#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;
}



Measured memory_bytes: 3836