#include <bits/stdc++.h>
#include "homecoming.h"
using namespace std;
long long pref[2000010];
int n, k;
long long sup(int i)
{
if(i + k - 1 < n)
return (pref[i + k - 1] - (i == 0 ? 0 : pref[i - 1]));
return pref[n - 1] - pref[i - 1] + pref[k - (n - i) - 1];
}
long long f(int i, int x, int y, int arri, int barri)
{
if(x == 0)
return 0ll;
if(y == 0)
return (arri - sup(i));
return arri - barri;
}
long long f2(int i, int x, int y, int arri, int barri)
{
if(y == 0)
return 0ll;
if(x == 0)
return (arri - sup(i));
return arri - barri;
}
long long solve(int N, int K, int *A, int *B)
{
n = N, k = K;
if(K == 1)
{
long long sum = 0;
for(int i = 0; i < N; i++)
sum += ((int) max(0, A[i] - B[i]));
return sum;
}
pref[0] = B[0];
for(int i = 1; i < N; i++)
pref[i] = pref[i - 1] + B[i];
long long dp1[N][2][2], dp2[N][2][2];
for(int i = 0; i < N; i++)
{
for(int k2 = 0; k2 < 2; k2++)
dp1[i][k2][0] = dp1[i][k2][1] = dp2[i][k2][0] = dp2[i][k2][1] = -1e15;
}
dp1[N - 1][0][0] = 0ll;
dp1[N - 1][1][1] = A[N - 1] - sup(N - 1);
for(int i = N - 2; i >= 0; i--)
{
for(int p = 0; p < 2; p++)
{
for(int z = 0; z < 2; z++)
{
for(int h = 0; h < 2; h++)
dp1[i][p][z] = max(dp1[i][p][z], dp1[i + 1][h][z] + f(i, p, h, A[i], B[i]));
}
}
}
// for(int i = 0; i < N; i++)
// {
// for(int p = 0; p < 2; p++)
// cout << dp1[i][p][0] << ' ' << dp1[i][p][1] << ' ';
// cout << '\n';
// }
// exit(0);
dp2[0][0][0] = 0;
dp2[0][1][1] = A[0] - sup(0);
for(int i = 1; i < N; i++)
{
for(int p = 0; p < 2; p++)
{
for(int z = 0; z < 2; z++)
{
for(int h = 0; h < 2; h++)
dp2[i][p][z] = max(dp2[i][p][z], dp2[i - 1][p][h] + f2(i, h, z, A[i], B[(i + k - 1) % n]));
}
}
}
long long mx = 0;
for(int i = 0; i < N; i++)
mx += (A[i] - B[i]);
mx = max({mx, dp1[0][0][0], dp1[0][0][1]});
for(int i = 1; i < N; i++)
{
int j = i - 1;
for(int h = 0; h < 2; h++)
{
for(int z = 0; z < 2; z++)
{
for(int p = 0; p < 2; p++)
{
long long res = dp1[i][0][h] + dp2[j][z][p];
if(h && z && K > 1)
res = res + pref[K - 2];
mx = max(mx, res);
}
}
}
}
return mx;
}
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