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#include <algorithm>
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#include <functional>
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#include <numeric>
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#include <iostream>
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#include <iomanip>
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#include <cstdio>
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#include <cmath>
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#include <complex>
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#include <cstdlib>
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#include <ctime>
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#include <cstring>
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#include <cassert>
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#include <string>
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#include <vector>
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#include <list>
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#include <map>
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#include <set>
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#include <deque>
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#include <queue>
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#include <stack>
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#include <bitset>
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#include <sstream>
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using namespace std;
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#define LL long long
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#define LD long double
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#define PR pair<int,int>
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#define Fox(i,n) for (i=0; i<n; i++)
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#define Fox1(i,n) for (i=1; i<=n; i++)
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#define FoxI(i,a,b) for (i=a; i<=b; i++)
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#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
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#define FoxR1(i,n) for (i=n; i>0; i--)
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#define FoxRI(i,a,b) for (i=b; i>=a; i--)
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#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
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#define Min(a,b) a=min(a,b)
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#define Max(a,b) a=max(a,b)
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#define Sz(s) int((s).size())
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#define All(s) (s).begin(),(s).end()
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#define Fill(s,v) memset(s,v,sizeof(s))
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#define pb push_back
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#define mp make_pair
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#define x first
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#define y second
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template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
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template<typename T> T Sqr(T x) { return(x*x); }
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const int INF = (int)1e9;
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const LD EPS = 1e-9;
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const LD PI = acos(-1.0);
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bool Read(int &x)
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{
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char c,r=0,n=0;
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x=0;
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for(;;)
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{
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c=getchar();
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if ((c<0) && (!r))
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return(0);
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if ((c=='-') && (!r))
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n=1;
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else
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if ((c>='0') && (c<='9'))
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x=x*10+c-'0',r=1;
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else
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if (r)
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break;
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}
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if (n)
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x=-x;
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return(1);
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}
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#define LIM 800008
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int L[2];
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LL BLT[2][2][LIM];
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void Update(int a,int b,int i,int v)
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{
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for(i++;i<=L[a];i+=(i&-i))
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BLT[a][b][i]+=v;
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}
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LL Query(int a,int b,int i)
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{
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LL v=0;
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for(i++;i>0;i-=(i&-i))
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v+=BLT[a][b][i];
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return(v);
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}
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int main()
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{
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int T,t;
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int N,A,B,C;
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LL K;
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int i,j,c,v,ans;
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int r1,r2,m;
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LL s;
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static int H[LIM];
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static int n1,n2,c1[LIM],c2[LIM],v1[LIM],v2[LIM],vc1[LIM],vc2[LIM];
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Read(T);
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Fox1(t,T)
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{
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scanf("%d%lld",&N,&K);
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Read(v),Read(A),Read(B),Read(C);
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Fox(i,N)
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{
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H[i]=v;
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v=((LL)A*v+B)%C+1;
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}
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j=0;
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Fox(i,N)
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if (H[i]>H[j])
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j=i;
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Fox(i,N)
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if ((i!=j) && (H[i]>H[j]-K-abs(i-j)))
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break;
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if (i==N)
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{
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ans=0;
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Fox(i,N)
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if (i!=j)
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Max(ans,H[j]-(int)K+H[i]+abs(i-j));
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goto Done;
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}
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n1=n2=0;
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Fox(i,N)
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{
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c1[n1++]=v1[i]=i-H[i];
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c2[n2++]=v2[i]=-i-H[i];
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}
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sort(c1,c1+n1);
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sort(c2,c2+n2);
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L[0]=n1=unique(c1,c1+n1)-c1;
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L[1]=n2=unique(c2,c2+n2)-c2;
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Fox(i,N)
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{
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vc1[i]=lower_bound(c1,c1+n1,v1[i])-c1;
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vc2[i]=lower_bound(c2,c2+n2,v2[i])-c2;
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}
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Fill(BLT,0);
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Fox(i,N)
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{
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Update(1,0,vc2[i],1);
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Update(1,1,vc2[i],v2[i]);
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}
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ans=2*INF+N;
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Fox(i,N)
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{
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Update(0,0,vc1[i],1);
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Update(0,1,vc1[i],v1[i]);
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Update(1,0,vc2[i],-1);
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Update(1,1,vc2[i],-v2[i]);
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r1=max(i+1,N-i),r2=INF+N;
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while (r2>=r1)
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{
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m=(r1+r2)>>1;
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v=i-m;
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c=lower_bound(c1,c1+n1,v)-c1-1;
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s=Query(0,0,c)*v-Query(0,1,c);
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v=-i-m;
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c=lower_bound(c2,c2+n2,v)-c2-1;
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s+=Query(1,0,c)*v-Query(1,1,c);
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if (s<=K)
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r2=m-1,Min(ans,2*m);
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else
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r1=m+1;
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}
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if (i==N-1)
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break;
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r1=max(i+1,N-i-1),r2=INF+N;
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while (r2>=r1)
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{
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m=(r1+r2)>>1;
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v=i-m;
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c=lower_bound(c1,c1+n1,v)-c1-1;
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s=Query(0,0,c)*v-Query(0,1,c);
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v=-(i+1)-m;
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c=lower_bound(c2,c2+n2,v)-c2-1;
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s+=Query(1,0,c)*v-Query(1,1,c);
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if (s<=K)
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r2=m-1,Min(ans,2*m+1);
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else
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r1=m+1;
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}
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}
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Done:;
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printf("Case #%d: %d\n",t,ans);
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}
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return(0);
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}
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