Problem:
Score : 400 points

Problem Statement

There are N squares aligned in a row.
The i-th square from the left contains an integer a_i.

Initially, all the squares are white.
Snuke will perform the following operation some number of times:

Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.

After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares.
Find the maximum possible score.

Constraints

1≤N≤10^5

1≤K≤N

a_i is an integer.

|a_i|≤10^9

Input

The input is given from Standard Input in the following format:

N K
a_1 a_2 ... a_N

Output

Print the maximum possible score.

Sample Input 1

5 3
-10 10 -10 10 -10

Sample Output 1

10

Paint the following squares black: the second, third and fourth squares from the left.

Sample Input 2

4 2
10 -10 -10 10

Sample Output 2

20

One possible way to obtain the maximum score is as follows:

Paint the following squares black: the first and second squares from the left.

Paint the following squares black: the third and fourth squares from the left.

Paint the following squares white: the second and third squares from the left.

Sample Input 3

1 1
-10

Sample Output 3

0

Sample Input 4

10 5
5 -4 -5 -8 -4 7 2 -4 0 7

Sample Output 4

17

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Net;
using static System.Console;
using static System.Math;
using System.Numerics;
using CS_Contest.Graph;
using CS_Contest.Loop;
using CS_Contest.Utils;
using static Nakov.IO.Cin;
using static CS_Contest.IO.IO;

namespace CS_Contest {
	using Li = List<int>;
	using LLi = List<List<int>>;
	using Ll = List<long>;
	using ti3=Tuple<int,int,int>;
	using II=Tuple<int,int>;
	using LL=Tuple<long,long>;
	internal class Program {
		private static void Main(string[] args) {
			var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
			SetOut(sw);
			new Calc().Solve();
			Out.Flush();
		}

		public class Calc {
			public void Solve() {
				int N = NextInt(), K = NextInt();
				var A = new Li {0}.Concat(GetIntList()).ToList();
				var B = new Li {0,Max(0, A[0])};

				for (var i = 0; i < N-1; i++) {
					B.Add(B[i] + Max(0, A[i + 1]));
				}

				for (var i = 0; i < N-1; i++) {
					A[i + 1] += A[i];
				}

				A.Zip(B, (x, y) => x+y).Max().WL();

			}
		}
	}



	

}
namespace Nakov.IO {
	using System;
	using System.Text;
	using System.Globalization;

	public static class Cin {
		public static string NextToken() {
			StringBuilder tokenChars = new StringBuilder();
			bool tokenFinished = false;
			bool skipWhiteSpaceMode = true;
			while (!tokenFinished) {
				int nextChar = Console.Read();
				if (nextChar == -1) {
					tokenFinished = true;
				} else {
					char ch = (char)nextChar;
					if (char.IsWhiteSpace(ch)) {
						if (!skipWhiteSpaceMode) {
							tokenFinished = true;
							if (ch == '\r' && (Environment.NewLine == "\r\n")) {
								Console.Read();
							}
						}
					} else {
						skipWhiteSpaceMode = false;
						tokenChars.Append(ch);
					}
				}
			}

			string token = tokenChars.ToString();
			return token;
		}

		public static int NextInt() {
			string token = Cin.NextToken();
			return int.Parse(token);
		}
		public static long NextLong() {
			string token = Cin.NextToken();
			return long.Parse(token);
		}
		public static double NextDouble(bool acceptAnyDecimalSeparator = true) {
			string token = Cin.NextToken();
			if (acceptAnyDecimalSeparator) {
				token = token.Replace(',', '.');
				double result = double.Parse(token, CultureInfo.InvariantCulture);
				return result;
			} else {
				double result = double.Parse(token);
				return result;
			}
		}
		public static decimal NextDecimal(bool acceptAnyDecimalSeparator = true) {
			string token = Cin.NextToken();
			if (acceptAnyDecimalSeparator) {
				token = token.Replace(',', '.');
				decimal result = decimal.Parse(token, CultureInfo.InvariantCulture);
				return result;
			} else {
				decimal result = decimal.Parse(token);
				return result;
			}
		}

