Xenia and Ringroad

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Codeforces

Easy

Arrays

Math

Xenia and Ringroad

Compute the total time needed to visit a sequence of houses on a circular ring road.

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Codeforces 339B

gfg

Primary

Problem Statement

A ring road has houses numbered from $1 $to$ n $in clockwise order. Xenia starts at house \$ 1$ and needs to visit a given sequence of houses in order.

Moving from one house to the next adjacent house takes one unit of time. Because the road is circular, after house $n$ comes house $1$.

Your task is to determine the total time required for Xenia to complete the entire sequence of visits.

Task

Given the number of houses and the list of houses to visit, simulate the movement along the ring road and sum the distances traveled for each step.

Input Format

The first line contains two integers $n$ and $m$ — the number of houses on the ring road and the number of houses to visit.
The second line contains $m$ integers $a_1, a_2, \dots, a_m$ — the sequence of houses Xenia must visit in order.

Output Format

Print one integer: the total time needed to visit all houses in the given order.

Constraints

$1 \le n, m \le 10^5$
$1 \le a_i \le n$
Xenia starts at house $1$

Examples

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Example 1

Input

4 3
3 2 3

Output

Explanation

Start at 1.

Go to 3: 2 steps.
Go to 2: 3 steps (3 -> 4 -> 1 -> 2).
Go to 3: 1 step. Total = 6.

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