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++ (GCC 9.2.1) (judge verdict: Accepted)


// Problem : B - Contiguous Repainting
// Contest : AtCoder - AtCoder Grand Contest 008
// URL : https://atcoder.jp/contests/agc008/tasks/agc008_b
// Memory Limit : 256 MB
// Time Limit : 2000 ms
// Powered by CP Editor (https://github.com/cpeditor/cpeditor)

//look at my code
//my code is amazing
#include<bits/stdc++.h>
using namespace std;
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define ll long long
#define int long long
#define mod 1000000007 //998244353
#define fast  ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define f(i,n) for(ll i=0;i<n;i++)
#define fore(i, a, b) for (ll i = (ll)(a); i <= (ll)(b); ++i)
#define nl "\n"
#define trace(x) cerr<<#x<<": "<<x<<" "<<endl
#define trace2(x, y) cerr<<#x<<": "<<x<<" | "<<#y<<": "<<y<<endl
#define trace3(x, y, z) cerr<<#x<<":" <<x<<" | "<<#y<<": "<<y<<" | "<<#z<<": "<<z<<endl
#define trace4(a, b, c, d) cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<endl
#define cout1(a) cout<<a<<nl
#define cout2(a,b) cout<<a<<" "<<b<<nl
#define cout3(a,b,c) cout<<a<<" "<<b<<" "<<c<<nl
#define cout4(a,b,c,d) cout<<a<<" "<<b<<" "<<c<<" "<<d<<nl
#define vcout(v,i) cout<<v[i].fi<<" "<<v[i].se<<nl
#define x first
#define y second
#define vc vector
#define pb push_back
#define ar array
#define all(a) (a).begin(), (a).end()
#define ms(v,n,x) fill(v,v+n,x);
#define init(c,a) memset(c,a,sizeof(c))
#define pll pair<ll,ll>
#define mll map<ll,ll>
#define sll set<ll>
#define vll vector<ll>
#define vpll vector<pll>
#define maxi(a,b,c) max(a,max(b,c))
#define maxii(a,b,c,d) max(max(a,b),max(c,d))
#define mini(a,b,c) min(a,min(b,c))
#define md(a,b)  ((a%mod)*(b%mod)+mod)%mod 
#define inf 9e18
#define cases ll T;cin>>T;while(T--)
#define BLOCK 500
//const double PI = 3.141592653589793238460;
template<typename T> bool mmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool mmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
typedef std::complex<double> Complex;
typedef std::valarray<Complex> CArray;
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
// void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif

std::mt19937 rng((int) std::chrono::steady_clock::now().time_since_epoch().count());

// const int N=;

int32_t main()
{
    
	fast	
	cout << fixed << setprecision(12);
	ll n,k;
	cin>>n>>k;
	
	vll a(n+1),b(n+1),p(n+1);
	
	fore(i,1,n){
		cin>>a[i];
		p[i]=p[i-1]+a[i];
		b[i]=b[i-1]+max(0ll,a[i]);
	}
	
	ll ans=0;
	
	for(ll i=k;i<=n;i++){
		ans=max(ans, (p[i]-p[i-k]) + b[n]-(b[i]-b[i-k]));
		ans=max(ans,b[n]-(b[i]-b[i-k]));
		
	}
	
	cout<<ans;

	



    

	return 0;
    
}