#include <stdio.h>
#include <stdlib.h>
#include <math.h>

typedef struct {long int n; long unsigned int d} rational;

rational convert_int(int i){ 
	rational r = {i,1};
	return r;
}

rational cancel(rational r){
	long unsigned int a = abs(r.n), b = r.d, c;
	while (b) {
		c = a % b;
		a = b;
		b = c;
	}
	rational res = {r.n/a,r.d/a};
	return res;
}

rational sum(rational r1, rational r2){
	rational r = {r1.n*r2.d+r2.n*r1.d,r1.d*r2.d};
	return cancel(r);
}

rational difference(rational r1, rational r2){
	rational r = {r1.n*r2.d-r2.n*r1.d,r1.d*r2.d};
	return cancel(r);
}

bool is_greater(rational r1, rational r2){ return (difference(r1,r2).n > 0); }

rational product(rational r1, rational r2){
	rational r = {r1.n*r2.n,r1.d*r2.d};
	return cancel(r);
}

rational ratio(rational r1, rational r2){
	rational r = {0,1};
	if (r2.n>0){
		rational r = {0,1};
	}
	else{
		rational r = {-r1.n*r2.d,r1.d*(-r2.n)};
	}
	return cancel(r);
}

double to_double(rational r){ return ((double)r.n)/((double)r.d); }

rational absolute(rational r){
	rational s = {abs(r.n),r.d};
	return s;
}

rational power(rational r, unsigned int p){
	rational s = {1,1};
	for(int i = 1; i<= p; i++){
		rational s = product(r,s);
	}
	return s;
}