Daenerys frequently invents games to help teach her second grade Computer Science class about various aspects of the discipline. For this week’s lesson she has the children form a circle and (carefully) throw around a petrified dragon egg.

The $n$ children are numbered from $0$ to $n - 1$ (it is a Computer Science class after all) clockwise around the circle. Child $0$ always starts with the egg. Daenerys will call out one of two things:
 - a number $t$, indicating that the egg is to be thrown to the child who is $t$ positions clockwise from the current egg holder, wrapping around if necessary. If $t$ is negative, then the throw is to the counter-clockwise direction.
 - the phrase undo $m$, indicating that the last $m$ throws should be undone. Note that undo commands never undo other undo commands; they just undo commands described in item $1$ above.

For example, if there are $5$ children, and the teacher calls out the four throw commands 8 -2 3 undo 2, the throws will start from child $0$ to child $3$, then from child $3$ to child $1$, then from child $1$ to child $4$. After this, the undo 2 instructions will result in the egg being thrown back from child $4$ to child $1$ and then from child $1$ back to child $3$. If Daenerys calls out $0$ (or $n, -n, 2n, -2n$, etc.) then the child with the egg simply throws it straight up in the air and (carefully) catches it again.

Daenerys would like a little program that determines where the egg should end up if her commands are executed correctly. Don’t ask what happens to the children if this isn’t the case.

-----Input-----
Input consists of two lines. The first line contains two positive integers $n$$k$ ($1\leq n \leq 30$, $1 \leq k \leq 100$) indicating the number of students and how many throw commands Daenerys calls out, respectively. The following line contains the $k$ throw commands. Each command is either an integer $p$ ($-10000 \leq p \leq 10000$) indicating how many positions to throw the egg clockwise or undo $m$ ($m \geq 1$) indicating that the last $m$ throws should be undone. Daenerys never has the kids undo beyond the start of the game.

-----Output-----
Display the number of the child with the egg at the end of the game.

-----Examples-----
Sample Input:
5 4
8 -2 3 undo 2
Sample Output:
3

Source: kattis | Difficulty: EASY


Solutions: