Alpine Reservoir Evaporation Total

A mountain research station manages a network of n alpine catchment reservoirs that store glacial meltwater collected over the season. Each evening, for exactly k consecutive cycles, the station's automated controller identifies whichever reservoir currently holds the most water and lets it evaporate down to floor(sqrt(volume)) liters — the thermal-loss model the station uses for its fullest reservoir each cycle. (If several reservoirs are tied for the most water, the controller may pick any one of them; the network's final total is the same no matter which tied reservoir is chosen.) After all k cycles have run, the station wants to know how much water remains across the whole network.

Input format

• Line 1: two integers n and k — the number of reservoirs and the number of evaporation cycles to run.
• Line 2: n integers v_1 ... v_n — the initial volume, in liters, of each reservoir.

Output format

A single integer: the total volume, in liters, remaining across all n reservoirs after exactly k evaporation cycles.

Constraints

• 1 <= n <= 10^5
• 0 <= k <= 10^5
• 0 <= v_i <= 10^9

3 2
16 25 4

13

4 1
9 9 9 9

30