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.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {
	static ArrayList<Integer> adj[];
	static PrintWriter out = new PrintWriter(System.out);
	public static long mod;

	static int [][][]notmemo;
	static int k;
	static int a[];
	static int b[];
	static int m;
	static char c[];


	static class Pair implements Comparable<Pair>{
    	int x;
    	int y;
    	public Pair(int a,int b) {
		x=a;
		y=b;
		
    	}
		@Override
		public int compareTo(Pair o) {
			return x-o.x;
		}
    	
    }
    static Pair s1[];
    static int s[];
	public static void main(String args[]) throws IOException {
		Scanner sc = new Scanner(System.in);
		long k=sc.nextInt();
		int n=sc.nextInt();
		long a[]=new long[n];
		for (int i = 0; i < a.length; i++) {
			a[i]=sc.nextLong();
		}
		long min[]=new long[n];
		long minans=Long.MAX_VALUE;
		for (int i = 0; i < a.length; i++) {
			if(i==0) {
				minans=Math.min(minans,Math.min(a[n-1]-a[0], a[0]+(k-a[i+1])));
			}
			else if(i==n-1) {
				minans=Math.min(minans,Math.min(a[n-1]-a[0], a[n-2]+(k-a[i])));
					
			}
			else {
				minans=Math.min(minans,Math.min(a[i-1]+(a[n-1]-a[i]), a[i]+(k-a[i+1])));
				
			}

		
		}
	System.out.println(minans);
	}
	static boolean mini[];
	static boolean mini(int x,int count) {
		if(vis[x]) {
			return mini[x];
		}
		vis[x]=true;
		int z=a[x];
		for (int i = x+z; i<n; i+=z) {
			
			if(a[i]>a[x]&&!mini(i,(count+1)%2)) {
				return mini[x]=true;
			}
		}
		for (int i = x-z; i>=0; i-=z) {
         if(a[i]>a[x]&&!mini(i,(count+1)%2)) {
        			return mini[x]=true;
    				
			}
		}
		return mini[x]=false;
	}
    static int dp(int idx,int count,int last) {
    	if(idx==n&&count<3) {
    		return (int) 1e9;
    	}
    	if(count==3) {
    		return 0;
    	}
    	if(notmemo[idx][count][last]!=-1) {
    		return notmemo[idx][count][last];
    	}
    	int take=(int) 1e9;
    	int leave=(int) 1e9;
    
    	if(s1[idx].x>last)
    	 take=dp(idx+1,count+1,s1[idx].x)+s1[idx].y;
        leave=dp(idx+1,count,last);
    	return notmemo[idx][count][last]=Math.min(take,leave);
      }
        static void sieve(int N)	// O(N log log N) 
	{
		isComposite = new int[N+1];					
		isComposite[0] = isComposite[1] = 1;			// 0 indicates a prime number
		primes = new ArrayList<Integer>();
 
		for (int i = 2; i <= N; ++i) 					//can loop till i*i <= N if primes array is not needed O(N log log sqrt(N)) 
			if (isComposite[i] == 0) 					//can loop in 2 and odd integers for slightly better performance
			{
				primes.add(i);
				if(1l * i * i <= N)
					for (int j = i * i; j <= N; j += i)	// j = i * 2 will not affect performance too much, may alter in modified sieve
						isComposite[j] = 1;
			}   
	}
    static TreeSet<Integer> factors;
    static ArrayList<Integer> primeFactors(int N)		// O(sqrt(N) / ln sqrt(N))
	{
		ArrayList<Integer> factors = new ArrayList<Integer>();		//take abs(N) in case of -ve integers
		int idx = 0, p = primes.get(idx);

		while(1l*p * p <= N)
		{
			while(N % p == 0) { factors.add(p); N /= p; }
			p = primes.get(++idx);
		}

		if(N != 1)						// last prime factor may be > sqrt(N)
			factors.add(N);				// for integers whose largest prime factor has a power of 1
		return factors;
	}
    
    static String y;
    	static int nomnom[];
	static long fac[];
	
	static class book implements Comparable<book> {
		int idx;
		long score;

		public book(int i, long s) {
			idx = i;
			score = s;
		}

		public int compareTo(book o) {
			return (int) (o.score - score);
		}
	}

	static class library implements Comparable<library> {
		int numofbooks;
		int signup;
		int shiprate;
		int idx;

		public library(int a, int b, int c, int idx) {
			numofbooks = a;
			signup = b;
			shiprate = c;
			this.idx = idx;
		}

		@Override
		public int compareTo(library o) {
		if(signup==o.signup) {
			  return o.numofbooks-numofbooks;
		}
		return signup - o.signup;
		
		}
	}





	static boolean isOn(int S, int j) {
		return (S & 1 << j) != 0;
	}


	static boolean f = true;

	static class SegmentTree { // 1-based DS, OOP

		int N; // the number of elements in the array as a power of 2 (i.e. after padding)
		int[] array, sTree, lazy;

