#include <bits/stdc++.h>
#include "homecoming.h"
using namespace std;
typedef long long ll;
const int MAXN = 4e6 + 25;
ll dp[MAXN], pref_a[MAXN], pref_b[MAXN];
ll solve (int n, int k, int *A, int *B) {
for (int i = 0; i < 2 * n; i++) {
pref_a[i] = pref_b[i] = dp[i] = 0;
}
for (int i = 0; i < n; i++) {
pref_a[i] = A[i] + (i == 0 ? 0 : pref_a[i - 1]);
}
for (int i = 0; i < n + k; i++) {
pref_b[i] = B[i % k] + (i == 0 ? 0 : pref_b[i - 1]);
}
ll ret = 0, cur = 0;
for (int i = 0; i < n; i++) {
dp[i] = pref_a[i] - pref_b[i + k - 1] + cur;
if (i) dp[i] = max(dp[i], dp[i - 1]);
else dp[i] = max(dp[i], 0ll);
cur = max(cur, dp[i] - pref_a[i] + pref_b[i]);
ret = max(ret, dp[i]);
}
cur = 0;
for (int i = 0; i < n; i++) {
dp[i] = pref_a[i] - pref_b[i + k - 1] + cur;
if (i) dp[i] = max(dp[i], dp[i - 1]);
cur = max(cur, dp[i] - pref_a[i] + pref_b[i]);
}
ret = max(ret, dp[n - 1]);
return ret;
}
