11181.cpp

//BISMILLAHIRRAHMANIRRAHIM
/*
 manus tar shopner soman boro
 all my suceesses are dedicated to my parents
 Author :: Shakil Ahmed
.............AUST_CSE27.........
 prob   ::
 Type   ::
 verdict::
 */

#include <bits/stdc++.h>
#define pb push_back
#define mp make_pair

// Macro
#define pi acos(-1.0)
#define ff first
#define ss second
#define re return
#define QI queue<int>
#define SI stack<int>
#define SZ(x) ((int) (x).size())
#define all(x) (x).begin(), (x).end()
#define sq(a) ((a)*(a))
#define distance(a,b) (sq(a.x-b.x) + sq(a.y-b.y))
#define eps (1e-9)
#define iseq(a,b) (fabs(a-b)<eps)
#define eq(a,b) iseq(a,b)
#define ms(a,b) memset((a),(b),sizeof(a))
#define G() getchar()
#define MAX3(a,b,c) max(a,max(b,c))
#define II ( { int a ; read(a) ; a; } )
#define LL ( { Long a ; read(a) ; a; } )
#define DD ({double a; scanf("%lf", &a); a;})


using namespace std;

#define FI freopen ("input.txt", "r", stdin)
#define FO freopen ("output.txt", "w", stdout)

typedef long long Long;
typedef long long int64;
typedef unsigned long long ull;
typedef vector<int> vi ;
typedef set<int> si;
typedef vector<Long>vl;
typedef pair<int,int>pii;
typedef pair<string,int>psi;
typedef pair<Long,Long>pll;
typedef pair<double,double>pdd;
typedef vector<pii> vpii;

// For loop

#define forab(i, a, b)	for (__typeof (b) i = (a) ; i <= b ; ++i)
#define rep(i, n)		forab (i, 0, (n) - 1)
#define For(i, n)		forab (i, 1, n)
#define rofba(i, a, b)	for (__typeof (b)i = (b) ; i >= a ; --i)
#define per(i, n)		rofba (i, 0, (n) - 1)
#define rof(i, n)		rofba (i, 1, n)
#define forstl(i, s)	for (__typeof ((s).end ()) i = (s).begin (); i != (s).end (); ++i)

template< class T > T gcd(T a, T b) { return (b != 0 ? gcd<T>(b, a%b) : a); }
template< class T > T lcm(T a, T b) { return (a / gcd<T>(a, b) * b); }

//Fast Reader
template<class T>inline bool read(T &x){int c=getchar();int sgn=1;while(~c&&c<'0'||c>'9'){if(c=='-')sgn=-1;c=getchar();}for(x=0;~c&&'0'<=c&&c<='9';c=getchar())x=x*10+c-'0'; x*=sgn; return ~c;}

//int dx[]={1,0,-1,0};int dy[]={0,1,0,-1}; //4 Direction
//int dx[]={1,1,0,-1,-1,-1,0,1};int dy[]={0,1,1,1,0,-1,-1,-1};//8 direction

//int dx[]={2,1,-1,-2,-1,1};int dy[]={0,1,1,0,-1,-1}; //Hexagonal Direction

/* **************************************  My code start here ****************************************** */
const int NX = 25 ;

double tot[ NX ] , p [ NX ] ;

int n , r ;

bool input()
{
    n = II , r = II ;
    if( n == 0 && r == 0 ) return 0 ;
    rep ( i , n )
    {
        tot[i] = 0 ;
        scanf("%lf",&p[i]);
    }
    return 1 ;
}

double DP( int pos , double P , int taken )
{
    if( pos == n )
    {
        if( taken == r ) return P ;
        else return 0.0 ;
    }
    double ans1 = 0 , ans2 = 0 ;
    if( taken < r ) // its possible to buy
    {
       ans1 = DP( pos + 1 , P * p[pos] , taken + 1 );
       tot[ pos ] += ans1 ;
    }
    ans2 = DP( pos + 1 , P * ( 1 - p[pos] ) , taken );
    return ans1 + ans2 ;

}
int main()
{
   // I will always use scanf and printf
       int cs = 1 ;

       while(input()) {
       double ans = DP( 0 , 1 ,  0 );
       printf("Case %d:\n",cs++);
       rep( i , n ) printf("%lf\n",tot[i]/ans);
   }
    return 0;
}
/*
2 2 2
10000 1
20000 2
30000 1 2
40000 1 2
0 0 0

*/