现一次。

游戏共进行 $m$ 轮。在每一轮中，当前领导者（其位置索引为 $i$）从下一个人开始，沿顺时针方向数出 $a_i$ 个人；被数到的第 $a_i$ 个人成为新的领导者。

现给出 $l_1,\,l_2,\,\dots,\,l_m$ —— 每轮开始时领导者的位置索引。编号为 $l_1$ 的孩子是游戏的第一位领导者。

请编写一个程序，还原出一个可能的排列 $a_1,\,a_2,\,\dots,\,a_n$。若存在多个解，输出任意一个即可；若无解，则输出 $-1$。

The first line contains two integer numbers n, m (1 ≤ n, m ≤ 100).

The second line contains m integer numbers _l_1, _l_2, ..., l__m (1 ≤ l__i ≤ n) — indices of leaders in the beginning of each step.

第一行包含两个整数 $n$、$m$（$1 \leq n, m \leq 100$）。

第二行包含 $m$ 个整数 $l_1, l_2, ..., l_m$（$1 \leq l_i \leq n$）—— 每一步开始时领导者们的下标。

Print such permutation of n numbers _a_1, _a_2, ..., a__n that leaders in the game will be exactly _l_1, _l_2, ..., l__m if all the rules are followed. If there are multiple solutions print any of them.

If there is no permutation which satisfies all described conditions print -1.

输出一个由 $n$ 个数 $a_1,\,a_2,\,\dots,\,a_n$ 构成的排列，使得在遵循所有规则的前提下，游戏中的“领导者”（leaders）恰好为 $l_1,\,l_2,\,\dots,\,l_m$。若存在多个满足条件的解，输出任意一个即可。

若不存在满足上述所有条件的排列，则输出 $-1$。

Let's follow leadership in the first example:

• Child 2 starts.
• Leadership goes from 2 to 2 + _a_2 = 3.
• Leadership goes from 3 to 3 + _a_3 = 5. As it's greater than 4, it's going in a circle to 1.
• Leadership goes from 1 to 1 + _a_1 = 4.
• Leadership goes from 4 to 4 + _a_4 = 8. Thus in circle it still remains at 4.

我们来跟随第一个示例中的领导权传递过程：

• 儿童 2 首先开始。
• 领导权从 2 传递到 $2 + a_2 = 3$。
• 领导权从 3 传递到 $3 + a_3 = 5$；由于该值大于 4，因此在环中绕回至 1。
• 领导权从 1 传递到 $1 + a_1 = 4$。
• 领导权从 4 传递到 $4 + a_4 = 8$；因此在环中它仍停留在 4。