/* 
Geometric Series
computes x = sum(z^k)[k=0..k-1], y = z^(k-1)
*/
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, a, k;
    long long x, y, c, az;
    z = __VERIFIER_nondet_int();
    assume_abort_if_not(z>=0 && z<=1);
    a = __VERIFIER_nondet_int();
    assume_abort_if_not(a>=0 && a<=1);
    k = __VERIFIER_nondet_int();
    assume_abort_if_not(k>=0 && k<=1);

    x = a;
    y = 1;
    c = 1;
    az = (long long) a * z;

/*@
loop invariant (((((((0 <= k) && (k <= 1)) && (y == 1)) && (a == x)) && (c == 1)) && (((long long) a * z) == az)));
@*/
    while (1) {
        __VERIFIER_assert(z*x - x + a - az*y == 0);

        if (!(c < k))
            break;

        c = c + 1;
        x = x * z + a;
        y = y * z;
    }
    __VERIFIER_assert(z*x - x + a - az*y == 0);
    return x;
}