Multiplicative Inverse: Test Cases Failing

#1

Here is my code, I have made an extended euclidian function, but Testcases #2, #4 and #5 still fails

#include<iostream>
using namespace std;
#define ll long long
#define MOD 1000000007

ll ex, ey,ed;
void ExtendedEuclid(ll a, ll b){
    if(b==0){
        ex=1; ey=0; ed=a;
    }
    else{
        ExtendedEuclid(b, a%b);
        ll temp = ex;
        ex = ey;
        ey = temp-((a/b)*ey);
    }

}


int main(){
    ll n;
    cin>>n;
    ExtendedEuclid(n,MOD);
    cout<<ex<<endl;

}

Also I am not able to clearly comprehend the implementation, As I know that Extended Euclidean is used to find out the solution of equations of the form Ax+By = C where C is a multiple of divisor of A and B, so we calculate x and y from Ext. Euclid, now what I am able to understand is we are passing B as MOD and A as n and C as 1 so it becomes

nx + MODy = 1, 
hence nx =  1 - MODy
so x = (1/n)*(1-MODy)

so why is x giving us the solution of inverse of n?

Also, will this code work every-time as it is known that for this to work as GCD(n,MOD) must always be 1, and it might not be true for some cases?

@Saurabh-Kumar-1331476656958199

#2

nx +MODy =1
(nx+MODy=1)MOD
nx+0=1(MOD)
therefore
nx=1(MOD)
hence , x is modulo inverse of n

#3

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