#include "bits/stdc++.h"
#include "homecoming.h"
using namespace std;
#define intl long long
intl solve(int n, int k, int *A, int *B) {
vector <intl> a, b, pref(n);
function <intl(intl)> get=[&](intl l) {
intl r = l + k - 1;
if(r < n) return pref[r] - (l?pref[l-1]:0LL);
r %= n;
return pref[r] + (pref[n-1] - (l?pref[l-1]:0LL));
};
for(int i = 0; i < n; i ++) a.push_back(A[i]);
for(int i = 0; i < n; i ++) b.push_back(B[i]);
for(int i = 0; i < n; i ++) {
if(i) pref[i] = pref[i-1];
pref[i] += b[i];
}
intl dp[n][2];
for(int i = 0; i < n; i ++) {
for(int j = 0; j < n; j ++) dp[i][j] = -1e18;
}
dp[0][1] = a[0] - pref[k-1];
for(int i = 1; i < n; i ++) {
dp[i][0] = max(dp[i-1][1], dp[i-1][0]);
dp[i][1] = max(dp[i-1][1] + a[i] - (i + k - 1 < n ? b[i+k-1] : 0LL),
dp[i-1][0] + a[i] - (pref[min(n-1,i+k-1)] - (i ? pref[i-1] : 0LL)));
}
intl ans = max(dp[n-1][1], dp[n-1][0]);
for(int i = 0; i < n; i ++) {
for(int j = 0; j < n; j ++) dp[i][j] = -1e18;
}
dp[0][0] = 0;
for(int i = 1; i < n; i ++) {
dp[i][0] = max(dp[i-1][1], dp[i-1][0]);
dp[i][1] = max(dp[i-1][1] + a[i] - b[(i + k - 1) % n], dp[i-1][0] + a[i] - get(i));
}
ans = max({ans, dp[n-1][0], dp[n-1][1]});
return ans;
}
