#include <iostream>
#include <deque>
#include <vector>
#include <set>
using namespace std;
int const NN=2e6+10;
long long dp[NN],pre[NN],val[NN];
long long sol(deque<int>a,deque<int>b,int k)
{
int n=a.size();
pre[0]=0;
for (int i=0;i<n;i++)
pre[i+1]=pre[i]+b[i];
for (int i=0;i<n;i++)
dp[i]=-1e15;
dp[0]=a[0]-pre[k];
multiset<long long>s;
s.insert(dp[0]+pre[k]);
val[0]=dp[0]+pre[k];
long long mx=dp[0];
for (int i=1;i<n;i++)
{
if (i>k)
s.erase(s.find(val[i-k-1]));
long long sm=pre[min(n,i+k)]-pre[i];
dp[i]=mx;
if (s.size())
dp[i]=max(dp[i],*rbegin(s)-pre[i+1]);
dp[i]=dp[i]+a[i]-sm;
mx=max(mx,dp[i]);
val[i]=dp[i]+sm;
s.insert(dp[i]+sm);
}
return mx;
}
long long solve(int N, int K, int *A, int *B)
{
long long ans=0;
int n=N;
deque<int>a,b;
for (int i=0;i<n;i++)
a.push_back(A[i]),b.push_back(B[i]);
for (int i=0;i<n;i++)
{
ans=max(ans,sol(a,b,K));
a.push_back(a.front());
a.pop_front();
b.push_back(b.front());
b.pop_front();
}
return ans;
}
