Enumerating Rational Numbers Consider the following method of enumerating all rational numbers be-

tween 0 and 1 (inclusively). for d = 1 to infinity do for n = 0 to d do if gcd(n,d) = 1 then print n/d where gcd(n, d) is the greatest common divisor of n and d. For example, the start of the sequence looks like: 0/1, 1/1, 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6, 5/6, 1/7, . . . Input The input consists of a series of test cases. Each test case consists of a single integer 1 ≤ k ≤ 12, 158, 598, 919. Input is terminated by ‘0’; this case should not be processed. Output For each test case, output the k-th fraction that would be printed by the program above in the format n/d. Sample Input 1 2 3 12158598919 0 Sample Output 0/1 1/1 1/2 199999/200000