/*
  hardware integer division program, by Manna
  returns q==A//B
  */
void abort() { };
extern void abort();
                                                                                                                                                          
                                                                         
extern unsigned int __VERIFIER_nondet_uint();
                        
/*@ 
    requires (1);
    ensures ((cond != 0));
@*/
void assume_abort_if_not(int cond) {
  if(!cond) {abort();}
}
/*@ 
    requires ((cond != 0)) && (cond != 0);
    ensures ((cond != 0)) && (1);
@*/
void __VERIFIER_assert(int cond) {
    if (!(cond)) {
    ERROR:
        {/*@ assert(0); */;}
    }
    return;
}

int main() {
    unsigned int A, B;
    long long r, d, p, q;
    A = __VERIFIER_nondet_uint();
    assume_abort_if_not(A>=0 && A<=1);
    B = __VERIFIER_nondet_uint();
    assume_abort_if_not(B>=0 && B<=1);
    assume_abort_if_not(B >= 1);

    r = A;
    d = B;
    p = 1;
    q = 0;

/*@
loop invariant ((((((((B == 1) && (p == 2)) && (r == 1)) && (A == 1)) && (d == 2)) && (q == 0)) || ((((((B == 1) && (A == r)) && (A <= 1)) && (d == 1)) && (q == 0)) && (p == 1))));
@*/
    while (1) {
        __VERIFIER_assert(q == 0);
        __VERIFIER_assert(r == A);
        __VERIFIER_assert(d == B * p);
        if (!(r >= d)) break;

        d = 2 * d;
        p = 2 * p;
    }

/*@
loop invariant (((((((((B == 1) && (p == 2)) && (r == 1)) && (A == 1)) && (d == 2)) && (q == 0)) || ((((((B == 1) && (r == 0)) && (A == 1)) && (d == 1)) && (q == 1)) && (p == 1))) || ((((d == B) && (A == r)) && (q == 0)) && (p == 1))));
@*/
    while (1) {
        __VERIFIER_assert(A == q*B + r);
        __VERIFIER_assert(d == B*p);

        if (!(p != 1)) break;

        d = d / 2;
        p = p / 2;
        if (r >= d) {
            r = r - d;
            q = q + p;
        }
    }

    __VERIFIER_assert(A == d*q + r);
    __VERIFIER_assert(B == d);    
    return 0;
}