// verifast_options{disable_overflow_check target:ILP32}
/*
  Cohen's integer division
  returns x % y
  http://www.cs.upc.edu/~erodri/webpage/polynomial_invariants/cohendiv.htm
*/
extern void abort(void);
//@ requires integer(&counter, ?veri_req_counter) &*& true;
//@ ensures integer(&counter, ?veri_ens_counter) &*& true;
void reach_error()
//@ requires false;
//@ ensures true;
{}extern int __VERIFIER_nondet_int(void);
//@ requires integer(&counter, ?veri_req_counter) &*& true;
//@ ensures integer(&counter, ?veri_ens_counter) &*& true;
void assume_abort_if_not(int cond) 
//@ requires integer(&counter, ?veri_req_counter) &*& (veri_req_counter == 0);
//@ ensures integer(&counter, ?veri_ens_counter) &*& (((cond != 0) && (veri_ens_counter == veri_req_counter)) && (veri_ens_counter == 0));
{  if(!cond) {abort();}
}
void __VERIFIER_assert(int cond) 
//@ requires integer(&counter, ?veri_req_counter) &*& (cond != 0);
//@ ensures integer(&counter, ?veri_ens_counter) &*& ((cond != 0) && (veri_ens_counter == veri_req_counter));
{    if (!(cond)) {
    ERROR:
	{reach_error();}
    }
    return;
}

int counter = 0;
int main() 
//@ requires module(cohendiv_ll_unwindbound100__verifast_instrumented, true) &*& (counter == 0);
//@ ensures (counter == 0) &*& junk();
{
    //@ open_module(); 
    int x, y;
    long long q, r, a, b;

    x = __VERIFIER_nondet_int();
    y = __VERIFIER_nondet_int();

    assume_abort_if_not(y >= 1);

    q = 0;
    r = x;
    a = 0;
    b = 0;

while (counter++<100)
//@ invariant integer(&counter, ?veri_inv_counter) &*& (((((((q * y) + r) + (a * y)) == (b + x)) && (veri_req_counter == 0)) && (1 <= y)) && (b == (a * y)));
    {
	__VERIFIER_assert(b == y*a);
	__VERIFIER_assert(x == q*y + r);
    
	if (!(r >= y))
	    break;
	a = 1;
	b = y;

while (counter++<100)
//@ invariant integer(&counter, ?veri_inv_counter) &*& (((((1 <= r) && ((((q * y) + r) + (a * y)) == (b + x))) && (veri_req_counter == 0)) && (1 <= y)) && (b == (a * y)));
    {
	    __VERIFIER_assert(b == y*a);
	    __VERIFIER_assert(x == q*y + r);
	    __VERIFIER_assert(r >= 0);

	    if (!(r >= 2 * b))
		break;
	    
	    __VERIFIER_assert(r >= 2 * y * a);
	    
	    a = 2 * a;
	    b = 2 * b;
	}
	r = r - b;
	q = q + a;
    }
    
    __VERIFIER_assert(x == q*y + r);
    return 0;
}