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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using dbl = double;
using pii = pair<int, int>;
using pl4 = pair<ll, ll>;
using vi = vector<int>;
using vvi = vector<vi>;
using vs = vector<string>;
using vvs = vector<vs>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using vpii = vector<pii>;
using vvpii = vector<vpii>;
using vpl4 = vector<pl4>;
using vvpl4 = vector<vpl4>;
using vd = vector<dbl>;
using vvd = vector<vd>;

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define pob pop_back()
#define sz size()
#define be begin()
#define en end()
#define asn assign
#define emp empty()
#define ft front()
#define bk back()
#define clr clear()
#define ins insert
#define ers erase
#define res resize
#define tp top()

#define p_q priority_queue

#define FOR(i,a,b) for(int i=(a);i<=(b);i++)
#define rFOR(i,a,b) for(int i=(b);i>=(a);i--)
#define ROR(v,i) for(auto &(i):(v))
#define SORT(a) sort((a).be,(a).en)
#define rSORT(a) sort((a).rbegin(),(a).rend())
#define UNIQUE(a) (a).erase(unique((a).be,(a).en),(a).en)
#define PREVP(a) prev_permutation((a).be,(a).en)
#define NEXTP(a) next_permutation((a).be,(a).en)
#define BINS(a,b) binary_search((a).be,(a).en,(b))
#define LOWB(a,b) (lower_bound((a).be,(a).en,(b))-(a).be)
#define UPB(a,b) (upper_bound((a).be,(a).en,(b))-(a).be)
#define CNT(a,b) count((a).be,(a).en,b)
#define SUM(a) accumulate((a).be,(a).en,0)
#define REV(a) reverse((a).be,(a).en)
#define REGS(a,b) regex_search((a),regex(b))
#define REGM(a,b) regex_match((a),regex(b))
#define yn(a) cout <<((a)?"yes":"no")<<endl;
#define Yn(a) cout <<((a)?"Yes":"No")<<endl;
#define YN(a) cout <<((a)?"YES":"NO")<<endl;
#define say(a) cout <<(a);
#define sal(a) cout <<(a)<<endl;
#define sas cout <<" ";
#define sak cout <<endl;
#define dbg(a) cout <<(#a)<<": "<<(a)<<endl;
#define c2l(a) ((ll)(a-48))
#define a2l(a) ((ll)(a-97))
#define A2l(a) ((ll)(a-65))
#define l2c(a) ((char)(a+48))
#define l2a(a) ((char)(a+97))
#define l2A(a) ((char)(a+65))
#define DigN2(a) ((llabs(a)==0)?(1):((ll)(log2(double(llabs(a))))+1))
#define DigN10(a) ((llabs(a)==0)?(1):((ll)(log10(double(llabs(a))))+1))
#define Dig2(a,b) (((a)>>(b))&1)
#define Dig10(a,b) (ll)(((a)/((ll)(pow(10.0,(double)(b)))))%10)
#define Pow2(a) (1<<(a))
#define Pow10(a) ((ll)(pow(10.0,double(a))))
#define llin(a) ll (a);cin >>(a);
#define stin(a) string (a);cin >>(a);
#define vin(v) ROR((v),(i)){cin >>(i);};
#define vllin(v,N) vll (v)((N));vin(v);
#define vsin(v,N) vs (v)((N));vin(v);
#define rdn(a,b) ((a)/(b))
#define rou(a,b) ((((double(a)/double(b))-((a)/(b)))<0.5)?((a)/(b)):(((a)/(b))+1))
#define rup(a,b) ((((a)%(b))==0)?((a)/(b)):(((a)/(b))+1))
#define min(a,b) ((a<b)?(a):(b))
#define max(a,b) ((a>b)?(a):(b))
#define powll(a,b) (ll)(pow((double)(a),(double)(b)))
#define Triangle(x1,y1,x2,y2,x3,y3) (((x1)-(x2))*((y1)-(y3))-((x1)-(x3))*((y1)-(y2)))

