#include<bits/stdc++.h>
//#include "homecoming.h"
using namespace std;
int N1;
long long sa[2000009], sb[2000009];
long long Sb(long long l, long long r){
while(l >= N1) l -=N1;
while(r >= N1) r -=N1;
if(!l) return sb[r];
if(l <= r) return sb[r] - sb[l-1];
return sb[N1-1] - sb[l - 1] + sb[r];
}
long long Sa(long long l, long long r){
while(l >= N1) l -=N1;
while(r >= N1) r -=N1;
if(!l) return sa[r];
if(l <= r) return sa[r] - sa[l-1];
return sa[N1-1] - sa[l - 1] + sa[r];
}
long long su(long long l, long long r){
return Sa(l,r) - Sb(l,r);
}
long long M[2000009][21];
long long dp[4000009][2];
long long A1[6000009];
long long B1[6000009];
long long int solve(int N, int K, int *A, int *B){
//if(N > 1e5) return 1/0;
N1 = N;
for(long long i = 0; i < N; i++)
A1[i] = A[i],
B1[i] = B[i];
for(long long i = 0; i < 2*N; i++)
A1[i+N] = A1[i],
B1[i+N] = B1[i];
sa[0] = A1[0];
sb[0] = B1[0];
for(long long i = 1; i < N; i++)
sa[i] = sa[i-1] + A1[i],
sb[i] = sb[i-1] + B1[i];
for(int i = 0 ;i < N; i++)
M[i][0] = su(i,i);
for(long long i = 1; (1 << i) <= N; i++){
for(long long j = 0; j < N; j++){
long long m1 = M[j][i-1];
long long m2 = M[(j+(1<<(i-1)))%N][i-1];
M[j][i] = max(m2, m1 +
su(j+(1<<i-1), j+(1<<i) - 1));
}
}
long long masof = 1e18, FI = -1;
for(long long i = N; i < 2*N; i++){
long long S = A1[i] - Sb(i, i+K-1);
long long x = i, ss = 0;
for(long long L = 20; L >= 0; L--){
if(x - (1<<L) < 0) continue;
if(M[(x - (1<<L))%N][L] + ss + S >= 0) continue;
ss += su(x - (1 << L), x -1);
x = x - (1 << L);
}
int l;
if(S >= 0) l = i;
else l = x - 1;
if(l <= i - N) l = -1;
if(l != -1 && masof > i - l) {
FI = i;
masof = i - l;
}
}
if(FI == -1 || N == K) return max((long long)0, sa[N-1] - sb[N-1]);
FI -= N;
dp[FI][0] = -1e18;
dp[FI][1] = A1[FI] - Sb(FI, FI+K-1);
for(long long i = FI + 1; i < FI + N - K; i++){
dp[i][0] = max(dp[i-1][0] , dp[i-1][1]);
dp[i][1] = dp[i-1][1] + A1[i] - B1[i + K - 1];
if(i - K >= FI) dp[i][1] =max(dp[i][1],
max(dp[i - K][0] , dp[i - K][1]) +
A1[i] - Sb(i, i+K-1));
}
long long ans = max(dp[FI + N - K - 1][0], dp[FI+ N - K - 1][1]);
long long s = 0;
for(long long i = FI - 1; i > FI - N + K; i --){
s += A1[i+N] - B1[i+N];
ans =max(ans, s + max(dp[i + N - K - 1][0], dp[i + N - K - 1][1]));
}
return max(max((long long)0,ans), sa[N-1]-sb[N-1]);
return 0;
}
int a[100009], b[100009];
long long ans[100009];
main(){
/* int t;
cin>>t;
int T= t;
vector<long long >v;
for(int i = 0; i <t; i++){
cin >> ans[i];
}*/
vector<long long> v;
int t;
cin>>t;
while(t--){
long long n, K;
cin >> n >> K;
for(long long i= 0 ; i < n; i++)
cin >> a[i];
for(long long i = 0; i < n; i++){
cin >> b[i];
}
v.push_back( solve(n, K, a, b) );
cout<<v.back()<<endl;
//if(v.back() != ans[T-t-1]) cout << ans[T-t-1]<<"!!!!", cin >> n;
}
for(int i = 0; i < v.size(); i++)
cout<<v[i] <<endl;
}/*
10 3
2 3 2 3 2 4 2 6 3 2
1 2 0 8 0 2 1 2 15 0
*/
Compilation message
homecoming.cpp: In function 'long long int solve(int, int, int*, int*)':
homecoming.cpp:48:37: warning: suggest parentheses around '-' inside '<<' [-Wparentheses]
su(j+(1<<i-1), j+(1<<i) - 1));
~^~
homecoming.cpp: At global scope:
homecoming.cpp:93:6: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
main(){
^
homecoming.cpp: In function 'int main()':
homecoming.cpp:116:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for(int i = 0; i < v.size(); i++)
~~^~~~~~~~~~
/tmp/cc9BXy21.o: In function `main':
homecoming.cpp:(.text.startup+0x0): multiple definition of `main'
/tmp/ccgalzEl.o:grader.cpp:(.text.startup+0x0): first defined here
collect2: error: ld returned 1 exit status
