CANTON.cpp

#include <iostream>
#include <math.h>
using namespace std;

#define ull unsigned long long

/*	sum	 	term		id	x
*	 2		1			1	1	
*	 3		2	3		2	2
*	 4		4	5	6	3	4
*	 5		7	8	9	4	7
*
*	1,2,4,7,...=> x1 = 1, x_n = 1 + n(n-1)/2;
*	we have term = a => 1 + n(n-1)/2 = a => n = (1 + sqrt(8a-7))/2
*/

int main()
{
	//freopen("input.txt","r",stdin);
	ull t = 0;
	cin >> t;
	for(int tc = 0; tc < t; tc++)
	{
		ull a = 0;
		cin >> a;

		ull id  = (1 + (ull) sqrt(8*a-7))/2;
		ull sum = id + 1;
		ull start = 1 + (id * (id-1))/ 2;
		ull delta = (a - start);

		ull y = 1;
		ull x = sum - y;

		x -= delta;
		y += delta;

		if(sum%2 == 0)
		{
			// form: x/y
			cout << "TERM " << a << " IS " << x << "/" << y << endl;
		}
		else
		{
			// form: y/x
			cout << "TERM " << a << " IS " << y << "/" << x << endl;
		}
	}
	return 0;
}