C++ :

#pragma GCC optimize ("O2")
#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
using namespace std;
const double eps=1e-11;
const int maxn=1010;
const double inf=1000000;
int n,m,S,T,du[maxn],lst[maxn],cnt,vis[maxn],id[maxn],cnta,cntb,to[maxn],total,Now,flag[maxn];
double len[maxn],sum[maxn*maxn],f[maxn];
struct Node{
    double f;
    int id;
}g[maxn*maxn],e[maxn*maxn],d[maxn*maxn];
int dcmp(double x){
    if(x<eps&&x>-eps)return 0;
    return x>0?1:-1;
}
bool cmp(const int &a,const int &b){
    if(a==Now)return 0;
    else if(b==Now)return 1;
    return f[a]<f[b];
}
bool cmp1(const Node &a,const Node &b){
    return a.f<b.f;
}
struct Edge{
    int to,next;
    double w;
};
queue<int>que;
#define p edge[i].to
struct Graph{
    Edge edge[maxn];
    int head[maxn],tot;
    void add(int x,int y,double w){
        edge[++tot].to=y;
        edge[tot].next=head[x];
        edge[tot].w=w;
        head[x]=tot;
    }
    void Tupo(){
        vis[T]=1;
        for(int i=1;i<=n;i++)if(!du[i]||i==T)que.push(i);
        while(!que.empty()){
            int x=que.front();
            lst[++cnt]=x;
            que.pop();
            for(int i=head[x];i;i=edge[i].next){
                du[p]--;
                if(vis[x])vis[p]=1;
                if(!du[p])que.push(p);
            }
        }
    }
    void before(int x){
        total=0;
        Now=x;
        cnta=0;cntb=0;total=0;
        for(int i=head[x];i;i=edge[i].next){
            len[++total]=edge[i].w;
            to[total]=edge[i].to;
        }
        sort(to+1,to+total+1,cmp);
        for(int i=1;i<=total;i++)
            for(int j=1;j<=total;j++){
                if(to[j]==x)e[++cntb].f=len[i],e[cntb].id=j;
                else g[++cnta].f=len[i]+f[to[j]],g[cnta].id=j;
            }
        sort(e+1,e+cntb+1,cmp1);
        sort(g+1,g+cnta+1,cmp1);
    }
    double query(int x,double mid){
        total=0;
        for(int i=head[x];i;i=edge[i].next){
            e[++total].id=p;
            e[total].f=p==x?mid:f[p];
            len[total]=edge[i].w;
        }
        sort(e+1,e+total+1,cmp1);
        double ans=0;
        for(int i=1;i<=total;i++)
            for(int j=1;j<=total;j++){
                double P=1;
                for(int k=1;k<=total;k++){
                    int Count=0;
                    if(k==j){
                        P/=k;
                        continue;
                    }
                    for(int k1=1;k1<=total;k1++){
                        if(k1==i)continue;
                       if((k>j&&dcmp(len[k1]+e[k].f-len[i]-e[j].f)>0)||(k<j&&dcmp(len[k1]+e[k].f-len[i]-e[j].f)>=0)){
                           Count++;
                       }
                   }
                   P=P*(Count-(k-1-(k>j)))/k;
                }   
                ans+=P*(len[i]+e[j].f);
           }
        return ans;
    }
    double solve(int x){
        double l=0,r=inf,maxx=0;
       for(int i=1;i<=64;i++){
            double mid=(l+r)/2.0;
            double t=query(x,mid);
            if(dcmp(mid-t)<=0)l=mid;
            else r=mid;
        }
        return (l+r)/2.0;
    }
}E,G;
double query(int x,double mid){
    for(int i=1;i<=cntb;i++)e[i].f+=mid;
    int c=0,temp1=1,temp2=1;
    while(temp1<=cnta||temp2<=cntb){ 
        if(temp1>cnta)d[++c]=e[temp2],temp2++;
        else if(temp2>cntb)d[++c]=g[temp1],temp1++;
        else{
            if(g[temp1].f<e[temp2].f)d[++c]=g[temp1],temp1++;
            else d[++c]=e[temp2],temp2++;
        }
       
    } 
    int type=0;
    for(int i=0;i<=total;i++){ 
        if(i!=0)id[i]=i;
        if(i==total||f[to[i+1]]>mid){
            type=i+1;
            for(int j=i+1;j<=total;j++)if(to[j]==x)id[j]=type++;
            for(int j=i+1;j<=total;j++){                
                if(to[j]==x)break;
                id[j]=type++;
            }
            break;
        }
    }
    for(int i=1;i<=total;i++)flag[i]=0;
    int appe=0;
    long double now=1.0;
    sum[c+1]=0;
    for(int i=c;i>=1;i--){
        int t=d[i].id;
        if(flag[t]+1==id[t]){
             flag[t]++;
             appe++;
             now/=appe;
        }
        else if(flag[t]>=id[t]){
            now=now/(flag[t]-id[t]+1)*(flag[t]-id[t]+2);
            flag[t]++;
        }
        else flag[t]++;
    //   if(x==1) cout<<x<<"***"<<mid<<" "<<now<<" "<<appe<<" "<<flag[t]<<endl;
        if(appe==total)sum[i]=now;
        else sum[i]=0;
    }
    for(int i=1;i<=cntb;i++)e[i].f-=mid;
    long double ans=0;
    for(int i=c;i>=1;i--){
        ans+=(sum[i]-sum[i+1])*d[i].f;
    } 
    return ans;
}
double solve(int x){
    if(!cntb){
        return query(x,inf);
   }
   double l=0,r=inf,maxx=0;
    for(int i=1;i<=64;i++){
        double mid=(l+r)/2.0;
        double t=query(x,mid);
        if(dcmp(mid-t)<=0)l=mid;
        else r=mid;
    }
    return (l+r)/2.0;
}
int main(){
  //  freopen("tomoya2.in","r",stdin);freopen("tomoya.out","w",stdout);
    scanf("%d%d%d%d",&n,&m,&S,&T);
    for(int i=1;i<=m;i++){
        int x,y;
        double w;
        scanf("%d%d%lf",&x,&y,&w);
        E.add(x,y,w);
        G.add(y,x,w);
        if(x!=y)du[x]++;
    }
    G.Tupo();
    if(!vis[S]){
        printf("-1");
        return 0;
    }
   
    for(int i=1;i<=n;i++)f[i]=inf; 
    for(int i=1;i<=cnt;i++){
        int x=lst[i];
        if(!vis[x])continue;
        if(x==T){
            f[x]=0;
            continue;
        }
            E.before(x);
            f[x]=solve(x);
    }
    printf("%.6lf",f[S]);
	return 0;
}