Can someone explain to me how to get this formula in calculatin inverse of the number with respect to modulo :

```
int fac[N]={1,1};
int inv[N]={0,1};
int invfac[N]={1,1};
for(n=2;n<N;n++)
{
fac[n]=LL(n)*fac[n-1]%MOD;
inv[n]=LL(inv[MOD%n])*(MOD-MOD/n)%MOD;
invfac[n]=LL(inv[n])*invfac[n-1]%MOD;
}
```

fac and invfac are clear to me. Problem is with inv[]. I know I can get this number qith little fermat’s theorem (inv[n] = n^(MOD-2) ), but I cant derive this equation - inv[n]=(inv[MOD%n])*(MOD-MOD/n)%MOD. If someone know how I can get it, please help me. Thanks.