#include<bits/stdc++.h>
using namespace std;
const int N=1919810;
#define double long double
typedef long long ll;
typedef pair<ll,ll> PII;
int n,m,k;
// int a[N],b[N];
double a[N],b[N];
char s[N];
double C[3000][3000];
double pw[N];

bool check(double K,double B,double x,double y){
    if(y>K*x+B) return true;
    return false;
}

void __(){
    // cin>>n>>m;
    cin>>n>>m;
    for(int i=1;i<=n;i++) cin>>a[i]>>b[i];
    for(int i=1;i<=n*2;i++){
        a[i+n]=a[i];
        b[i+n]=b[i];
        // a[i+n]=a[i];
        // b[i+n]=b[i];
    }
    
    double ans=0;
    for(int i=1;i<=n;i++){
        for(int j=i+1;j<=n;j++){
            if(a[i]==a[j]) continue;
            double K=(b[j]-b[i])/(a[j]-a[i]);
            double B=b[i]-a[i]*K;
            double res=(b[i]+b[j])*fabs(a[i]-a[j])/2;
            // cout<<"--"<<res<<" ";
            double rres=(C[j-i-1][m-2]-C[n-(j-i+1)][m-2])/C[n][m];
            rres*=res;
            
            // if(j==i+2){
                // cout<<j-i-1<<" "<<m-2<<" "<<n-(j-i+1)<<" "<<C[j-i-1][m-2]/C[n][m]<<" "<<C[n-(j-i+1)][m-2]/C[n][m]<<endl;
                // cout<<rres<<endl;
            // }
            // if(j==i+1){
                bool flag=0;
                if(j==i+n-1){
                    if(check(K,B,a[i+1],b[i+1])){
                    // double rres=
                    ans-=rres;
                }else{
                    // double rres=(val[j-i-1][m-2]-val[n-(j-i+1)][m-2])*res;
                    ans+=rres;
                }
                }else
                if(check(K,B,a[j+1],b[j+1])){
                    // double rres=
                    ans+=rres;
                }else{
                    // double rres=(val[j-i-1][m-2]-val[n-(j-i+1)][m-2])*res;
                    ans-=rres;
                }
            // }
            // cout<<i<<" "<<j<<" "<<rres<<" "<<ans<<endl;
        }
    }
    // printf("%.20f\n",ans);
    cout << fixed << setprecision(20) << ans<< '\n' ;
}


int main(){
    
    
    for(int i=0;i<=2550;i++){
        C[i][0]=1;
    }
    for(int i=1;i<=2550;i++){
        for(int j=1;j<=i;j++){
            C[i][j]=(C[i-1][j]+C[i-1][j-1]);
        }
    }
    pw[0]=1;
    for(int i=1;i<=2550;i++) pw[i]=pw[i-1]*2;
    // val[0][0]=0;
    // for(int i=0;i<=10;i++){
    //     for(int j=0;j<=10;j++) cout<<val[i][j]<<" ";
    //     cout<<endl;
    // }
    int _=1;
    // cin>>_;
    while(_--){
        __();
    }
}