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// Hacker Cup 2017
// Round 3
// Steadfast Snakes
// 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 800008
int L[2];
LL BLT[2][2][LIM];
void Update(int a,int b,int i,int v)
{
for(i++;i<=L[a];i+=(i&-i))
BLT[a][b][i]+=v;
}
LL Query(int a,int b,int i)
{
LL v=0;
for(i++;i>0;i-=(i&-i))
v+=BLT[a][b][i];
return(v);
}
int main()
{
// vars
int T,t;
int N,A,B,C;
LL K;
int i,j,c,v,ans;
int r1,r2,m;
LL s;
static int H[LIM];
static int n1,n2,c1[LIM],c2[LIM],v1[LIM],v2[LIM],vc1[LIM],vc2[LIM];
// testcase loop
Read(T);
Fox1(t,T)
{
// input
scanf("%d%lld",&N,&K);
Read(v),Read(A),Read(B),Read(C);
Fox(i,N)
{
H[i]=v;
v=((LL)A*v+B)%C+1;
}
// check if there's a single dominating ladder
j=0;
Fox(i,N)
if (H[i]>H[j])
j=i;
Fox(i,N)
if ((i!=j) && (H[i]>H[j]-K-abs(i-j)))
break;
if (i==N)
{
// special case - only shorten the dominating ladder
ans=0;
Fox(i,N)
if (i!=j)
Max(ans,H[j]-(int)K+H[i]+abs(i-j));
goto Done;
}
// compress diagonal coordinates
n1=n2=0;
Fox(i,N)
{
c1[n1++]=v1[i]=i-H[i];
c2[n2++]=v2[i]=-i-H[i];
}
sort(c1,c1+n1);
sort(c2,c2+n2);
L[0]=n1=unique(c1,c1+n1)-c1;
L[1]=n2=unique(c2,c2+n2)-c2;
Fox(i,N)
{
vc1[i]=lower_bound(c1,c1+n1,v1[i])-c1;
vc2[i]=lower_bound(c2,c2+n2,v2[i])-c2;
}
// init BLTs
Fill(BLT,0);
Fox(i,N)
{
Update(1,0,vc2[i],1);
Update(1,1,vc2[i],v2[i]);
}
// try every possible pyramid center x-coordinate
ans=2*INF+N;
Fox(i,N)
{
// move ladder i from right to left BLT
Update(0,0,vc1[i],1);
Update(0,1,vc1[i],v1[i]);
Update(1,0,vc2[i],-1);
Update(1,1,vc2[i],-v2[i]);
// centered on i
r1=max(i+1,N-i),r2=INF+N;
while (r2>=r1)
{
m=(r1+r2)>>1;
// left
v=i-m;
c=lower_bound(c1,c1+n1,v)-c1-1;
s=Query(0,0,c)*v-Query(0,1,c);
// right
v=-i-m;
c=lower_bound(c2,c2+n2,v)-c2-1;
s+=Query(1,0,c)*v-Query(1,1,c);
if (s<=K)
r2=m-1,Min(ans,2*m);
else
r1=m+1;
}
// centered on i+0.5
if (i==N-1)
break;
r1=max(i+1,N-i-1),r2=INF+N;
while (r2>=r1)
{
m=(r1+r2)>>1;
// left
v=i-m;
c=lower_bound(c1,c1+n1,v)-c1-1;
s=Query(0,0,c)*v-Query(0,1,c);
// right
v=-(i+1)-m;
c=lower_bound(c2,c2+n2,v)-c2-1;
s+=Query(1,0,c)*v-Query(1,1,c);
if (s<=K)
r2=m-1,Min(ans,2*m+1);
else
r1=m+1;
}
}
Done:;
printf("Case #%d: %d\n",t,ans);
}
return(0);
}
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