#include<bits/stdc++.h>

#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define EPS (1e-8)
#define equals(a,b) (fabs((a)-(b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1 
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

class Point{
public:
  double x,y;

  Point(double x = 0,double y = 0): x(x),y(y){}

  Point operator + (Point p){return Point(x+p.x,y+p.y);}
  Point operator - (Point p){return Point(x-p.x,y-p.y);}
  Point operator * (double a){return Point(a*x,a*y);}
  Point operator / (double a){return Point(x/a,y/a);}

  bool operator < (const Point& p) const{ return !equals(x,p.x)?x<p.x:(!equals(y,p.y)&&y<p.y); }
  bool operator == (const Point& p)const{ return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS; }
};

struct Segment{
  Point p1,p2;
  Segment(Point p1 = Point(),Point p2 = Point()):p1(p1),p2(p2){}
  bool operator <  (const Segment& s) const { return ( p2 == s.p2 ) ? p1 < s.p1 : p2 < s.p2; }
  bool operator == (const Segment& s) const { return ( s.p1 == p1 && s.p2 == p2 ) || ( s.p1 == p2 && s.p2 == p1 ); }

};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

double dot(Point a,Point b){ return a.x*b.x + a.y*b.y; }
double cross(Point a,Point b){ return a.x*b.y - a.y*b.x; }
double norm(Point a){ return a.x*a.x+a.y*a.y; }
double abs(Point a){ return sqrt(norm(a)); }

int ccw(Point p0,Point p1,Point p2){
  Point a = p1-p0;
  Point b = p2-p0;
  if(cross(a,b) > EPS)return COUNTER_CLOCKWISE;
  if(cross(a,b) < -EPS)return CLOCKWISE;
  if(dot(a,b) < -EPS)return ONLINE_BACK;
  if(norm(a) < norm(b))return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersectSS(Line s, Line t) {
  return ccw(s.p1,s.p2,t.p1)*ccw(s.p1,s.p2,t.p2) <= 0 &&
         ccw(t.p1,t.p2,s.p1)*ccw(t.p1,t.p2,s.p2) <= 0;
}

Point crosspoint(Line l, Line m) {
  double A = cross(l.p2 - l.p1, m.p2 - m.p1);
  double B = cross(l.p2 - l.p1, l.p2 - m.p1);
  if (abs(A) < EPS && abs(B) < EPS) return m.p1; // same line
  if (abs(A) < EPS) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
  return m.p1 +   (m.p2 - m.p1) * (B / A);
}

double cross3p(Point p,Point q,Point r) { return (r.x-q.x) * (p.y -q.y) - (r.y - q.y) * (p.x - q.x); }
bool collinear(Point p,Point q,Point r) { return fabs(cross3p(p,q,r)) < EPS; }
bool onSegment(Point p,Point q,Point r){
  return collinear(p,q,r) && equals(sqrt(pow(p.x-r.x,2)+pow(p.y-r.y,2)) + sqrt(pow(r.x-q.x,2) + pow(r.y-q.y,2) ),sqrt(pow(p.x-q.x,2)+pow(p.y-q.y,2)) ) ;
}

double angle(Point a,Point b,Point c) {
  double ux = b.x - a.x, uy = b.y - a.y;
  double vx = c.x - a.x, vy = c.y - a.y;
  return acos((ux*vx + uy*vy)/sqrt((ux*ux + uy*uy) * (vx*vx + vy*vy)));
}  
  
bool inPolygon(Polygon poly,Point p){
  if((int)poly.size() == 0)return false;
  rep(i,poly.size()) if(onSegment(poly[i],poly[(i+1)%poly.size()],p))return true;
  double sum = 0;
  for(int i=0; i < (int)poly.size() ;i++) {
    if( equals(cross(poly[i]-p,poly[(i+1)%poly.size()]-p),0.0) ) continue;
    if( cross3p(p,poly[i],poly[(i+1)%poly.size()]) < 0 ) sum -= angle(p,poly[i],poly[(i+1)%poly.size()]);
    else                                                 sum += angle(p,poly[i],poly[(i+1)%poly.size()]);
  }
  const double eps = 1e-6;
  return (fabs(sum - 2*M_PI) < eps || fabs(sum + 2*M_PI) < eps);
}  

Polygon andrewScan(Polygon s){
  Polygon u,l;
  if(s.size() < 3)return s;
  sort(s.begin(),s.end());
  u.push_back(s[0]); u.push_back(s[1]);
  l.push_back(s[s.size()-1]); l.push_back(s[s.size()-2]);

  for(int i=2;i<s.size();i++) {
    for(int n=u.size();n >= 2 && ccw(u[n-2],u[n-1],s[i]) != CLOCKWISE; n--) u.pop_back();
    u.push_back(s[i]);
  }

  for(int i=s.size()-3; i>=0 ; i--){
      for(int n=l.size(); n >= 2 && ccw(l[n-2],l[n-1],s[i]) != CLOCKWISE; n--) l.pop_back();
      l.push_back(s[i]);
  }
  reverse(l.begin(),l.end());
  for(int i = u.size()-2; i >= 1; i--) l.push_back(u[i]);
  return l;
}

