// Slower C++ solution:
#include <iostream>

#include <iomanip>

#include <complex>

#include <vector>

#include <algorithm>

#include <cmath>

#include <array>

using namespace std;



const double EPS = 1e-10;

const double INF = 1e12;

#define EQ(n,m) (abs((n)-(m)) < EPS)

#define X real()

#define Y imag()



typedef complex<double> P;

typedef vector<P> VP;

struct L : array<P, 2>{

    L(const P& a, const P& b){ at(0)=a; at(1)=b; }

    L(){}

};



namespace std{

    bool operator < (const P& a, const P& b){

        return (a.X!=b.X) ? a.X<b.X : a.Y<b.Y;

    }

    bool operator == (const P& a, const P& b){

        return abs(a-b) < EPS;

    }

}



double dot(P a, P b){

    return (conj(a)*b).X;

}

double cross(P a, P b){

    return (conj(a)*b).Y;

}

int ccw(P a, P b, P c){

    b -= a;

    c -= a;

    if(cross(b,c) > EPS) return +1; //ccw

    if(cross(b,c) < -EPS) return -1; //cw

    if(dot(b,c) < -EPS) return +2; //c-a-b

    if(abs(c)-abs(b) > EPS) return -2; //a-b-c

    return 0; //a-c-b

}

P unit(const P &p){

    return p/abs(p);

}



bool isParallel(const P &a, const P &b){

    return abs(cross(a,b)) < EPS;

}

bool isParallel(const L &a, const L &b){

    return isParallel(a[1]-a[0], b[1]-b[0]);

}



bool intersectLS(const L& l, const L& s){

    return cross(l[1]-l[0], s[0]-l[0])*

        cross(l[1]-l[0], s[1]-l[0]) < EPS;

}

bool intersectSS(const L& a, const L& b){

    return ( ccw(a[0],a[1],b[0]) *ccw(a[0],a[1],b[1]) <= 0 ) &&

        ( ccw(b[0],b[1],a[0]) *ccw(b[0],b[1],a[1]) <= 0 );

}

bool intersectSP(const L& s, const P& p){

    return abs(s[0]-p) +abs(s[1]-p) -abs(s[1]-s[0]) < EPS;

}

P crosspointLL(const L &l, const L &m) {

  double A = cross(l[1]-l[0], m[1]-m[0]);

  double B = cross(l[1]-l[0], l[1]-m[0]);

  return m[0] + B/A *(m[1]-m[0]);

}



double L1distance(const P &a, const P &b){

    return abs(b.X -a.X) +abs(b.Y -a.Y);

}

double L1distanceSP(const L &s, const P &p){

    double ret = INF;

    for(int i=0; i<2; i++){

        L gl(p, p +P(i, 1-i));

        if(!isParallel(s, gl) && intersectLS(gl, s)){

            P cp = crosspointLL(s, L(p, p+P(i,1-i)));

            ret = min(ret, abs(p -cp));

        }

        ret = min(ret, L1distance(p, s[i]));

    }

    return ret;

}



int in_poly(const P &p, const VP &poly){

    int n = poly.size();

    int cn=0;

    for(int i=0; i<n; i++){

        if(intersectSP(L(poly[i], poly[(i+1)%n]), p)){

            return 0;

        }

    }

    L ray(p, p+P(INF, 0));

    for(int i=0; i<n; i++){

        if((poly[i].Y <= p.Y && poly[(i+1)%n].Y > p.Y) ||

           (poly[i].Y > p.Y && poly[(i+1)%n].Y <= p.Y)){

            if(intersectSS(ray, L(poly[i],poly[(i+1)%n]))){

                cn++;

            }

        }

    }

    if(cn%2!=0) return 1;

    else return -1;

}

vector<L> arrangement(const vector<L> &e){

    VP cp;

    cp.reserve(e.size()*e.size());

    for(int i=0; i<(int)e.size(); i++){

        for(int j=i+1; j<(int)e.size(); j++){

            if(!isParallel(e[i], e[j]) && intersectSS(e[i], e[j])){

                cp.push_back(crosspointLL(e[i], e[j]));

