/* 
Geometric Series
computes x=(z-1)* sum(z^k)[k=0..k-1] , y = z^k
returns 1+x-y == 0
*/
void abort() { };
extern void abort();
                                                                                                                                                          
                                                                         
extern int __VERIFIER_nondet_int();
                        
/*@ 
    requires ((counter == 0));
    ensures (((cond != 0) && (counter == 0)));
@*/
void assume_abort_if_not(int cond) {
  if(!cond) {abort();}
}
/*@ 
    requires ((cond == 1)) && (cond != 0);
    ensures ((cond == 1)) && (1);
@*/
void __VERIFIER_assert(int cond) {
    if (!(cond)) {
    ERROR:
        {/*@ assert(0); */;}
    }
    return;
}
int counter = 0;
/*@ 
    requires ((counter == 0));
    ensures ((\old(counter) == 0));
@*/
int main() {
    int z, k;
    unsigned long long x, y, c;
    z = __VERIFIER_nondet_int();
    k = __VERIFIER_nondet_int();
    assume_abort_if_not(z >= 1);
    assume_abort_if_not(k >= 1);

    x = 1;
    y = z;
    c = 1;

/*@
loop invariant ((((((((1 <= counter) && (1 <= z)) && (((long long) z * z) == y)) && (x == ((long long) z + 1))) || ((((2 <= counter) && (y == ((__int128) ((long long) z * z) * z))) && (1 <= z)) && (x == ((((long long) z * z) + z) + 1)))) || ((((z == y) && (x == 1)) && (counter == 0)) && (1 <= z))) && (\old(counter) == 0)));
@*/
    while (counter++<2) {
        __VERIFIER_assert(x*z - x - y + 1 == 0);

        if (!(c < k)) 
            break;

        c = c + 1;
        x = x * z + 1;
        y = y * z;

    }  //geo1

    x = x * (z - 1);

    __VERIFIER_assert(1 + x - y == 0);
    return 0;
}