#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<queue>
#define LL long long
#define M 802
#define N 202
#define INF 1010000000
#define eps (1e-5)
using namespace std;
int read(){int nm=0,fh=1; char cw=getchar();for(;!isdigit(cw);cw=getchar()) if(cw=='-') fh=-fh;for(;isdigit(cw);cw=getchar()) nm=nm*10+(cw-'0');return nm*fh;
}
struct STA{int nd; double dst;STA();STA(int _nd,int _dst){nd=_nd,dst=_dst;}bool operator <(const STA&ot)const{return dst>ot.dst;}
};
priority_queue<STA> Q;
int n,m,X[M],Y[M],fs[N],nt[M],to[M],tmp,S,T;
double dis[N];
bool vis[N];
void link(int x,int y,int t1,int t2){nt[tmp]=fs[x],fs[x]=tmp,to[tmp]=y,X[tmp]=t1,Y[tmp++]=t2;}
double DJ(double V){for(int i=1;i<=n;i++) dis[i]=INF*1.0,vis[i]=false;while(!Q.empty()) Q.pop(); dis[S]=0.0,Q.push(STA(S,0.0));while(!Q.empty()){int x=Q.top().nd; Q.pop();if(vis[x]) continue; vis[x]=true;for(int i=fs[x];i!=-1;i=nt[i]){double dt=dis[x]+(X[i]*V)+(Y[i]*(1.0-V));if(dt>=dis[to[i]]) continue;dis[to[i]]=dt,Q.push(STA(to[i],dt));}}return dis[T];
}
double calc(double L,double R){double mid=(L+R)/2.0,ans,ls,rs;ans=DJ(mid),ls=DJ(L),rs=DJ(R);if(fabs(ans-(ls+rs)/2.0)*(R-L)<eps) return ans*(R-L);return calc(L,mid)+calc(mid,R);
}
int main(){n=read(),m=read(),S=read(),T=read(),memset(fs,-1,sizeof(fs));for(int i=1;i<=m;i++){int u=read(),v=read(),t1=read(),t2=read();link(u,v,t1,t2),link(v,u,t1,t2);}printf("%.10f\n",calc(0.0,1.0)); return 0;
}