            }

        }

    }

    sort(cp.begin(), cp.end());

    cp.erase(unique(cp.begin(), cp.end()), cp.end());



    vector<L> ret;

    for(int i=0; i<(int)e.size(); i++){

        VP vlist;

        vlist.reserve(e.size());

        for(int j=0; j<(int)cp.size(); j++){

            if(intersectSP(e[i], cp[j])){

                vlist.push_back(cp[j]);

            }

        }

        for(int j=0; j<(int)vlist.size()-1; j++){

            ret.push_back(L(vlist[j], vlist[j+1]));

        }

    }

    sort(ret.begin(), ret.end());

    ret.erase(unique(ret.begin(), ret.end()), ret.end());

    return ret;

}





int main(){

    while(1){

        int n,r;

        cin >> n >> r;

        if(n==0) break;

        

        VP v(n);

        for(int i=0; i<n; i++){

            double x,y;

            cin >> x >> y;

            v[i] = P(x,y);

        }

        vector<VP> sq(n, VP(4));

        for(int i=0; i<n; i++){

            sq[i][0] = v[i] +P(r, 0);

            sq[i][1] = v[i] +P(0, r);

            sq[i][2] = v[i] +P(-r, 0);

            sq[i][3] = v[i] +P(0, -r);

        }



        vector<L> l;

        l.reserve(9*n);

        for(int i=0; i<n; i++){

            l.push_back(L(v[i], v[(i+1)%n]));

            for(int j=0; j<4; j++){

                l.push_back(L(sq[i][j], sq[(i+1)%n][j]));

                l.push_back(L(sq[i][j], sq[i][(j+1)%4]));

            }

        }

        vector<L> cand = arrangement(l);



        double ans = 0;

        for(int i=0; i<(int)cand.size(); i++){

            bool rem = true;

            for(int j=0; j<n; j++){

                P mid = (cand[i][0] +cand[i][1])/2.0;

                if(L1distanceSP(L(v[j], v[(j+1)%n]), mid) +EPS < r || in_poly(mid, v) == -1){

                    rem = false;

                    break;

                }

            }

            if(rem){

                ans += abs(cand[i][1] -cand[i][0]);

            }

        }

        cout << fixed;

        cout << setprecision(10);

        cout << ans << endl;

    }

    return 0;

}




// Faster C++ solution for the same problem (measured speedup: 1.1689004290529101x):
#include <iostream>

#include <iomanip>

#include <complex>

#include <vector>

#include <algorithm>

#include <cmath>

#include <array>

using namespace std;



const double EPS = 1e-10;

const double INF = 1e12;

#define EQ(n,m) (abs((n)-(m)) < EPS)

#define X real()

#define Y imag()



typedef complex<double> P;

typedef vector<P> VP;

struct L : array<P, 2>{

    L(const P& a, const P& b){ at(0)=a; at(1)=b; }

    L(){}

};



namespace std{

    bool operator < (const P& a, const P& b){

        return (a.X!=b.X) ? a.X<b.X : a.Y<b.Y;

    }

    bool operator == (const P& a, const P& b){

        return abs(a-b) < EPS;

    }

}



double dot(P a, P b){

    return (conj(a)*b).X;

}

double cross(P a, P b){

    return (conj(a)*b).Y;

}

int ccw(P a, P b, P c){

    b -= a;

    c -= a;

    if(cross(b,c) > EPS) return +1; //ccw

    if(cross(b,c) < -EPS) return -1; //cw

    if(dot(b,c) < -EPS) return +2; //c-a-b

    if(abs(c)-abs(b) > EPS) return -2; //a-b-c

    return 0; //a-c-b

}



bool isParallel(const P &a, const P &b){

    return abs(cross(a,b)) < EPS;

}

bool isParallel(const L &a, const L &b){

    return isParallel(a[1]-a[0], b[1]-b[0]);

}



bool intersectLS(const L& l, const L& s){

    return cross(l[1]-l[0], s[0]-l[0])*

        cross(l[1]-l[0], s[1]-l[0]) < EPS;

}

bool intersectSS(const L& a, const L& b){

    return ( ccw(a[0],a[1],b[0]) *ccw(a[0],a[1],b[1]) <= 0 ) &&

        ( ccw(b[0],b[1],a[0]) *ccw(b[0],b[1],a[1]) <= 0 );

