#include<bits/stdc++.h>
using namespace std;

void solve(int t){
    int n,m;
    cin>>n>>m;
    
    vector val((1<<(m-1)),0);
    
    for(int i=0;i<(1<<(m-1));i++){
        int tmp=0,pot=1;
        for(int j=0;j<m-1;j++){
            if(i&(1<<j))tmp+=pot;
            pot*=3;
        }
        val[i]=tmp;
    }
    
    array<int,50'000'000> cont={},succ={};
    vector cont0((1<<(m-1)),0),cont1((1<<(m-1)),0);
    
    auto ind = [&](int mask,int submask)->int{
        return val[mask]+val[submask];
    };
    
    for(int i=0;i<n;i++){
        string s;
        cin>>s;
        int tmp=0;
        for(int j=1;j<m;j++){
            if(s[j]=='1'){
                tmp+=(1<<(j-1));
            }
        }
        
        if(s[0]=='1'){
            cont1[tmp]++;
            cont[ind((1<<(m-1))-1,tmp)]++;
        }else{
            cont0[tmp]++;
        }
    }
    
    vector dpsup(m,vector(1<<(m-1),0)),dpdis(m,vector(1<<(m-1),0));
    auto f = [&](int pos,int mask)->int{
        if(pos==m-1)return cont1[mask];
        
        int res = dpsup[pos+1][mask];
        if((mask&(1<<pos)) == 0){
            res+=dpsup[pos+1][mask^(1<<pos)];
        }
        return res;
    };
    
    auto g = [&](int pos,int mask)->int{
        if(pos==m-1)return cont0[mask];
        
        int res = dpdis[pos+1][mask^(1<<pos)];
        if((mask&(1<<pos)) == 0){
            res+=dpdis[pos+1][mask];
        }
        return res;
    };
    
    for(int i=m-1;i>=0;i--){
        for(int j=0;j<(1<<(m-1));j++){
            dpsup[i][j]=f(i,j);
            dpdis[i][j]=g(i,j);
            
            //cout<<i<<" "<<j<<" "<<dpsup[i][j]<<" "<<dpdis[i][j]<<"\n";
        }
    }
    
    auto h = [&](int pos,int mask,int submask)->int{
        int res=0;
        if(mask&(1<<pos)){
            res+=cont[ind(mask,submask)];
        }else{
            res+=cont[ind(mask^(1<<pos),submask)];
            res+=cont[ind(mask^(1<<pos),submask^(1<<pos))];
        }
        return res;
    };
    
    
    for(int i=m-2;i>=0;i--){
        for(int j=0;j<(1<<(m-1));j++){
            for(int k=j;;k=(k-1)&j){
                succ[ind(j,k)]=h(i,j,k);
                
                //cout<<i<<" "<<j<<" "<<k<<" "<<succ[ind(j,k)]<<"\n";
                if(k==0)break;
            }
        }
        swap(succ,cont);
    }
    
    vector dp((1<<(m-1)),-1.0);
    auto solve = [&](auto &solve,int mask)->double{
        if(dp[mask]>-0.5)return dp[mask];
        
        int num = n-dpsup[0][mask]-dpdis[0][mask];
        if(num==0)return dp[mask]=1.0;
        
        double res = 0.0;
        for(int i=(mask-1)&mask;;i=(i-1)&mask){
            res+=solve(solve,i)*cont[ind(mask,i)]/num;
            if(i==0)break;
        }
        
        return dp[mask]=res;
    };
    
    cout<<setprecision(20)<<solve(solve,(1<<(m-1))-1)<<"\n";
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    
    int t=1;
    //cin>>t;
    for(int i=1;i<=t;i++)solve(i);
    
    return 0;
}