PROBLEM LINK :
Author : Rahul Agarwal
Tester : Rahul Agarwal
Editorialist : Rahul Agarwal
DIFFICULTY :
Medium-Hard
PREREQUISITES :
Number Theory, Lucas Theorem
PROBLEM :
Find the number of ways of selecting K distinct items from a group of N distinct items.
As the output can be large print the answer modulo P.
Flawed Code :
#define ll long long
ll fact[1000000];
int pwr(int x,int p,int mod){
ll t = 1,a=x;
while(p)
{
a=(a*a)%mod;p=p>>1;
}
return t;}
ll abc(int n,int r,int MOD){
ll tem=(fact[r]*fact[n-r])%MOD;
tem=pwr(tem,MOD-1,MOD);
return (tem*fact[n])%MOD;}
ll xyz(ll n,ll m,int p){
if(n==0)return 1;
if(m==0)return 1;
int ni=n%p;
int mi=m%p;
return xyz(n/p,m/p,p)*abc(ni,mi,p)%p;}
ll C(ll n,ll r,int MOD){
fact[0]=1; for(int i=1;i!=MOD;i++) fact[i]=(i*fact[i-1])%MOD;
return xyz(n,r,MOD);}
int main(){
int t;cin>>t;
while(t–){
ll n,k;int p;
cin>>n>>k>>p;
printf(“%lld”,C(n,k,p));
}}
EXPLANATION :
This question was a simple implementation of the Lucas Theorem
The corrected code can be view at, Corrected Code.