#include <bits/stdc++.h>
#include "homecoming.h"
using namespace std;
const int MAX_N=2000000;
const int N=1000001;
long long int solve(int N, int K, int *A, int *B) {
int n=N, k=K;
cin >> n >> k;
long long a[n], b[n], pref[n];
for(int i=0; i<n; ++i) a[i] = A[i];
for(int i=0; i<n; ++i) {
b[i] = B[i];
pref[i] = b[i];
if(i) pref[i] += pref[i-1];
}
long long dp[n][2], ans=0;
dp[0][0] = -1e18;
dp[0][1] = a[0] - pref[k-1];
for(int i=1; i<n; ++i) {
dp[i][0] = max(dp[i-1][0], dp[i-1][1]);
long long val1 = dp[i-1][1] + a[i];
if((i+k-1)<n) val1 -= b[i+k-1];
long long val2 = dp[i-1][0] + a[i] - pref[min(i+k-1, n-1)] + pref[i-1];
dp[i][1] = max(val1,val2);
}
ans = max(ans, dp[n-1][1]);
ans = max(ans, dp[n-1][0]);
dp[0][1] = -1e18;
dp[0][0] = 0;
for(int i=1; i<n; ++i) {
dp[i][0] = max(dp[i-1][0], dp[i-1][1]);
long long val1 = dp[i-1][1] + a[i] - b[(i+k-1)%n];
long long val2 = dp[i-1][0] + a[i];
if((i+k-1)<n) val2 -= pref[i+k-1] - pref[i-1];
else val2 -= pref[n-1] - pref[i-1] + pref[(i+k-1)%n];
dp[i][1] = max(val1, val2);
}
ans = max(ans, dp[n-1][0]);
return ans;
}
