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.

Examples

Input

5 3
-10 10 -10 10 -10


Output

10


Input

4 2
10 -10 -10 10


Output

20


Input

1 1
-10


Output

0


Input

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


Output

17
import std.stdio;
import std.string;
import std.conv;
import std.typecons;
import std.algorithm;
import std.functional;
import std.bigint;
import std.numeric;
import std.array;
import std.math;
import std.range;
import std.container;
import std.ascii;
import std.concurrency;
import core.bitop : popcnt;
alias Generator = std.concurrency.Generator;

void main() {
    int N, K;
    scanln(N, K);
    long[] as = readln.split.to!(long[]);

    (N-K+1).iota.map!(
        i => as[0..i].filter!"a>=0".sum + max(0, as[i..i+K].sum) + as[i+K..$].filter!"a>=0".sum
    ).fold!max(0L).writeln;
}

// ----------------------------------------------

void scanln(Args...)(ref Args args) {
    foreach(i, ref v; args) {
        "%d".readf(&v);
        (i==args.length-1 ? "\n" : " ").readf;
    }
    // ("%d".repeat(args.length).join(" ") ~ "\n").readf(args);
}

void times(alias fun)(int n) {
    // n.iota.each!(i => fun());
    foreach(i; 0..n) fun();
}
auto rep(alias fun, T = typeof(fun()))(int n) {
    // return n.iota.map!(i => fun()).array;
    T[] res = new T[n];
    foreach(ref e; res) e = fun();
    return res;
}

// fold was added in D 2.071.0
static if (__VERSION__ < 2071) {
    template fold(fun...) if (fun.length >= 1) {
        auto fold(R, S...)(R r, S seed) {
            static if (S.length < 2) {
                return reduce!fun(seed, r);
            } else {
                return reduce!fun(tuple(seed), r);
            }
        }
    }
}

// cumulativeFold was added in D 2.072.0
static if (__VERSION__ < 2072) {
    template cumulativeFold(fun...)
    if (fun.length >= 1)
    {
        import std.meta : staticMap;
        private alias binfuns = staticMap!(binaryFun, fun);

        auto cumulativeFold(R)(R range)
        if (isInputRange!(Unqual!R))
        {
            return cumulativeFoldImpl(range);
        }

        auto cumulativeFold(R, S)(R range, S seed)
        if (isInputRange!(Unqual!R))
        {
            static if (fun.length == 1)
                return cumulativeFoldImpl(range, seed);
            else
                return cumulativeFoldImpl(range, seed.expand);
        }

        private auto cumulativeFoldImpl(R, Args...)(R range, ref Args args)
        {
            import std.algorithm.internal : algoFormat;

            static assert(Args.length == 0 || Args.length == fun.length,
                algoFormat("Seed %s does not have the correct amount of fields (should be %s)",
                    Args.stringof, fun.length));

            static if (args.length)
                alias State = staticMap!(Unqual, Args);
            else
                alias State = staticMap!(ReduceSeedType!(ElementType!R), binfuns);

            foreach (i, f; binfuns)
            {
                static assert(!__traits(compiles, f(args[i], e)) || __traits(compiles,
                        { args[i] = f(args[i], e); }()),
                    algoFormat("Incompatible function/seed/element: %s/%s/%s",
                        fullyQualifiedName!f, Args[i].stringof, E.stringof));
            }

            static struct Result
            {
            private:
                R source;
                State state;

                this(R range, ref Args args)
                {
                    source = range;
                    if (source.empty)
                        return;

                    foreach (i, f; binfuns)
                    {
                        static if (args.length)
                            state[i] = f(args[i], source.front);
                        else
                            state[i] = source.front;
                    }
                }

            public:
                @property bool empty()
                {
                    return source.empty;
                }

                @property auto front()
                {
                    assert(!empty, "Attempting to fetch the front of an empty cumulativeFold.");
                    static if (fun.length > 1)
                    {
                        import std.typecons : tuple;
                        return tuple(state);
                    }
                    else
                    {
                        return state[0];
                    }
                }

                void popFront()
                {
                    assert(!empty, "Attempting to popFront an empty cumulativeFold.");
                    source.popFront;

                    if (source.empty)
                        return;

                    foreach (i, f; binfuns)
                        state[i] = f(state[i], source.front);
                }

                static if (isForwardRange!R)
                {
                    @property auto save()
                    {
                        auto result = this;
                        result.source = source.save;
                        return result;
                    }
                }

                static if (hasLength!R)
                {
                    @property size_t length()
                    {
                        return source.length;
                    }
                }
            }

            return Result(range, args);
        }
    }
}

// minElement/maxElement was added in D 2.072.0
static if (__VERSION__ < 2072) {
    auto minElement(alias map, Range)(Range r)
    if (isInputRange!Range && !isInfinite!Range)
    {
        alias mapFun = unaryFun!map;
        auto element = r.front;
        auto minimum = mapFun(element);
        r.popFront;
        foreach(a; r) {
            auto b = mapFun(a);
            if (b < minimum) {
                element = a;
                minimum = b;
            }
        }
        return element;
    }
    auto maxElement(alias map, Range)(Range r)
    if (isInputRange!Range && !isInfinite!Range)
    {
        alias mapFun = unaryFun!map;
        auto element = r.front;
        auto maximum = mapFun(element);
        r.popFront;
        foreach(a; r) {
            auto b = mapFun(a);
            if (b > maximum) {
                element = a;
                maximum = b;
            }
        }
        return element;
    }
}
