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

  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;

ostream& operator << (ostream& os,const Point& a){ os << "(" << a.x << "," << a.y << ")"; }

ostream& operator << (ostream& os,const Segment& a){ os << "( " << a.p1 << " , " << a.p2 << " )"; }

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)); }

//rad は角度をラジアンで持たせること
Point rotate(Point a,double rad){ return Point(cos(rad)*a.x - sin(rad)*a.y,sin(rad)*a.x + cos(rad)*a.y); }

// 度をラジアンに変換
double toRad(double agl){ return agl*M_PI/180.0; }

// a => prev, b => cur, c=> next
// prev から cur へ行って next へ行く際の角度を求める
double getArg(Point a,Point b,Point c){
  double arg1 = atan2(b.y-a.y,b.x-a.x);
  double arg2 = atan2(c.y-b.y,c.x-b.x);
  double arg = fabs( arg1 - arg2 );
  while( arg > M_PI ) arg -= 2.0 * M_PI;
  return fabs(arg);
}

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 intersectLL(Line l, Line m) {
  return abs(cross(l.p2-l.p1, m.p2-m.p1)) > EPS || // non-parallel
         abs(cross(l.p2-l.p1, m.p1-l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2-l.p1, s.p1-l.p1)*       // s[0] is left of l
         cross(l.p2-l.p1, s.p2-l.p1) < EPS; // s[1] is right of l
}
bool intersectLP(Line l,Point p) {
  return abs(cross(l.p2-p, l.p1-p)) < EPS;
}
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;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1-p)+abs(s.p2-p)-abs(s.p2-s.p1) < EPS; // triangle inequality
}

Point projection(Line l,Point p) {
  double t = dot(p-l.p1, l.p1-l.p2) / norm(l.p1-l.p2);
  return l.p1 + (l.p1-l.p2)*t;
}
Point reflection(Line l,Point p) {
  return p + (projection(l, p) - p) * 2;
}
double distanceLP(Line l, Point p) {
  return abs(p - projection(l, p));
}
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s)) return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r)) return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t)) return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}

/*
same lineの時注意
もしm.p1が中心でなかったときに正しい答えとならない
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){
    vector<Point> vec;
    vec.push_back(l.p1),vec.push_back(l.p2),vec.push_back(m.p1),vec.push_back(m.p2);
    sort(vec.begin(),vec.end());
    assert(vec[1] == vec[2]); //同じセグメントかもよ
    return vec[1];
    //return m.p1;
  }
  if(abs(A) < EPS)assert(false);
  return m.p1 + (m.p2-m.p1)*(B/A);
}

*/
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);
}

//cross product of pq and pr
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); }
  
//returns true if point r is on the same line as the line pq
bool collinear(Point p,Point q,Point r) { return fabs(cross3p(p,q,r)) < EPS; }
  
//returns true if point t is on the left side of line pq
bool ccwtest(Point p,Point q,Point r){
  return cross3p(p,q,r) > 0; //can be modified to accept collinear points
}
 
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)) ) ;
}

bool isConvex(vector<Point> p) {
  int sz = (int)p.size();
  if(sz < 3)return false;//boundary case, we treat a point or a line as not convex
  bool isLeft = ccwtest(p[0],p[1],p[2]);
  for(int i=1; i<(int)p.size();i++)
    if(ccwtest(p[i],p[(i+1)%sz],p[(i+2)%sz]) != isLeft) return false;
  return true;
}


