C++ :

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <vector>
#include <cmath>
#include <algorithm>
 
 
using namespace std;
 
const int MAXN = 10000;
const double PI = atan(1.0) * 4;
const double EPS = 1e-10;
 
class Point {
public:
    double x, y;
    Point() {}
    Point(double x, double y) : x(x), y(y) {}
    Point operator - (const Point &r) const { return Point(x-r.x, y-r.y); }
    Point operator + (const Point &r) const { return Point(x+r.x, y+r.y); }
    Point &operator += (const Point &r) { x += r.x; y += r.y; return *this; }
    Point &operator *= (double m) { x *= m; y *= m; return *this; }
    Point pOfRotate(double angle) const {
        double cosA = cos(angle);
        double sinA = sin(angle);
        return Point(cosA*x-sinA*y, sinA*x+cosA*y);
    }
    Point pOfRotate90() const { return Point(-y, x); }
    double length() const { return sqrt(x*x+y*y); }
    Point pOfNormal() const {
        double len = length();
        return Point(x/len, y/len);
    }
    double angle() const { return atan2(y, x); }
};
 
ostream & operator <<(ostream &os, const Point &v)
{
    os << "(" << v.x << "," << v.y << ")";
    return os;
}
 
class Segment;
class Circle;
 
class Seg {
public:
    virtual double getLeft() const = 0;
    virtual double getRight() const = 0;
    virtual double getY(double x) const = 0;
    virtual double getLength(double x1, double x2) const = 0;
    virtual void intersect(Seg *r) const = 0;
    virtual void intersect(const Segment &v) const = 0;
    virtual void intersect(const Circle &v) const = 0;
    bool contains(double x) const { return x>=getLeft() && x<=getRight(); }
    virtual void acceptPrint(ostream &os) const = 0;
};
 
ostream & operator <<(ostream &os, const Seg &v)
{
    v.acceptPrint(os);
    return os;
}
 
Point intersectRet[4];
int tIntersectRet;
 
class Segment : public Seg {
public:
    Point a, b;
    Segment &moveLeft(double dis)
    {
        Point tmp = ((b-a).pOfRotate90().pOfNormal() *= dis);
        a += tmp;
        b += tmp;
        return *this;
    }
    virtual double getLeft() const { return a.x; }
    virtual double getRight() const { return b.x; }
    virtual double getY(double x) const {
        return (x-a.x)*(b.y-a.y)/(b.x-a.x)+a.y;
    }
    virtual double getLength(double x1, double x2) const {
        return (x2-x1) * (b-a).length() / (b.x-a.x);
    }
    virtual void intersect(Seg *r) const {
        r->intersect(*this);
    }
    virtual void intersect(const Segment &v) const {
        tIntersectRet = 0;
        double ang = (b-a).angle();
        Point c = (v.a-a).pOfRotate(-ang);
        Point d = (v.b-a).pOfRotate(-ang);
        // Bug
        //double di = b.length();
        double di = (b-a).length();
        if (!((c.y>0&&d.y<0) || (c.y<0&&d.y>0)))
            return ;
        double x = (d.x-c.x) * (-c.y) / (d.y-c.y) + c.x;
        if (x<0 || x>di)
            return ;
        Point ret = Point(x,0).pOfRotate(ang)+a;
        intersectRet[tIntersectRet++] = ret;
    }
    virtual void intersect(const Circle &v) const;
    virtual void acceptPrint(ostream &os) const {
        os << a << "-" << b;
    }
};
 
