probleme

#include <fstream>
#define M 1000003
using namespace std;

long long Invers_Modular(long long x)
{
    long long InvM=1;
    int p=M-2;
    while(p>0)
    {
        if(p%2==1)
            InvM=InvM*x%M;
        x=x*x%M;
        p=p/2;
    }
    return InvM;
}

int main()
{
    int n,m,k,s;
    ifstream f("probleme.in");
    f>>n>>m>>k>>s;
    f.close();
    long long F[M+2],solutie=0;
    F[0]=1;
    for(int i=1;i<=M;++i)
        F[i]=F[i-1]*i%M;
    for(int i=0;i<=min(m-s,k-s);++i) /// Calcul suma C(m,s)*C(n-m,k-s)+C(m,s+1)*C(n-m,k-s-1)+...+C(m,min(m,k-m))*C(n-m,k-min(m,k))
    {
        if(n-m>=k-s-i)
        {
            /// In cate moduri se pot alege s+i problemele usoare din cele m
            long long Numarator=F[m],Numitor=F[s+i]*F[m-s-i]%M;
            long long Usoare=Numarator*Invers_Modular(Numitor)%M;
            /// In cate moduri se pot alege k-s-i probleme dificile din cele n-m
            long long Dificile_Numarator=F[n-m],Dificile_Numitor=F[k-s-i]*F[n-m-k+s+i]%M;
            long long Dificile=Dificile_Numarator*Invers_Modular(Dificile_Numitor)%M;
            solutie=(solutie+Usoare*Dificile%M)%M;
        }
    }
    ofstream g("probleme.out");
    g<<solutie%M;
    g.close();
    return 0;
}