bool inPolygon(const Polygon &poly,Segment seg){
  vector<Point> vp;
  vp.push_back(seg.p1);
  vp.push_back(seg.p2);
  rep(i,(int)poly.size()) {
    Segment edge = Segment(poly[i],poly[(i+1)%(int)poly.size()]);
    if( equals(cross(seg.p1-seg.p2,edge.p1-edge.p2),0.0) ) {
      if( onSegment(seg.p1,seg.p2,edge.p1) ) vp.push_back(edge.p1);
      if( onSegment(seg.p1,seg.p2,edge.p2) ) vp.push_back(edge.p2);
    } else {
      if( intersectSS(seg,edge) ) vp.push_back(crosspoint(seg,edge));
    }
  }
  sort(vp.begin(),vp.end());
  vp.erase(unique(vp.begin(),vp.end()),vp.end());
  rep(i,(int)vp.size()-1) {
    Point middle_point = ( vp[i] + vp[i+1] ) / 2.0;
    if( !inPolygon(poly,middle_point) ) return false;
  }
  return true;  
}

double getArea(const Polygon &poly){
  double sum = 0;
  rep(i,(int)poly.size()) sum += cross(poly[i],poly[(i+1)%(int)poly.size()]);
  return fabs(sum) * 0.5;
}

struct Edge {
  int dst,area;
  double length;
};

const double DINF = 1e30;

bool LTE(double a,double b) { return equals(a,b) || a < b; } 
bool LT(double a,double b) { return !equals(a,b) && a < b; }

bool veri(const Polygon& poly,Segment seg) {
  rep(i,(int)poly.size()) {
    Segment edge = Segment(poly[i],poly[(i+1)%poly.size()]);
    if( edge == seg ) return false;
    vector<Point> vec;
    vec.push_back(seg.p1), vec.push_back(seg.p2), vec.push_back(edge.p1), vec.push_back(edge.p2);
    sort(vec.begin(),vec.end());
    vec.erase(unique(vec.begin(),vec.end()),vec.end());
    if( vec.size() == 3 ) continue;
    assert( vec.size() == 4);
    if( equals(cross(edge.p1-edge.p2,seg.p1-seg.p2),0.0) ) {
      if( onSegment(edge.p1,edge.p2,seg.p1) || onSegment(edge.p1,edge.p2,seg.p2) ||
          onSegment(seg.p1,seg.p2,edge.p1)  || onSegment(seg.p1,seg.p2,edge.p2) ) return false;
    } else {
      if( intersectSS(edge,seg) ) return false;
    }
  }
  return true;
}

int V;
Polygon poly;
double r;
const int LIMIT = 21000;
double dp[70][LIMIT+1];

vector<Edge> G[70];

void make_graph(){
  rep(i,poly.size()+1) G[i].clear();
  Polygon convex = andrewScan(poly);
  map<Point,int> mp;
  rep(i,(int)poly.size()) mp[poly[i]] = i;
  rep(i,(int)convex.size()) {
    int s = mp[convex[i]], t = mp[convex[(i+1)%(int)convex.size()]];
    if( (s+1)%V == t ) continue;
    for(int j=s;;(j+=1)%=V){
      for(int l=j;;(l+=1)%=V){
        if( j != l ){
          Segment seg = Segment(poly[j],poly[l]);
          if( !inPolygon(poly,seg) && veri(poly,seg) ) {
            vector<Point> vec;
            for(int k=j;;(k+=1)%=V) {
              vec.push_back(poly[k]);
              if( k == l ) break;
            }
            if( l ) G[min(j,l)].push_back((Edge){max(l,j),getArea(vec)*2,abs(poly[j]-poly[l])});
            else  G[j].push_back((Edge){V,getArea(vec)*2,abs(poly[j]-poly[l])});
          }
        }
        if( l == t ) break;
      }
      if( j == t ) break;
    }
  }
}

int CNT;

void compute(){
  make_graph();
  rep(i,V+1) rep(j,LIMIT+1) dp[i][j] = DINF;
  double maxi = getArea(poly);
  dp[0][(int)(maxi*2)] = 0;
  rep(i,V){
    rep(area,LIMIT)if( !equals(dp[i][area],DINF) ){
      rep(j,(int)G[i].size()){
        int next = G[i][j].dst;
        int cost = G[i][j].area;
        double length = G[i][j].length;
        if( area + cost < LIMIT && LT(dp[i][area]+length,dp[next][area+cost]) ) {
          dp[next][area+cost] = dp[i][area]+length;
        }
      }
    }
    rep(j,LIMIT) dp[i+1][j] = min(dp[i+1][j],dp[i][j]);
  }
  for(int i=LIMIT;i>=0;i--) if( !equals(dp[V][i],DINF) && LTE(dp[V][i],r) ) { 
      maxi = i * 0.5; break; 
    }
  printf("case %d: %.1f\n",CNT++,maxi);
}

int main(){
  int temp;
  CNT = 1;
  while( cin >> V >> temp, V|temp){
    r = temp;
    poly.clear();
    poly.resize(V);
    rep(i,V) cin >> poly[i].x >> poly[i].y;
    Point mini = poly[0];
    rep(i,V) mini = min(mini,poly[i]);
    int sp = -1;
    rep(i,V) if( mini == poly[i] ) { sp = i; break; }
    Polygon ps;
    for(int i=sp;i<V;i++) ps.push_back(poly[i]);
    for(int i=0;i<sp;i++) ps.push_back(poly[i]);
    poly = ps; 
    compute();
  }
  return 0;
}

Measured memory_bytes: 12064