#include<bits/stdc++.h>
using namespace std;
#define FOR(i,s,t) for(int i=(s),_t=(t); i<=_t; ++i)
#define DOR(i,s,t) for(int i=(s),_t=(t); i>=_t; --i)
typedef long long ll;
typedef double db;
const int N=2505;
int C[N][N];
db x[N],y[N];
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(9);
    int n,K;
    cin >> n >> K;
    FOR(i,0,n-1) cin >> x[i] >> y[i];
    double res=0;
    FOR(d,2,n) {
        if(K-2>n-d) continue;
        double s=0;
        FOR(i,0,n-1) {
            int j=(i+d-1)%n;
            s+=x[i]*y[j]-x[j]*y[i];
        }
        vector<int> a={n-d,K,n-K};
        vector<int> b={K-2,n-d-K+2,n};
        s/=2;
        double ss=s;
        s=1;
        while(true) {
            while(a.size() && a.back()==0) a.pop_back();
            while(b.size() && b.back()==0) b.pop_back();
            if(!a.size()) break;
            if(!b.size()) break;
            if(s<1) s*=a.back()--;
            else s/=b.back()--;
        }
        for(auto v: a) while(v) s*=v--;
        for(auto v: b) while(v) s/=v--;
        // cerr << d << ' ' << s << endl;
        res+=ss*s;
    }
    cout << -res << '\n';
    return 0;
}