An exchange rate is logged as a positive integer on each of n consecutive days. Over every block of exactly k consecutive days, consider the average rate. Report the maximum such average as a fraction in lowest terms.
Because the window width k is fixed, the average equals the window sum divided by k. Output the maximum sum divided by k, reduced to lowest terms, written as p/q (with q >= 1 and gcd(p, q) = 1). When the reduced denominator is 1, still print it (for example 5/1).
Input format
Line 1: two integers n and k.
Line 2: n space-separated positive integers, the daily rates.
Output format
One line: the maximum k-day average as a reduced fraction p/q.
Constraints
- 1 ≤ k ≤ n ≤ 100000
- 1 ≤ each rate ≤ 1000000