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#define DEBUG 0
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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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string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
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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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#define GETCHAR getchar
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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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int main()
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{
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if (DEBUG)
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freopen("in.txt","r",stdin);
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int TT,tt;
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int N,M,K,T,R;
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LD P;
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int i,j,k,b;
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LD d,v;
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int S[20];
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static int up[100000],down[100000],dist[100000],dir[20][20];
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static vector<int> con[100000];
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static LD exRN[100001],exNR[100001],exP[100001],exT[100001];
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static LD dyn[1<<20][21];
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queue<int> Q;
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Read(TT);
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Fox1(tt,TT)
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{
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Read(N),Read(M),Read(K),Read(T),Read(R);
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Fox(i,N)
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con[i].clear();
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cin >> P;
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Fox(i,K)
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Read(S[i]),S[i]--;
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while (M--)
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{
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Read(i),Read(j);
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con[i-1].pb(j-1);
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}
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Fox(i,K)
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dyn[(1<<K)-1][i]=0;
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Fill(up,-1);
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Q.push(0),up[0]=0;
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while (!Q.empty())
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{
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i=Q.front(),Q.pop();
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Fox(j,Sz(con[i]))
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if (up[k=con[i][j]]<0)
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Q.push(k),up[k]=up[i]+1;
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}
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Fill(down,-1);
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Fox(b,K)
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{
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Fill(dist,-1);
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Q.push(S[b]),dist[S[b]]=0;
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while (!Q.empty())
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{
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i=Q.front(),Q.pop();
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if ((!Sz(con[i])) && (down[b]<0))
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down[b]=dist[i];
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Fox(j,Sz(con[i]))
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if (dist[k=con[i][j]]<0)
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Q.push(k),dist[k]=dist[i]+1;
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}
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Fox(i,K)
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dir[b][i]=dist[S[i]];
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}
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exRN[0]=0;
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Fox1(i,N)
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{
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v=(P*T + (1-P)*(R+exRN[i-1])) / P;
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exRN[i]=exRN[i-1]+v;
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}
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exNR[0]=R;
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Fox1(i,N)
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exNR[i]=P*(T + exNR[i-1]) + (1-P)*R;
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exP[0]=1;
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exT[0]=0;
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Fox1(i,N)
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{
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exP[i]=exP[i-1]*P;
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exT[i]=exT[i-1] + exP[i-1]*(1-P)*((i-1)*T + R);
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}
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FoxR(b,(1<<K)-1)
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{
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d=-1;
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Fox(i,K)
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if (!(b&(1<<i)))
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{
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v=dyn[b][i]=dyn[b|(1<<i)][i];
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v+=exRN[up[S[i]]];
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if ((d<0) || (d>v))
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d=v;
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}
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dyn[b][K]=d;
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Fox(i,K)
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if (b&(1<<i))
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{
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d=exNR[down[i]]+dyn[b][K];
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Fox(j,K)
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if (!(b&(1<<j)))
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if (dir[i][j]>=0)
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{
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k=dir[i][j];
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v=exP[k]*(k*T + dyn[b][j]) + exT[k] + (1-exP[k])*dyn[b][K];
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Min(d,v);
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}
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dyn[b][i]=d;
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}
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}
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printf("Case #%d: ",tt);
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cout << fixed << setprecision(9) << dyn[0][K] << endl;
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}
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return(0);
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} |
