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: Accepted)



import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws java.lang.Exception {
		MyScanner sc = new MyScanner();
		out = new PrintWriter(new BufferedOutputStream(System.out));

		String input[] = sc.nextLine().split(" ");
		int k = Integer.parseInt(input[0]);
		int n = Integer.parseInt(input[1]);
		int ar[] = new int[n];
		String input2[] = sc.nextLine().split(" ");
		for(int i = 0; i < n; i++)
			ar[i] = Integer.parseInt(input2[i]);
		int tour[] = new int[(2 * n) - 1];
		for(int i = 0; i < n; i++)
			tour[i] = ar[i];
		
		for(int i = 0; i < n - 1; i++)
			tour[i + n] = ar[i] + k;
		
		/*for(int i = 0; i < tour.length; i++)
			System.out.print(tour[i] + " ");
		
		System.out.println();*/
		int distance = 0;
		for(int i = 1; i < n; i++)
			distance = distance + (tour[i] - tour[i - 1]);
		//System.out.println(distance);
		int mindistance = distance;
		
		for(int i = 1; i < n; i++) {
			distance = distance - Math.abs(ar[i] - ar[i - 1]);
			distance = distance + Math.abs((tour[i + n -1] - tour[i + n -2]));
			//System.out.println(ar[i]+" : " +distance+ " ");
			mindistance = Math.min(distance, mindistance);
		}
		System.out.println(mindistance);
		out.close();
	}

	public static PrintWriter out;

	public static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

	}

}