#define int ll

const ll MOD = 1e9 + 7;
//const ll MOD = 998244353;
//const ll MOD = 9007199254740881;
const ll INF = 1LL << 60;
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

ll gcd(ll a, ll b) { if (b == 0)return a; return gcd(b, a%b); }
ll lcm(ll a, ll b) { return a / gcd(a, b)*b; }

pl4 Bezout(ll a, ll b) {
	if (b != 0) {
		pl4 xy;
		xy = Bezout(b, a%b);
		return mp(xy.se, xy.fi - ((a / b)*xy.se));
	}
	if (b == 0) {
		return mp(1, 0);
	}
}
pl4 Bez(ll a, ll b, ll c) {
	pl4 xy;
	ll x, y, z, gc;
	xy = Bezout(a, b);
	gc = gcd(a, b);
	if (c%gc != 0) return mp(-1, -1);
	x = xy.fi*(c / gc); y = xy.se*(c / gc);
	if (x < 0) z = rup(-x, (b / gc));
	if (x >= 0) z = -x / (b / gc);
	x += z * (b / gc);
	y -= z * (a / gc);
	return mp(x, y);
}

void salv(vll v) {
	say("{");
	FOR(i, 0, v.sz - 1) {
		say(v[i]);
		if (i != v.sz - 1) say(",");
	}
	sal("}")
}

ll DigS10(ll n) {
	ll m = 0;
	FOR(i, 0, DigN10(n) - 1) {
		m += (ll)((llabs(n) % (ll)(pow(10.0, (double)(i + 1)))) / (ll)(pow(10.0, (double)i)));
	}
	return m;
}

ll isP(ll n) {
	if (n <= 1) return 0;
	FOR(i, 2, (ll)sqrt(n)) {
		if (n%i == 0) return 0;
	}
	return 1;
}

vll FactM(1, 1);
vll FactMI(1, 1);

ll PowM(ll a, ll b) {
	ll ans = 1, x = (a%MOD);
	FOR(i, 0, DigN2(b) - 1) {
		if (Dig2(b, i) == 1) ans = (ans*x) % MOD;
		if (i != (DigN2(b) - 1)) x = (x*x) % MOD;
	}
	return ans;
}

void CFactM(ll n) {
	if (FactM.sz <= n) {
		FOR(i, FactM.sz, n) {
			FactM.pb((FactM[i - 1] * (i%MOD)) % MOD);
		}
	}
	return;
}

void CFactMI(ll n) {
	CFactM(n);
	if (FactMI.sz < (n + 1)) FactMI.res(n + 1, -1);
	if (FactMI[n] == -1) FactMI[n] = PowM(FactM[n], MOD - 2);
	rFOR(i, 1, n - 1) {
		if (FactMI[i] != -1) break;
		FactMI[i] = ((FactMI[i + 1] * ((i + 1) % MOD)) % MOD);
	}
	return;
}

ll CombM(ll n, ll k) {
	if ((n < 0) || (k < 0)) return 0;
	if (n < k) return 0;
	if (n + 1 > FactMI.sz) CFactMI(n);
	return ((((FactMI[k] * FactMI[n - k]) % MOD)*FactM[n]) % MOD);
}

signed main() {

	ll N, K;
	cin >> N >> K;
	ll msum = 0;
	ll asum = 0;
	ll sum = 0;
	ll minmax = -INF;
	ll maxmin = INF;
	vll a(N);
	FOR(i, 0, N - 1) {
		cin >> a[i];
		if (a[i] > 0) sum += a[i];
		msum += min(0, a[i]);
		asum += max(0, a[i]);
		if (i >= K) {
			msum -= min(0, a[i - K]);
			asum -= max(0, a[i - K]);
			minmax = max(minmax, msum);
			maxmin = min(maxmin, asum);
		}
	}
	if (N == K) minmax = maxmin = 0;
	sal(max(sum + minmax,sum - maxmin));

}