[algogeeks] Explain algo behind code

[amrit harry]

#include <cstdio>
 

#define MOD 1000000007

int powmod(int base, int expo){
        if(expo==0)
                return 1;
        else if(expo&1)
                return (long long)base*powmod(base, expo-1)%MOD;
        else{
                int root=powmod(base, expo>>1);
                return (long long)root*root%MOD;
        }
}
 
int inverse(int x){
        return powmod(x, MOD-2);
}
 
void init(){
        fact[0]=1;
        for(int i=1; i<=5000; i++)
                fact[i]=(long long)i*fact[i-1]%MOD;
        invfact[5000]=inverse(fact[5000]);
        for(int i=5000; i>0; i--)
                invfact[i-1]=(long long)i*invfact[i]%MOD;
}
 
int nCr(int n, int r){
        if(r>n || r<0)
                return 0;
        return (long long)((long long)fact[n]*invfact[r]%MOD)*invfact[n-r]%MOD;
}
 
int main(){
        init();
        int N, K;
        while(scanf("%d %d", &N, &K) && (N||K)){
                
                print("%d",nCr(N,K));
        }
}

This is code for calculating binomial cofficient = fact(n)/fact(n-r)*fact(r) 
value of fact(r)*fact(n-r) lead to overflow so in this code they use a method 
of calculating inverse of fact. i could not able to understand how inverse 
function work please explain. 

Thanks.

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