#include "bits/stdc++.h"
#include "homecoming.h"
using namespace std;
const long long inf = 1e17;
long long S[2000010];
long long dp[2][2000010];
long long solve(int N, int K, int *A, int *B) {
long long all = 0;
for(int i = 0; i < N; i++) {
all += A[i] - B[i];
}
long long ans = all;
long long sum = 0;
for(int i = 0; i < K; i++) {
sum += B[i];
}
for(int i = 0; i < N; i++) {
S[i] = sum;
sum += B[(i + K) % N] - B[i];
}
for(int i = 0; i < N; i++) {
dp[0][i] = 0;
dp[1][i] = -inf;
for(int j = 1; j < N; j++) {
int id = (i + j) % N;
int prev = (id + N - 1) % N;
dp[0][id] = max(dp[0][prev], dp[1][prev]);
dp[1][id] = max(dp[0][prev] + A[id] - S[id], dp[1][prev] + A[id] - B[(id + K - 1) % N]);
}
ans = max(ans, dp[0][(i + N - 1) % N]);
ans = max(ans, dp[1][(i + N - 1) % N]);
}
return ans;
}