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)));
}  
  
//多角形poly内（線分上も含む）に点pが存在するかどうは判定する  
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; // ３点が平行だとangleがnanを返しsumがnanになり死ぬ
    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()]);
  }
  // あまり誤差を厳しくしすぎると良くないので以下のほうが良い 
  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 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;
  /*
  cout << "convex ---- " << endl;
  rep(i,(int)convex.size()) cout << poly[mp[convex[i]]] << " "; cout << endl;
  */
  rep(i,(int)convex.size()) {
    int s = mp[convex[i]], t = mp[convex[(i+1)%(int)convex.size()]];
    //cout << s << " " << t << endl;
    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;
            }
            //cout << "add " << j << " to " << l << " ||| " << seg<< endl;
            //G[j].push_back((Edge){l,abs(poly[j]-poly[l]),getArea(vec)});
            if( l ) G[min(j,l)].push_back((Edge){max(l,j),getArea(vec)*2,abs(poly[j]-poly[l])});
            else {
              /* 
                 poly の最後に先頭をくっつけるとこんな処理しなくても良いかも?
              */
              G[j].push_back((Edge){V,getArea(vec)*2,abs(poly[j]-poly[l])});
            }
            //G[l].push_back((Edge){j,abs(poly[j]-poly[l]),getArea(vec)});
          }
        }
        if( l == t ) break;
      }
      if( j == t ) break;
    }
  }
  /*
  rep(i,V) for(int j=(i+1)%V;j!=i;(j+=1)%=V){
    if( min(i,j)+1 == max(i,j) ) continue;
    Segment seg = Segment(poly[i],poly[j]);
    if( inPolygon(poly,seg) ) continue;
    vector<Point> vec;
    int sp,ep;
    if( i && j && i < j ) { sp = i, ep = j; }
    else                  { sp = max(i,j), ep = min(i,j); }
    for(int k=sp;;(k+=1)%=V) {
      vec.push_back(poly[k]);
      if( k == ep ) break;
    }
    G[i].push_back((Edge){j,abs(poly[i]-poly[j]),getArea(vec)});
  }
  */
}

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

int CNT;

void compute(){

  make_graph();
  /*
  cout << endl;
  cout << "made graph" << endl;
  rep(i,V) {
    cout << i << "-th " << poly[i] << endl;
    rep(j,(int)G[i].size()) {
      cout << "(" << G[i][j].dst << "=>" << poly[G[i][j].dst] << ", " << G[i][j].length << "," << G[i][j].area << endl;
    }
  } cout << endl;
  */
  rep(i,V+1) rep(j,LIMIT+1) dp[i][j] = DINF;
  
  Polygon convex = andrewScan(poly);

  set<Point> temp_S;
  rep(i,(int)convex.size()) temp_S.insert(convex[i]);
  /*
  int sp = -1;
  //rep(i,(int)poly.size()) if( temp_S.count(poly[i]) ) { sp = i; break; }
  for(int i=(int)poly.size()-1;i>=0;i--)if( temp_S.count(poly[i]) ) { sp = i; break; }
  assert( sp != -1);
  */
  double maxi = getArea(poly);
  //cout << "first area = " << maxi << endl;
  //rep(i,V) dp[i][(int)r*100] = maxi;
  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) ) { 
      //cout << dp[V][i] << " " << r << endl;
      maxi = i * 0.5; break; 
    }
  /*
  for(int i=sp;;(i+=1)%=V){
    for(int j=LIMIT;j>=0;j--) if( !equals(dp[i][j],-DINF) ){
      rep(k,(int)G[i].size()){
        int dst = G[i][k].to;
        double cons = G[i][k].consumption;
        int icons = cons * 100.0;
        double area = G[i][k].area;


        if( LT(r,(double)j/100.0 - cons) ) continue;
        if( j - icons < 0 ) continue;
        cout << dp[dst][j-icons] << " < " << dp[i][j] + area << endl;
        if( LT(dp[dst][j-icons],dp[i][j]+area) ) {
          dp[dst][j-icons] = dp[i][j] + area;
          maxi = max(maxi,dp[dst][j-icons]);
        }
      }
    }
    rep(j,LIMIT+1) dp[(i+1)%V][j] = max(dp[(i+1)%V][j],dp[i][j]);
    if( i == ((sp-1+V)%V) ) 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; }
    assert( sp != -1 );
    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; 
    //rep(i,poly.size()) cout << poly[i] << endl;
    compute();
  }
  return 0;
}

Measured memory_bytes: 12064