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#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;
}
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