((3 * ‘N’ ) ! / ( 3! ^ ‘N’ ) )% ‘P

I HAVE TO SOLVE THIS. THE PROBLEM IS IF N=4; AND P=7 MY NUMERATOR BECOMES 0 AND THIS WILL GIVE ME WRONG ANSWER. THE ANSWER IS 6 BUT MY CODE IS GIVING 1.

THIS IS HOW IM DOING IT. IM ITERATING FROM 1 TO 3*N CALCULATING (3*N)FACTORIAL. CALCULATE THE DENOMINATOR, DO MOD INVERSE AND MULTIPLY. ANY SUGGESTIONS HOW CAN I DEAL WITH THIS.

#include <bits/stdc++.h>
#define ll long long
ll factorial(ll n,ll p){
    ll res=1;
    for(ll i=1;i<=n;i++){
        res=((res%p)*(i%p))%p;
    }
    return res;
}
ll power(ll num,ll d,ll p){
    ll res=1;
    while(d){
        if(d&1){
            res=((res%p)*(num%p))%p;
            d--;
        }
        d/=2;
        num=((num%p)*(num%p))%p;
    }
    return res;
}
ll mul(ll a,ll b,ll p){
    ll res=0;
    a%=p;
    while(b){
        if(b&1){
            res=((res%p)+(a%p))%p;
            b--;
        }
        b/=2;
        a=(2*(a%p))%p;
    }
    return res;
}
long long int factorialAgain(long long int n,long long int p)
{
    if(p==1)return 0;
	// Write your coder here.
    ll temp=3*n;
    ll numerator=factorial(temp,p);
    n%=(p-1);
    ll den=power(6,n,p);
    ll inverse=power(den,p-2,p);
    ll ans=mul(inverse,numerator,p);
    return ans;
}

PLEASE HELP ME.