		SegmentTree(int[] in) {
			array = in;
			N = in.length - 1;
			sTree = new int[N << 1]; // no. of nodes = 2*N - 1, we add one to cross out index zero
			lazy = new int[N << 1];
			//build(1, 1, N);
		}

		void build(int node, int b, int e) // O(n)
		{
			if (b == e)
				sTree[node] = array[b];
			else {
				int mid = b + e >> 1;
				build(node << 1, b, mid);
				build(node << 1 | 1, mid + 1, e);
				sTree[node] = sTree[node << 1] + sTree[node << 1 | 1];
			}
		}

		void update_point(int index, int val) // O(log n)
		{
			index += N - 1;				
			sTree[index] = val;			
			while(index>1)				
			{
				index >>= 1;
				sTree[index] = Math.max(sTree[index<<1] ,sTree[index<<1|1]);		
			}
		}

		void update_range(int i, int j, int val) // O(log n)
		{
			update_range(1, 1, N, i, j, val);
		}

		void update_range(int node, int b, int e, int i, int j, int val) {
			if (i > e || j < b)
				return;
			if (b >= i && e <= j) {
				sTree[node] += (e - b + 1) * val;
				lazy[node] += val;
			} else {
				int mid = b + e >> 1;
				propagate(node, b, mid, e);
				update_range(node << 1, b, mid, i, j, val);
				update_range(node << 1 | 1, mid + 1, e, i, j, val);
				sTree[node] = sTree[node << 1] + sTree[node << 1 | 1];
			}

		}

		void propagate(int node, int b, int mid, int e) {
			lazy[node << 1] += lazy[node];
			lazy[node << 1 | 1] += lazy[node];
			sTree[node << 1] += (mid - b + 1) * lazy[node];
			sTree[node << 1 | 1] += (e - mid) * lazy[node];
			lazy[node] = 0;
		}

		int query(int i, int j) {
			return query(1, 1, N, i, j);
		}

		int query(int node, int b, int e, int i, int j) // O(log n)
		{
			if (i > e || j < b)
				return 0;
			if (b >= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			// propagate(node, b, mid, e);
			int q1 = query(node << 1, b, mid, i, j);
			int q2 = query(node << 1 | 1, mid + 1, e, i, j);
			return Math.max(q1,q2);

		}
	}

	static int memo[];


	static class UnionFind {
		int[] p, rank, setSize;
		int numSets;
		int max[];

		public UnionFind(int N) {
			p = new int[numSets = N];
			rank = new int[N];
			setSize = new int[N];
			for (int i = 0; i < N; i++) {
				p[i] = i;
				setSize[i] = 1;
			}
		}

		public int findSet(int i) {
			return p[i] == i ? i : (p[i] = findSet(p[i]));
		}

		public boolean isSameSet(int i, int j) {
			return findSet(i) == findSet(j);
		}

		public void unionSet(int i, int j) {
			if (isSameSet(i, j))
				return;
			numSets--;
			int x = findSet(i), y = findSet(j);
			if (rank[x] > rank[y]) {
				p[y] = x;
				setSize[x] += setSize[y];


			} else {
				p[x] = y;
				setSize[y] += setSize[x];
				if (rank[x] == rank[y])
					rank[y]++;


			}
		}

		

		public int numDisjointSets() {
			return numSets;
		}

		public int sizeOfSet(int i) {
			return setSize[findSet(i)];
		}
	}

	/**
	 * private static void trace(int i, int time) { if(i==n) return;
	 * 
	 * 
	 * long ans=dp(i,time);
	 * if(time+a[i].t<a[i].burn&&(ans==dp(i+1,time+a[i].t)+a[i].cost)) {
	 * 
	 * trace(i+1, time+a[i].t);
	 * 
	 * l1.add(a[i].idx); return; } trace(i+1,time);
	 * 
	 * }
	 **/

	static class incpair implements Comparable<incpair> {
		int a;
		long b;
		int idx;

		incpair(int a, long dirg, int i) {
			this.a = a;
			b = dirg;
			idx = i;
		}

		public int compareTo(incpair e) {
			return (int) (b - e.b);
		}
	}

	static class decpair implements Comparable<decpair> {
		int a;
		long b;
		int idx;

		decpair(int a, long dirg, int i) {
			this.a = a;
			b = dirg;
			idx = i;
		}

		public int compareTo(decpair e) {
			return (int) (e.b - b);
		}
	}

	static long allpowers[];

	static class Quad implements Comparable<Quad> {
		int u;
		int v;
		char state;
		int turns;

		public Quad(int i, int j, char c, int k) {
			u = i;
			v = j;
			state = c;
			turns = k;
		}

		public int compareTo(Quad e) {
			return (int) (turns - e.turns);
		}

	}

	static long dirg[][];
	static Edge[] driver;

	static int n;

	static class Edge implements Comparable<Edge> {
		int node;
		long cost;

		Edge(int a, long dirg) {
			node = a;
			cost = dirg;
		}

		public int compareTo(Edge e) {
			return (int) (cost - e.cost);
		}
	}

	static long manhatandistance(long x, long x2, long y, long y2) {
		return Math.abs(x - x2) + Math.abs(y - y2);
	}

	static long fib[];

	static long fib(int n) {
		if (n == 1 || n == 0) {
			return 1;
		}
		if (fib[n] != -1) {
			return fib[n];
		} else
			return fib[n] = ((fib(n - 2) % mod + fib(n - 1) % mod) % mod);
	}

	static class Point  implements Comparable<Point>{
		long x, y;

