#include<bits/stdc++.h>
#define ll long long
#define int long long
using namespace std;

const int maxn = 1100000;
const double pi = acos(-1);

struct E
{
	double x,y;
	friend inline E operator +(const E &k1,const E &k2){ return (E){k1.x+k2.x,k1.y+k2.y}; }
	friend inline E operator -(const E &k1,const E &k2){ return (E){k1.x-k2.x,k1.y-k2.y}; }
	friend inline E operator *(const E &k1,const E &k2)
	{
		return (E){ k1.x*k2.x-k1.y*k2.y,k1.x*k2.y+k1.y*k2.x };
	}
};
namespace FFT
{
	int id[maxn];
	void DFT(E f[],const int N,const int sig)
	{
		for(int i=0;i<N;i++) if(i<id[i]) swap(f[i],f[id[i]]);
		for(int m=2;m<=N;m<<=1)
		{
			int t=m>>1;
			for(int i=0;i<t;i++)
			{
				E temp=(E){cos(2*pi*i/m),sin(2*pi*i/m*sig)};
				for(int j=i;j<N;j+=m)
				{
					E tx=f[j],ty=f[j+t]*temp;
					f[j]=tx+ty;
					f[j+t]=tx-ty;
				}
			}
		}
		if(sig==-1)
		{
			for(int i=0;i<N;i++) f[i].x/=(double)N;
		}
	}
	E f[maxn],g[maxn];
	void FFT(double f1[],double f2[],double ret[],const int n,const int m)
	{
		int N=1,ln=0;
		while(N<=(n+m)) N<<=1,ln++;
		for(int i=1;i<N;i++) id[i]=id[i>>1]>>1|(i&1)<<(ln-1);
		
		for(int i=0;i<N;i++)
		{
			if(i<=n) f[i]=(E){f1[i],0};
			else f[i]=(E){0,0};
			
			if(i<=m) g[i]=(E){f2[i],0};
			else g[i]=(E){0,0};
		}
		DFT(f,N,1); DFT(g,N,1);
		for(int i=0;i<N;i++) f[i]=f[i]*g[i];
		DFT(f,N,-1);
		
		for(int i=0;i<=n+m;i++) ret[i]=f[i].x;
	}
}

int n,K;
double p[maxn],q[maxn],sumq[maxn],sump[maxn];

double w1[maxn],w0[maxn],t1[maxn],t2[maxn],t3[maxn];
double sumw[maxn];

signed main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	
	cin>>n>>K;
	for(int i=0;i<n;i++) 
	{
		cin>>p[i];
		if(!i) sump[i]=p[i];
		else sump[i]=sump[i-1]+p[i];
	}
	p[n]=0;
	for(int i=1;i<=2*n-2;i++) 
	{
		cin>>q[i];
		sumq[i]=sumq[i-1]+q[i];
	}
	
	for(int i=0;i<=2*n-2;i++) t1[i]=sumq[i];
	for(int i=0;i<=n;i++) t2[n-i]=p[i];
	FFT::FFT(t1,t2,t3,2*n-2,n);
	for(int i=0;i<=n;i++) w1[i]= t3[2*n-i];
	
	for(int i=0;i<=n;i++) t1[i]=sumq[i];
	for(int i=0;i<=n;i++) t2[n-i]=p[i];
	FFT::FFT(t1,t2,t3,n,n);
	for(int i=0;i<=n;i++) w0[i]=t3[n-i];
	
	double temp=0;
	{
		double ss=0;
		for(int i=0;i<n;i++)
		{
			double cc=ss;
			if(i==0||sump[i-1]<1.0) cc+= w0[i]; // /(1.0-sump[i-1]);
			temp=max(temp, cc );
			ss+= p[i]*sumq[n-i-1];
		}
	}
	
	for(int i=1;i<=n;i++) sumw[i]= sumw[i-1]+p[i-1]*w1[i];
	
	for(int k=K-1,j=n;k>=1;k--)
	{
		while(j>1&& w1[j]<temp ) 
			j--;
		//w1[j]>=temp
		temp= sumw[j]+(1-sump[j-1])*temp;
	}
	
	cout<<fixed<<setprecision(12)<<temp<<endl;
	
	return 0;
}