#include <bits/stdc++.h>
#include "homecoming.h"
using namespace std;
long long first_forced(int n, int k, int *a, int *b){
long long mx, cur, cost, nxtcost;
cost = accumulate(b, b + k, 0ll);
mx = cur = a[0] - cost;
for(int i = 1; i < n; i++){
cost -= b[i - 1];
nxtcost = i + k - 1 < n ? b[i + k - 1] : 0;
cur = max(cur + a[i] - nxtcost, mx + a[i] - (cost + nxtcost));
mx = max(mx, cur);
cost += nxtcost;
}
return mx;
}
long long first_not_forced(int n, int k, int *a, int *b){
long long mx, cur, cost, nxtcost;
cost = accumulate(b, b + k, 0ll);
mx = max(0ll, a[0] - cost);
cur = a[0] - cost;
for(int i = 1; i < n; i++){
cost -= b[i - 1];
nxtcost = i + k - 1 < n ? b[i + k - 1] : b[i + k - 1 - n];
cur = max(cur + a[i] - nxtcost, mx + a[i] - (cost + nxtcost));
mx = max(mx, cur);
cost += nxtcost;
}
return mx;
}
long long solve(int n, int k, int *a, int *b){
return max(first_forced(n, k, a, b), first_not_forced(n, k, a, b));
}
