Nth Distinct Peak Elevation

A network of automated weather balloons phones in an elevation reading (in meters) every time it completes a lap; the same elevation value can be phoned in more than once during a flight. Mission control wants the k-th highest DISTINCT elevation value that was ever reported — two reports of the same elevation should only count once when ranking values. Given every reading and an integer k, report that value, or -1 if fewer than k distinct elevation values were ever reported.

Input format

• Line 1: two integers n and k — the number of readings and the requested rank.
• Line 2: n integers a_1 ... a_n — the elevation readings, in the order phoned in (values may repeat and may be negative).

Output format

Print a single integer: the k-th highest DISTINCT value among a_1..a_n, where the highest distinct value has rank 1. Print -1 if there are fewer than k distinct values.

Constraints

• 1 <= k <= n <= 100000
• -1000000000 <= a_i <= 1000000000

5 2
300 300 250 500 500

300

3 5
100 100 100

-1