}

bool intersectSP(const L& s, const P &p){

    return abs(cross(s[0]-p, s[1]-p))<EPS  && dot(s[0]-p, s[1]-p)<EPS;

}

P crosspointLL(const L &l, const L &m) {

  double A = cross(l[1]-l[0], m[1]-m[0]);

  double B = cross(l[1]-l[0], l[1]-m[0]);

  return m[0] + B/A *(m[1]-m[0]);

}



double L1distance(const P &a, const P &b){

    return abs(b.X -a.X) +abs(b.Y -a.Y);

}

double L1distanceSP(const L &s, const P &p){

    double ret = INF;

    for(int i=0; i<2; i++){

        L gl(p, p +P(i, 1-i));

        if(!isParallel(s, gl) && intersectLS(gl, s)){

            P cp = crosspointLL(s, L(p, p+P(i,1-i)));

            ret = min(ret, abs(p -cp));

        }

        ret = min(ret, L1distance(p, s[i]));

    }

    return ret;

}



int in_poly(const P &p, const VP &poly){

    int n = poly.size();

    int ret = -1;

    for(int i=0; i<n; i++){

        P a = poly[i]-p;

        P b = poly[(i+1)%n]-p;

        if(a.Y > b.Y) swap(a,b);

        if(intersectSP(L(a,b), P(0,0))) return 0;

        if(a.Y<=0 && b.Y>0 && cross(a,b)<0) ret = 1-ret;

    }

    return ret;

}

vector<L> arrangement(const vector<L> &e){

    vector<VP> cp(e.size());

    for(int i=0; i<(int)e.size(); i++){

        for(int j=i+1; j<(int)e.size(); j++){

            if(!isParallel(e[i], e[j]) && intersectSS(e[i], e[j])){

                P cpij = crosspointLL(e[i], e[j]);

                cp[i].push_back(cpij);

                cp[j].push_back(cpij);

            }

        }

        sort(cp[i].begin(), cp[i].end());

        cp[i].erase(unique(cp[i].begin(), cp[i].end()), cp[i].end());

    }



    vector<L> ret;

    for(int i=0; i<(int)e.size(); i++){

        for(int j=0; j<(int)cp[i].size()-1; j++){

            ret.push_back(L(cp[i][j], cp[i][j+1]));

        }

    }

    sort(ret.begin(), ret.end());

    ret.erase(unique(ret.begin(), ret.end()), ret.end());

    return ret;

}





int main(){

    while(1){

        int n,r;

        cin >> n >> r;

        if(n==0) break;

        

        VP v(n);

        for(int i=0; i<n; i++){

            double x,y;

            cin >> x >> y;

            v[i] = P(x,y);

        }

        vector<VP> sq(n, VP(4));

        for(int i=0; i<n; i++){

            sq[i][0] = v[i] +P(r, 0);

            sq[i][1] = v[i] +P(0, r);

            sq[i][2] = v[i] +P(-r, 0);

            sq[i][3] = v[i] +P(0, -r);

        }



        vector<L> l;

        l.reserve(9*n);

        for(int i=0; i<n; i++){

            l.push_back(L(v[i], v[(i+1)%n]));

            for(int j=0; j<4; j++){

                l.push_back(L(sq[i][j], sq[(i+1)%n][j]));

                l.push_back(L(sq[i][j], sq[i][(j+1)%4]));

            }

        }

        vector<L> cand = arrangement(l);



        double ans = 0;

        for(int i=0; i<(int)cand.size(); i++){

            bool rem = true;

            for(int j=0; j<n; j++){

                P mid = (cand[i][0] +cand[i][1])/2.0;

                if(L1distanceSP(L(v[j], v[(j+1)%n]), mid) +EPS < r || in_poly(mid, v) == -1){

                    rem = false;

                    break;

                }

            }

            if(rem){

                ans += abs(cand[i][1] -cand[i][0]);

            }

        }

        cout << fixed;

        cout << setprecision(10);

        cout << ans << endl;

    }

    return 0;

}