I have written program for printing catalan numbers.

With smaller primes output is correct, but with larger primes output is coming out to be incorrect. I am not able to figure out why.

Here is code :

#include<bits/stdc++.h>
using namespace std;

typedef long long int   ll;
#define int             ll

//some primes
int p1=1e9+7;
int p2=2097593;
int p3=6643838879;
int p4=5600748293801;

int mod=p2;

int mul(int a,int b){
    return ((a%mod)*(b%mod))%mod;
}

int binpow(int a,int b,int mod){
    a=(a%mod+mod)%mod;
    int res=1;
    while(b>0){
        if(b%2){
            res=mul(res,a);
            b--;
        }
        a=mul(a,a);
        b/=2;
    }
    return res%mod;
}

int fac[100000];
void init(){
    fac[0]=1;
    for(int i=1;i<100000;i++){
        fac[i]=mul(fac[i-1],i);
    }
}

signed main(){
    init();
    for(int n=0;n<=10;n++){
        cout<<n<<" : ";
        int x=fac[2*n];
        x=mul(binpow(fac[n],mod-2,mod),x);
        x=mul(binpow(fac[n],mod-2,mod),x);
        x=mul(binpow(n+1,mod-2,mod),x);
        cout<<x<<endl;
    }
}

Thanks in advance.