	}
}

namespace CS_Contest.Graph
{
	using Ll=List<long>;
	using Li=List<int>;

	public struct WeightedUnionFind
	{
		private readonly int N;
		public int[] Parent { get; private set; }
		public long[] Cost { get; private set; }
		public int[] Rank { get; private set; }

		public WeightedUnionFind(int n) {
			N = n;
			Parent = Enumerable.Range(0, N).ToArray();
			Cost = new long[N];
			Rank = new int[N];
		}

		public int Root(int u, out long cost) {
			if (Parent[u] == u) {
				cost = Cost[u];
				return u;
			}

			var v = Root(Parent[u], out cost);
			cost += Cost[u];
			Parent[u] = v;
			Cost[u] = cost;
			return v;
		}

		public void Unite(int lv, int rv, long cost) {
			long lc, rc;
			lv = Root(lv, out lc);
			rv = Root(rv, out rc);
			cost = -rc + cost + lc;

			if (Rank[lv] < Rank[rv]) {
				Unite(rv, lv, -cost);
				return;
			}

			Parent[rv] = lv;
			Cost[rv] = cost;
			Rank[lv] += Rank[rv] + 1;
		}

		public bool IsValid() {
			for (var i = 0; i < N; i++) {
				long _;
				Root(i, out _);
			}

			for (var i = 0; i < N; i++) {
				if (Parent[i] == i && Cost[i] != 0L) {
					return false;
				}
			}

			return true;
		}
	}

	/// <summary>
	/// UnionFind
	/// </summary>
	public struct UnionFind {
		private readonly int[] _data;

		public UnionFind(int size) {
			_data = new int[size];
			for (var i = 0; i < size; i++) _data[i] = -1;
		}

		public bool Unite(int x, int y) {
			x = Root(x);
			y = Root(y);

			if (x == y) return x != y;
			if (_data[y] < _data[x]) {
				var tmp = y;
				y = x;
				x = tmp;
			}
			_data[x] += _data[y];
			_data[y] = x;
			return x != y;
		}

		public bool IsSameGroup(int x, int y) {
			return Root(x) == Root(y);
		}

		public int Root(int x) {
			return _data[x] < 0 ? x : _data[x] = Root(_data[x]);
		}
	}
	public class BellmanFord : CostGraph {
		public BellmanFord(int size) : base(size) {
		}

		public List<long> Distance { get; set; }

		private bool[] _negative;
		public bool HasCycle => _negative[Size - 1];

		public void Run(int s) {
			Distance = new Ll();
			Size.REP(i => Distance.Add(Inf));
			Distance[s] = 0;
			_negative = new bool[Size];

			(Size - 1).REP(i => Size.REP(j => Adjacency[j].Count.REP(k =>
				{
					var src = Adjacency[j][k];
					if (Distance[src.To] > Distance[j] + src.Cost) Distance[src.To] = Distance[j] + src.Cost;
				}
			)));

			for (int i = 0; i < Size; i++) {
				Size.REP(j => {
					Adjacency[j].Count.REP(k => {
						var src = Adjacency[j][k];
						if (Distance[src.To] > Distance[j] + src.Cost) {
							Distance[src.To] = Distance[j] + src.Cost;
							_negative[src.To] = true;
						}
						if (_negative[j]) _negative[src.To] = true;
					});
				});
			}
		}
	}
	public class CostGraph {
		public struct Edge {
			public int To { get; set; }
			public long Cost { get; set; }


			public Edge(int to, long cost) {
				To = to;
				Cost = cost;
			}

		}

		public int Size { get; set; }
		public List<List<Edge>> Adjacency { get; set; }
		public const long Inf = (long)1e15;

		public CostGraph(int size) {
			Size = size;
			Adjacency = new List<List<Edge>>();
			Size.REP(_ => Adjacency.Add(new List<Edge>()));
		}

		public void Add(int s, int t, long c, bool dir = true) {
			Adjacency[s].Add(new Edge(t, c));
			if (!dir) Adjacency[t].Add(new Edge(s, c));
		}

	}

	/// <summary>
	/// 優先度付きキュー
	/// </summary>
	/// <typeparam name="T"></typeparam>
	public class PriorityQueue<T> {
		private readonly List<T> heap;
		private readonly Comparison<T> compare;
		private int size;

		public PriorityQueue() : this(Comparer<T>.Default) {
		}

		public PriorityQueue(IComparer<T> comparer) : this(16, comparer.Compare) {
		}

		public PriorityQueue(Comparison<T> comparison) : this(16, comparison) {
		}

		public PriorityQueue(int capacity, Comparison<T> comparison) {
			this.heap = new List<T>(capacity);
			this.compare = comparison;
		}

