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// Hacker Cup 2017
// Round 3
// Pie Packages
// Jacob Plachta
#include <algorithm>
#include <functional>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <sstream>
using namespace std;
#define LL long long
#define LD long double
#define PR pair<int,int>
#define Fox(i,n) for (i=0; i<n; i++)
#define Fox1(i,n) for (i=1; i<=n; i++)
#define FoxI(i,a,b) for (i=a; i<=b; i++)
#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
#define FoxR1(i,n) for (i=n; i>0; i--)
#define FoxRI(i,a,b) for (i=b; i>=a; i--)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Min(a,b) a=min(a,b)
#define Max(a,b) a=max(a,b)
#define Sz(s) int((s).size())
#define All(s) (s).begin(),(s).end()
#define Fill(s,v) memset(s,v,sizeof(s))
#define pb push_back
#define mp make_pair
#define x first
#define y second
template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
template<typename T> T Sqr(T x) { return(x*x); }
const int INF = (int)1e9;
const LD EPS = 1e-9;
const LD PI = acos(-1.0);
bool Read(int &x)
{
char c,r=0,n=0;
x=0;
for(;;)
{
c=getchar();
if ((c<0) && (!r))
return(0);
if ((c=='-') && (!r))
n=1;
else
if ((c>='0') && (c<='9'))
x=x*10+c-'0',r=1;
else
if (r)
break;
}
if (n)
x=-x;
return(1);
}
#define LIM 2000001
#define MOD 1000000007
#define DIV2 500000004
int Add(int a,int b)
{
a+=b;
if (a>=MOD)
a-=MOD;
return(a);
}
int Sub(int a,int b)
{
a-=b;
if (a<0)
a+=MOD;
return(a);
}
int Mult(int a,int b)
{
return((LL)a*b%MOD);
}
int main()
{
// vars
int T,t;
int N;
int O,Ao,Bo,Co,Do;
int C,Ac,Bc,Cc,Dc;
int i,j,k,d,d2,ans;
int r1,r2,m;
LL a,b,c;
static int E[LIM],dist[LIM],sum[LIM];
static LL D1[LIM],D2[LIM],S1[LIM],S2[LIM];
static vector<PR> con[LIM];
priority_queue<PR> Q;
// testcase loop
Read(T);
Fox1(t,T)
{
// input
Read(N);
Fox(i,N+1)
con[i].clear();
Read(O),Read(Ao),Read(Bo),Read(Co),Read(Do);
Fox(i,N)
{
E[i]=O;
j=(i+1)%N;
con[i].pb(mp(j,O));
con[j].pb(mp(i,O));
O=((LL)Ao*O+Bo)%Co+Do;
}
Read(C),Read(Ac),Read(Bc),Read(Cc),Read(Dc);
Fox(i,N)
{
con[N].pb(mp(i,C));
con[i].pb(mp(N,C));
C=((LL)Ac*C+Bc)%Cc+Dc;
}
// precompute outer distances/sums
D1[0]=D2[0]=S1[0]=S2[0]=0;
Fox(i,N*2)
{
D1[i+1]=D1[i]+E[i%N];
D2[i+1]=D2[i]+E[(N*2-i-1)%N];
S1[i+1]=Add(S1[i],D1[i+1]%MOD);
S2[i+1]=Add(S2[i],D2[i+1]%MOD);
}
// dijkstra's from center
Fill(dist,60);
Q.push(mp(0,N)),dist[N]=0;
while (!Q.empty())
{
d=-Q.top().x;
i=Q.top().y;
Q.pop();
if (d!=dist[i])
continue;
Fox(j,Sz(con[i]))
{
k=con[i][j].x;
d2=d+con[i][j].y;
if (d2<dist[k])
Q.push(mp(-d2,k)),dist[k]=d2;
}
}
// precompute center distance sums
sum[0]=0;
Fox(i,N*2)
sum[i+1]=Add(sum[i],dist[i%N]);
// process outer points
j=ans=0;
Fox(i,N)
{
// advance j to furthest node from i (along outside only)
for(;;)
{
c=D1[j]-D1[i];
a=min(c,D1[N]-c);
c=D1[j+1]-D1[i];
b=min(c,D1[N]-c);
if (b<=a)
break;
j++;
}
// binary search for furthest node in i..j which is closer along the ouside
r1=i,r2=j;
while (r2>r1)
{
m=(r1+r2+1)>>1;
if (D1[m]-D1[i]<dist[i]+dist[m%N])
r1=m;
else
r2=m-1;
}
a=r1;
// binary search for furthest node in j..(i+N) which is closer along the ouside
r1=j,r2=i+N;
while (r2>r1)
{
m=(r1+r2)>>1;
if (D1[i+N]-D1[m]<dist[i]+dist[m%N])
r2=m;
else
r1=m+1;
}
b=r1;
if (a==b)
{
c=D1[a]-D1[i];
if (c<D1[N]-c)
b++;
else
a--;
}
// add outer distances i -> i..a
ans=Add(ans,Sub(S1[a],S1[i]));
ans=Sub(ans,Mult(D1[i]%MOD,a-i));
// add outer distances i -> b..(i+N)
ans=Add(ans,Sub(S2[N*2-b],S2[N*2-(i+N)]));
ans=Sub(ans,Mult(D2[N*2-(i+N)]%MOD,i+N-b));
// add distances through center i -> (a+1)..(b-1)
if (a+1<=b-1)
{
ans=Add(ans,Mult(dist[i],b-a-1));
ans=Add(ans,Sub(sum[b],sum[a+1]));
}
}
// add center distances
ans=Mult(ans,DIV2);
ans=Add(ans,sum[N]);
// output
printf("Case #%d: %d\n",t,ans);
}
return(0);
}
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