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: Time Limit Exceeded)

import java.util.Scanner;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class Main {

	public static void main(final String[] args) {
		final Scanner sc = new Scanner(System.in);
		final int K = sc.nextInt();
		final int N = sc.nextInt();
		final Integer[] A = new Integer[N];
		for(int i = 0; i < N; i++) {
			A[i] = sc.nextInt();
		}
		sc.close();
		int min = Integer.MAX_VALUE;
		// Permutation.print(A);
		List<List<Integer>> list = Permutation.get(A);
		for(List<Integer> d : list) {
			int move = 0, mae = d.get(0);
			for(Integer a : d) {
				int p1 = K - a + mae;
				int p2 = Math.abs(a - mae);
				move = move + Math.min(p1, p2);
				mae = a;
			}
			// System.out.println("min=" + min + " move=" + move);
			if(move < min) min = move;
		}
		System.out.println(min);
	}
}

/**
 * 順列生成
 */
 class Permutation {

    /**
     * 順列のリストを返す
     * 
     * @param <T>
     * @param data 生成元配列
     * @return 順列リスト
     */
    public static <T> List<List<T>> get(final T[] data) {
		return permutation(data);
	}

    /**
     * 順列のリストを出力する
     * 
     * @param <T>
     * @param data 生成元配列
     */
    public static <T> void print(final T[] data) {
        int number = 0;
        for (final List<T> comb : permutation(data)) {
            System.out.println("#" + ++number + " " + Arrays.asList(comb));
        }
	}
    
    /**
     * 順列リストを作成する
     * @param <T>
     * @param data 生成元配列
     * @return 順列リスト
     */
    private static <T> List<List<T>> permutation(final T[] data) {
        final List<List<T>> result = new ArrayList<List<T>>();
		// 候補の配列
		final List<T> candidate = new ArrayList<>(Arrays.asList(data));
		// 順列の配列
		final List<T> perm = new ArrayList<>();
		permutation(candidate, perm, result);
        return result;
    }
	
    /**
     * 再帰呼び出し
     * @param <T>
     * @param candidate 候補の配列
     * @param perm 順列の配列
     * @param result 順列のリスト
     */    
    private static <T> void permutation(final List<T> candidate, final List<T> perm, final List<List<T>> result) {
		if(candidate.size() == 0) {
			result.add(perm);
		}
		for(int i = 0; i < candidate.size(); i++) {
			final List<T> p = new ArrayList<>(perm);
			final List<T> c = new ArrayList<>(candidate);
			p.add(c.get(i));
			c.remove(i);
			permutation(c, p, result);
		}
	}
}