A11014 | 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.

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.

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.