#include<stdio.h>
#include<queue>
#include<vector>
#include<algorithm>
using namespace std;
const int N=2e5+5;
int hd[N],to[2*N],nx[2*N],num;
int n,m,dep[N];
double f[N];
void add(int x,int y){
	nx[++num]=hd[x],hd[x]=num,to[num]=y;
}
struct po{
	int id,dep;
	bool operator <(const po &x)const{return dep<x.dep;}
}p[N];
queue<int>q;
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1,x,y;i<=m;i++){
		scanf("%d%d",&x,&y);
		add(x,y),add(y,x);
	}
	dep[n]=1;
	q.push(n);
	while(!q.empty()){
		int u=q.front();
		q.pop();
		for(int i=hd[u],v;v=to[i],i;i=nx[i])if(!dep[v]){
			dep[v]=dep[u]+1;
			q.push(v);
		}
	}
	for(int i=1;i<=n;i++)p[i].id=i,p[i].dep=dep[i];
	sort(p+1,p+n+1);
	for(int i=2;i<=n;i++){
		int u=p[i].id;
		vector<double>g;
		for(int j=hd[u],v;v=to[j],j;j=nx[j]){
			if(dep[v]>=dep[u])continue;
			g.push_back(f[v]);
		}
		sort(g.begin(),g.end());
		double h=1.0;
		for(int j=0;j<g.size();j++){
			double v=g[j];
			f[u]+=h*3.0/4.0*v+h;
			h/=4.0;
		}
		f[u]+=h*(g[0]+2.0);
	}
	printf("%.10lf\n",f[1]);
	return 0;
}