2013
11-11

# Choose and divide

The binomial coefficient C(m,n) is defined as
            m!
C(m,n) = --------
n!(m-n)!

Given four natural numbers p, q, r, and s, compute the the result of dividing C(p,q) by C(r,s).

Input consists of a sequence of lines. Each line contains four non-negative integer numbers giving values for p, q, r, and s, respectively, separated by a single space. All the numbers will be smaller than 10,000 with p>=q and r>=s.

For each line of input, print a single line containing a real number with 5 digits of precision in the fraction, giving the number as described above. You may assume the result is not greater than 100,000,000.

10 5 14 9
93 45 84 59
145 95 143 92
995 487 996 488
2000 1000 1999 999
9998 4999 9996 4998


0.12587
505606.46055
1.28223
0.48996
2.00000
3.99960


/* @author: */
import java.util.Scanner;
public class Main{

public static void main(String args[]){
Scanner sc=new Scanner(System.in);

int a[]=new int[3],b[]=new int[3],c[]=new int[3],d[]=new int[3],p,q,r,s;
int maxn;
double sum;

int i,flag;
maxn=100000001;
while(sc.hasNext())
{
p=sc.nextInt();
q=sc.nextInt();
r=sc.nextInt();
s=sc.nextInt();

a[0]=p;a[1]=s;a[2]=r-s;b[0]=r;b[1]=q;b[2]=p-q;
for(i=0;i< 3;i++)c[i]=d[i]=2;
sum=1;flag=1;
while(flag!=0)
{
flag=0;
for(i=0;i< 3;i++)
{
if(sum< maxn&&c[i]<=a[i])
{
flag=1;
sum*=c[i]++;
}
if(sum>0.00000001&&d[i]<=b[i])
{
flag=1;
sum/=d[i]++;
}
}
}
System.out.printf("%.5f\n",sum);
}
}
}