class Circle : public Seg {
public:
    Point c;
    double r;
    virtual double getLeft() const { return c.x - r; }
    virtual double getRight() const { return c.x + r; }
    virtual double getY(double x) const {
        double y2 = r * r - (c.x - x) * (c.x - x);
        if (y2<0) y2 = 0;
        return c.y + sqrt(y2);
    }
    virtual double getLength(double x1, double x2) const {
        x1 -= c.x; x2 -= c.x;
        double a1 = Point(x1, sqrt(abs(r*r-x1*x1))).angle(), a2 = Point(x2, sqrt(abs(r*r-x2*x2))).angle();
        return (a1-a2) * r;
    }
    virtual void intersect(Seg *r) const {
        r->intersect(*this);
    }
    virtual void intersect(const Segment &v) const {
        tIntersectRet = 0;
        Point a = v.a - c;
        Point b = v.b - c;
        double ang = (b-a).angle();
        Point nA = a.pOfRotate(-ang);
        Point nB = b.pOfRotate(-ang);
        double y = nA.y;
        if (y>r || y<-r)
            return ;
        double x = sqrt(r*r - y*y);
        if (x>=nA.x && x<=nB.x)
            intersectRet[tIntersectRet++] = Point(x, y).pOfRotate(ang) + c;
        if (-x>=nA.x && -x<=nB.x)
            intersectRet[tIntersectRet++] = Point(-x, y).pOfRotate(ang) + c;
    }
    virtual void intersect(const Circle &v) const {
        tIntersectRet = 0;
        Point p = v.c - c;
        double d = p.length();
        if (d > r + v.r || d==0)
            return ;
        double x = (r*r - v.r*v.r + d*d) / (2*d);
        if (x <= r)
        {
            double y = sqrt(abs(r*r - x*x));
            double ang = p.angle();
            intersectRet[tIntersectRet++] = Point(x,y).pOfRotate(ang) + c;
            intersectRet[tIntersectRet++] = Point(x,-y).pOfRotate(ang) + c;
        }
    }
    virtual void acceptPrint(ostream &os) const {
        os << c << "," << r;
    }
};
 
void Segment::intersect(const Circle &v) const {
    v.intersect(*this);
}
 
int n;
Point inps[MAXN];
vector<Seg *> segs;
vector<double> spes;
double radius = 1;
 
void input()
{
    scanf("%d%lf", &n, &radius);
    for (int i = 0; i < n; ++i)
    {
        double x, y;
        scanf("%lf%lf", &x, &y);
        inps[i] = Point(x, y);
    }
}
 
void process()
{
    segs.clear();
    spes.clear();
    for (int i = 1; i + 1 < n; ++i)
    {
        Circle *tmp = new Circle;
        tmp->c = inps[i];
        tmp->r = radius;
        segs.push_back(tmp);
    }
    for (int i = 0; i + 1 < n; ++i)
    {
        Segment *tmp = new Segment;
        tmp->a = inps[i];
        tmp->b = inps[i+1];
        tmp->moveLeft(radius);
        segs.push_back(tmp);
    }
    for (int i = 0; i < (int)segs.size(); ++i)
    {
        spes.push_back(segs[i]->getLeft());
        spes.push_back(segs[i]->getRight());
    }
    for (int i = 0; i < (int)segs.size(); ++i)
    {
        for (int j = i+1; j < (int)segs.size(); ++j)
        {
            segs[i]->intersect(segs[j]);
            if (tIntersectRet > 0)
            {
                for (int id = 0; id < tIntersectRet; ++id)
                {
                    //cout << *segs[i] << " " << *segs[j] << " : " << intersectRet[id] << endl;
                    spes.push_back(intersectRet[id].x);
                }
            }
        }
    }
    sort(spes.begin(), spes.end());
    double pre = spes[0];
    const double NONE = 1e30;
    double preEnd = NONE;
    double totalLen = 0;
    for (int i = 1; i < (int)spes.size(); ++i)
    {
        if (spes[i]-pre < EPS)
            continue;
        double cur = (pre+spes[i]) / 2;
        //cout << "Processing " << cur << "  from " << pre << " to " << spes[i] << endl;
        if (cur>=inps[0].x && cur<=inps[n-1].x)
        {
            double MY = -NONE;
            int who;
            for (int j = 0; j < (int)segs.size(); ++j)
            {
                if (!segs[j]->contains(cur))
                    continue;
                double y = segs[j]->getY(cur);
                if (y > MY)
                {
                    MY = y;
                    who = j;
                }
            }
            if (preEnd != NONE)
            {
                double LY = segs[who]->getY(pre);
                //cout << "Drop info " << *segs[who] << " " << "[" << pre << "]" << endl;
                totalLen += abs(preEnd-LY);
                //cout << "Pre drop = " << abs(preEnd-LY) << "  from " << preEnd << " to " << LY << endl;
            }
            double len = segs[who]->getLength(pre, spes[i]);
            if (len < 0)
                printf("Error!\n");
            //cout << "Curlen = " << len << " from " << pre << " to " << spes[i] << endl;
            totalLen += len;
            preEnd = segs[who]->getY(spes[i]);
        }
        pre = spes[i];
    }
    printf("%0.2lf\n", totalLen);
    for (int i = 0; i < (int)segs.size(); ++i)
        delete segs[i];
    segs.clear();
}
 
int main()
{
    input();
    process();
    return 0;
}