Problem:
Score : 300 points

Problem Statement

There is a circular pond with a perimeter of K meters, and N houses around them.

The i-th house is built at a distance of A_i meters from the northmost point of the pond, measured clockwise around the pond.

When traveling between these houses, you can only go around the pond.

Find the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Constraints

2 \leq K \leq 10^6

2 \leq N \leq 2 \times 10^5

0 \leq A_1 < ... < A_N < K

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K N
A_1 A_2 ... A_N

Output

Print the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Sample Input 1

20 3
5 10 15

Sample Output 1

10

If you start at the 1-st house and go to the 2-nd and 3-rd houses in this order, the total distance traveled will be 10.

Sample Input 2

20 3
0 5 15

Sample Output 2

10

If you start at the 2-nd house and go to the 1-st and 3-rd houses in this order, the total distance traveled will be 10.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

/**
 * C - Traveling Salesman around Lake
 * 1 周 K メートルの円形の湖があり、その周りに N 軒の家があります。
 * i 番目の家は、湖の北端から時計回りに Ai メートルの位置にあります。
 * 家の間の移動は、湖の周りに沿ってのみ行えます。
 * いずれかの家から出発して N 軒すべての家を訪ねるための最短移動距離を求めてください。
 */
public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner( System.in );
        // 湖の円周の長さ
        int k = sc.nextInt();
        // 周りの家の数
        int n = sc.nextInt();
        // 家の間のそれぞれの距離
        int[] a = new int[n];
        for( int i = 0; i < n; i++ ) {
            a[i] = sc.nextInt();
        }

        int result = 0;
        for( int i = 1; i < n; i++ ) {
//            System.out.println("a["+ i +"]:" +a[i]);
//            System.out.println("a["+ (i-1) +"]:" +a[i -1]);
            result += a[i] - a[i - 1];
        }

        System.out.println( result );

        sc.close();
    }
}