/* 
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 (1);
    ensures ((cond != 0));
@*/
void assume_abort_if_not(int cond) {
  if(!cond) {abort();}
}
/*@ 
    requires ((1 <= cond)) && (cond != 0);
    ensures ((1 <= cond)) && (1);
@*/
void __VERIFIER_assert(int cond) {
    if (!(cond)) {
    ERROR:
        {/*@ assert(0); */;}
    }
    return;
}
int main() {
    int z, k;
    long long x, y, c;
    z = __VERIFIER_nondet_int();
    assume_abort_if_not(z>=0 && z<=2);
    k = __VERIFIER_nondet_int();
    assume_abort_if_not(k>=0 && k<=2);
    assume_abort_if_not(z >= 1);
    assume_abort_if_not(k >= 1);

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

/*@
loop invariant (((((((__int128) z * x) + 1) == ((__int128) y + x)) && (1 <= c)) && (1 <= k)));
@*/
    while (1) {
        __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;
}