		public void Enqueue(T item) {
			this.heap.Add(item);
			var i = size++;
			while (i > 0) {
				var p = (i - 1) >> 1;
				if (compare(this.heap[p], item) <= 0)
					break;
				this.heap[i] = heap[p];
				i = p;
			}
			this.heap[i] = item;
		}

		public T Dequeue() {
			var ret = this.heap[0];
			var x = this.heap[--size];
			var i = 0;
			while ((i << 1) + 1 < size) {
				var a = (i << 1) + 1;
				var b = (i << 1) + 2;
				if (b < size && compare(heap[b], heap[a]) < 0) a = b;
				if (compare(heap[a], x) >= 0)
					break;
				heap[i] = heap[a];
				i = a;
			}
			heap[i] = x;
			heap.RemoveAt(size);
			return ret;
		}

		public T Peek() {
			return heap[0];
		}

		public int Count => size;

		public bool Any() {
			return size > 0;
		}
	}


	public class Dijkstra : CostGraph {
		public Dijkstra(int size) : base(size) { }
		public int[] PreviousNodeList { get; set; }
		public long[] Distance { get; set; }

		public void Run(int s) {
			PreviousNodeList = new int[Size];
			Distance = new long[Size];
			Size.REP(_ => Distance[_] = Inf);

			var pq = new PriorityQueue<Edge>((x, y) => x.Cost.CompareTo(y.Cost));
			Distance[s] = 0;
			pq.Enqueue(new Edge(s, 0));
			while (pq.Any()) {
				var src = pq.Dequeue();
				if (Distance[src.To] < src.Cost) continue;
				for (var i = 0; i < Adjacency[src.To].Count; i++) {
					var tmp = Adjacency[src.To][i];
					var cost = tmp.Cost + src.Cost;
					if (cost >= Distance[tmp.To]) continue;
					Distance[tmp.To] = cost;
					pq.Enqueue(new Edge(tmp.To, cost));
					PreviousNodeList[tmp.To] = src.To;
				}
			}
		}
	}


	public class WarshallFloyd : CostGraph {
		public WarshallFloyd(int size) : base(size) {
		}

		public List<Ll> Run() {
			var rt = new List<Ll>();
			Size.REP(_ => rt.Add(new Ll()));

			Size.REP(i => Size.REP(k => rt[i].Add(i == k ? 0 : Inf)));

			Adjacency.ForeachWith( (i, item) => {
				foreach (var k in item) {
					rt[i][k.To] = k.Cost;
				}
			});

			Size.REP(i => Size.REP(j => Size.REP(k => {
				rt[j][k] = Min(rt[j][k], rt[j][i] + rt[i][k]);
			})));

			return rt;
		}
	}

}

namespace CS_Contest.Loop
{
	public static class Loop
	{
		public static void REP(this int n, Action<int> act) {
			for (var i = 0; i < n; i++) {
				act(i);
			}
		}

		public static void REP(this long n, Action<long> act) {
			for (var i = 0; i < n; i++) act(i);
		}

		public static void FOR(this Tuple<int, int, int> t, Action<int> action) {
			for (var i = t.Item1; i < t.Item2; i += t.Item3) action(i);
		}

		public static void FOR(this Tuple<int, int> t, Action<int> action) =>
			new Tuple<int, int, int>(t.Item1, t.Item2, 1).FOR(action);

		public static void FOR(this Tuple<long, long, long> t, Action<long> action) {
			for (var i = t.Item1; i < t.Item2; i += t.Item3) action(i);
		}

		public static void FOR(this Tuple<long, long> t, Action<long> act) =>
			new Tuple<long, long, long>(t.Item1, t.Item2, 1).FOR(act);
	}
}

namespace CS_Contest.IO
{
	using Li = List<int>;
	using Ll = List<long>;

	public static class IO
	{
		public static void WL(this object obj) => WriteLine(obj);
		public static void WL(this string obj) => WriteLine(obj);
		public static void WL<T>(this IEnumerable<T> list) => list.ToList().ForEach(x => x.WL());

		public static Li GetIntList() => ReadLine().Split().Select(int.Parse).ToList();
		public static Ll GetLongList() => ReadLine().Split().Select(long.Parse).ToList();

		public static T Tee<T>(this T t, Func<T, string> formatter = null) {
			if (formatter == null) formatter = arg => arg.ToString();
			formatter(t).WL();
			return t;
		}
		public static void JoinWL<T>(this IEnumerable<T> @this, string sp = " ") => @this.StringJoin(sp).WL();
	}


