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D - Project Planning

Score : $400$ points

Problem Statement

KEYENCE has $N$ departments, where $A_i$ employees belong to the $i$-th department $(1 \leq i \leq N)$. No employee belongs to multiple departments.

The company is planning cross-departmental projects. Each project will be composed of exactly $K$ employees chosen from $K$ distinct departments.

At most how many projects can be made? No employee can participate in multiple projects.

Constraints

• $1 \leq K \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq 10^{12}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$

$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print the maximum possible number of projects.

3 3
2 3 4

2

There can be two projects, each composed of three employees from distinct departments.

4 2
1 1 3 4

4

4 3
1 1 3 4

2