		Point(long counth, long counts) {
			x = counth;
			y = counts;
		}

		@Override
		public int compareTo(Point p )
		{
			return Long.compare(p.y*1l*x, p.x*1l*y);
		}
		


	}

	static long[][] comb;

	static class Triple implements Comparable<Triple> {

		int l;
		int r;
		long cost;
		int idx;

		public Triple(int a, int b, long l1, int l2) {
			l = a;
			r = b;
			cost = l1;
			idx = l2;
		}

		public int compareTo(Triple x) {
			if (l != x.l || idx == x.idx)
				return l - x.l;
			return -idx;
		}

	}

	static TreeSet<Long> primeFactors(long N) // O(sqrt(N) / ln sqrt(N))
	{
		TreeSet<Long> factors = new TreeSet<Long>(); // take abs(N) in case of -ve integers
		int idx = 0, p = primes.get(idx);

		while (p * p <= N) {
			while (N % p == 0) {
				factors.add((long) p);
				N /= p;
			}
			if (primes.size() > idx + 1)
				p = primes.get(++idx);
			else
				break;
		}

		if (N != 1) // last prime factor may be > sqrt(N)
			factors.add(N); // for integers whose largest prime factor has a power of 1
		return factors;
	}

	static boolean visited[];

	/**
	 * static int bfs(int s) { Queue<Integer> q = new LinkedList<Integer>();
	 * q.add(s); int count=0; int maxcost=0; int dist[]=new int[n]; dist[s]=0;
	 * while(!q.isEmpty()) {
	 * 
	 * int u = q.remove(); if(dist[u]==k) { break; } for(Pair v: adj[u]) {
	 * maxcost=Math.max(maxcost, v.cost);
	 * 
	 * 
	 * 
	 * if(!visited[v.v]) {
	 * 
	 * visited[v.v]=true; q.add(v.v); dist[v.v]=dist[u]+1; maxcost=Math.max(maxcost,
	 * v.cost); } }
	 * 
	 * } return maxcost; }
	 **/
	public static boolean FindAllElements(int n, int k) {
		int sum = k;
		int[] A = new int[k];
		Arrays.fill(A, 0, k, 1);

		for (int i = k - 1; i >= 0; --i) {

			while (sum + A[i] <= n) {

				sum += A[i];
				A[i] *= 2;
			}
		}
		if (sum == n) {
			return true;
		} else
			return false;
	}

	static boolean vis2[][];

	static boolean f2 = false;

	static long[][] matMul(long[][] a2, long[][] b, int p, int q, int r) // C(p x r) = A(p x q) x (q x r) -- O(p x q x
																			// r)
	{
		long[][] C = new long[p][r];
		for (int i = 0; i < p; ++i) {
			for (int j = 0; j < r; ++j) {
				for (int k = 0; k < q; ++k) {
					C[i][j] = (C[i][j] + (a2[i][k] % mod * b[k][j] % mod)) % mod;
					C[i][j] %= mod;
				}

			}
		}
		return C;
	}

	static int memo1[];

	static boolean vis[];
	static TreeSet<Integer> set = new TreeSet<Integer>();

	static long modPow(long ways, long count, long mod) // O(log e)
	{
		ways %= mod;
		long res = 1;
		while (count > 0) {
			if ((count & 1) == 1)
				res = (res * ways) % mod;
			ways = (ways * ways) % mod;
			count >>= 1;
		}
		return res % mod;
	}

	static long gcd(long ans, long b) {
		if (b == 0) {
			return ans;
		}
		return gcd(b, ans % b);
	}

	static int[] isComposite;
	static int[] valid;

	static ArrayList<Integer> primes;
	static ArrayList<Integer> l1;

	
	static TreeSet<Integer> primus = new TreeSet<Integer>();
	
	static void sieveLinear(int N)
	{
		int[] lp = new int[N + 1];								//lp[i] = least prime divisor of i
		for(int i = 2; i <= N; ++i)
		{
			if(lp[i] == 0)
			{
				primus.add(i);
				lp[i] = i;
			}
			int curLP = lp[i];
			for(int p: primus)
				if(p > curLP || p * i > N)
					break;
				else
					lp[p * i] = i;
		}
	}
	

	public static int[] schuffle(int[] p) {
		for (int i = 0; i < p.length; i++) {
			int x = (int) (Math.random() * p.length);
			int temp = p[x];
			p[x] = p[i];
			p[i] = temp;
		}
		return p;
	}

	static int V;
	static long INF = (long) 1E16;

	static class Edge2 {
		int node;
		long cost;
		long next;

		Edge2(int a, int c, Long long1) {
			node = a;
			cost = long1;
			next = c;
		}

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}

		public int[] nxtArr(int n) throws IOException {
			int[] ans = new int[n];
			for (int i = 0; i < n; i++)
				ans[i] = nextInt();
			return ans;
		}
	}
}