#include "homecoming.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int len = 2e6+5;
const ll inf = 1e17;
int ar[len], br[len], n, k;
ll suf[len], sufa[len], sufb[len], mx[len], dp[len];
ll fix(int st){
for (int i = n-1; i >= 0; i--){
sufa[i] = ar[(st+i)%n] + sufa[i+1];
sufb[i] = br[(st+i)%n] + sufb[i+1];
}
mx[n] = dp[n] = suf[n] = 0;
for (int i = n-1; i >= 0; i--){
dp[i] = sufa[i]-sufb[i] + mx[i+1];
//for (int j = i+1; j <= n+1; j++)
// dp[i] = max(dp[i], sufa[i]-sufb[i] + sufb[j+k-1]-sufa[j]+suf[j]);
suf[i] = max(suf[i+1], dp[i]);
mx[i] = max(mx[i+1], sufb[i+k-1]-sufa[i]+suf[i]);
}
return dp[0];
}
void init(){
for (int i = 0; i <= 2*n; i++)
sufa[i] = sufb[i] = 0;
}
ll solve(int N, int K, int A[], int B[]){
n = N, k = K;
for (int i = 0; i < n; i++){
ar[i] = A[i];
br[i] = B[i];
}
init();
int pos = 0;
ll best = -inf;
for (int i = 2*n-1; i >= 0; i--){
sufa[i] = sufa[i+1] + ar[i%n];
sufb[i] = sufb[i+1] + br[i%n];
}
for (int i = 0; i < n; i++){
for (int j = i; j-i <= n-k+1; j++)
if (sufa[i]-sufb[i] + sufb[j+k-1]-sufa[j] > best)
best = sufa[i]-sufb[i] + sufb[j+k-1]-sufa[j], pos = i;
}
init();
return max(0LL, fix(pos));
}
/*
1
3 2
40 80 100
140 0 20
*/
