#include<bits/stdc++.h>
#include "homecoming.h"
using namespace std;
using lint = long long;
const int MAXN = 4000005;
lint a[MAXN], b[MAXN], dp[MAXN];
long long solve(int N, int K, int *A, int *B){
for(int i=1; i<=N; i++){
a[i] = a[i+N] = A[i-1];
b[i] = b[i+N] = B[i-1];
}
for(int i=1; i<=2*N; i++){
a[i] += a[i-1];
b[i] += b[i-1];
}
if(K == N){
return max(0ll, a[N] - b[N]);
}
// First DP : Go across the interval
lint ans = max(0ll, a[N] - b[N]);
dp[N+1] = 0;
lint curmax = -1e18;
for(int i=N; i; i--){
dp[i] = a[N] - a[i-1] - (b[N] - b[i-1]); // [i, N]
dp[i] = max(dp[i], dp[i+1]); // Fuck it
dp[i] = max(dp[i], curmax + b[i-1] - a[i-1]);
curmax = max(curmax, dp[i] - b[i + K - 2] + a[i - 1]);
if(i + K - 2 <= N) ans = max(ans, dp[i] + a[i-1] - b[i + K - 2]);
}
dp[N+1] = 0;
curmax = -1e18;
// Second DP : Act like it never existed
for(int i=N; i; i--){
dp[i] = dp[i+1];
dp[i] = max(dp[i], curmax + b[i-1] - a[i-1]);
curmax = max(curmax, dp[i] - b[i + K - 2] + a[i - 1]);
}
ans = max(ans, dp[1]);
return ans;
}