}

namespace CS_Contest.Utils
{
	using Li=List<int>;
	using Ll=List<long>;
	public static class Utils
	{
		public static List<T> Repeat<T>(Func<int, T> result, int range) =>
			Enumerable.Range(0, range).Select(result).ToList();

		public static long[,] CombinationTable(int n) {
			var rt = new long[n + 1, n + 1];
			for (var i = 0; i <= n; i++) {
				for (var j = 0; j <= i; j++) {
					if (j == 0 || i == j) rt[i, j] = 1L;
					else rt[i, j] = (rt[i - 1, j - 1] + rt[i - 1, j]);
				}
			}
			return rt;
		}
		public static long ModValue = (long)1e9 + 7;
		public static long INF = long.MaxValue;

		public static long Mod(long x) => x % ModValue;

		public static long ModPow(long x, long n) {
			long tmp = 1; while (n != 0) { if (n % 2 == 1) { tmp = Mod(tmp * x); } x = Mod(x * x); n /= 2; }
			return tmp;
		}

		public static long DivMod(long x, long y) => Mod(x * ModPow(y, (long)(1e9 + 5)));
		public static void Add<T1, T2>(this List<Tuple<T1, T2>> list, T1 t1, T2 t2) => list.Add(new Tuple<T1, T2>(t1, t2));

		public static bool IsPrime(int n) {
			if (n == 2) return true;
			if (n < 2||n%2==0) return false;
			var i = 3;
			int sq = (int)Sqrt(n);
			while (i <= sq) {
				if (n % i == 0) return false;
				i += 2;
			}
			return true;
		}

		public static IEnumerable<int> Primes(int maxnum) {
			yield return 2;
			yield return 3;
			var sieve = new BitArray(maxnum + 1);
			int squareroot = (int)Math.Sqrt(maxnum);
			for (int i = 2; i <= squareroot; i++) {
				if (sieve[i] == false) {
					for (int n = i * 2; n <= maxnum; n += i)
						sieve[n] = true;
				}
				for (var n = i * i + 1; n <= maxnum && n < (i + 1) * (i + 1); n++) {
					if (!sieve[n])
						yield return n;
				}
			}
		}

		public static T Min<T>(params T[] a) where T : IComparable<T> => a.Min();
		public static T Max<T>(params T[] a) where T : IComparable<T> => a.Max();


		public static string StringJoin<T>(this IEnumerable<T> l, string separator = "") => string.Join(separator, l);

		public static void ForeachWith<T>(this IEnumerable<T> ie, Action<int, T> act) {
			var i = 0;
			foreach (var item in ie) {
				act(i, item);
				i++;
			}
		}

		public static void Foreach<T>(this IEnumerable<T> ie, Action<T> act) {
			foreach (var item in ie) {
				act(item);
			}
		}


		public static int ManhattanDistance(int x1, int y1, int x2, int y2) => Abs(x2 - x1) + Abs(y2 - y1);

		public static Queue<T> ToQueue<T>(this IEnumerable<T> iEnumerable) {
			var rt = new Queue<T>();
			foreach (var item in iEnumerable) {
				rt.Enqueue(item);
			}
			return rt;
		}
		public static void Swap<T>(ref T x, ref T y) {
			var tmp = x;
			x = y;
			y = tmp;
		}
		public static Dictionary<TKey, int> CountUp<TKey>(this IEnumerable<TKey> l) {
			var dic = new Dictionary<TKey, int>();
			foreach (var item in l) {
				if (dic.ContainsKey(item)) dic[item]++;
				else dic.Add(item, 1);
			}
			return dic;
		}
		public static int Count<T>(this IEnumerable<T> l, T target) => l.Count(x => x.Equals(target));

		public static IEnumerable<T> SkipAt<T>(this IEnumerable<T> @this, int at) {
			for (var i = 0; i < @this.Count(); i++) {
				if(i==at) continue;
				yield return @this.ElementAt(i);
			}
		}
	}

	public class Map<TKey, TValue> : Dictionary<TKey, TValue> {
		public Map() : base() { }
		public Map(int capacity) : base(capacity) { }

		public new TValue this[TKey index] {
			get {
				TValue v;
				return this.TryGetValue(index, out v) ? v : base[index] = default(TValue);
			}
			set { base[index] = value; }
		}
	}

}