Getting wrong ans because of improper placements of modulo. Need Help

I need To Find The Summation Of the Below Series:
(n+1-1)C1+(n+2-1)C2+…+(n+k-1)CK(Hint:(n+k-1)Ck=(n+k-1)C(K)+(n+k-1)C(k-1))
The ans should be printed as Modulo m

Here n=Len and k=N and m=1000003

 #include<stdio.h>

 #define M 1000003

 int main(){

int t=0;

long long int sum=0,L,R,N,init=0,i=0,Len=0;

scanf("%d",&t);

while(t-- > 0){

    scanf("%lld%lld%lld",&N,&L,&R);
            
    Len=R-L+1;
    
    if(R==L){
             
       printf("%lld\n",N%M);
    }

    else if(N<=Len){

    init=Len%M;
    
    sum=init;

    for(i=2;i<=N;i++){
       //I think beacuse of improper placements of modulo m getting wromg ans
       init=((((init%M)*((Len%M+i%M-1)%M))%M)/(i%M))%M;
      
    
       //printf("%lld",init);
       sum=(sum%M+init%M)%M;
    }
    
    printf("%lld\n",sum);

    sum=0;
    }
   
}
//getch();

return 0;    

}
I am getting wrong ans because of improper placements of modulo

@aniruddha_paul: I see that you have participated in the April’15 long contest and this post is a clear violation of the contest rule. Please, remove the post.
In case you need help you can always google it or else wait for the editorials to come.
@admin ++

how to remove it??

but my points also gt removed!