Problem:
Score : 100 points

Problem Statement

Kyoto University Programming Contest is a programming contest voluntarily held by some Kyoto University students.
This contest is abbreviated as Kyoto University Programming Contest and called KUPC.

source: Kyoto University Programming Contest Information

The problem-preparing committee met to hold this year's KUPC and N problems were proposed there.
The problems are numbered from 1 to N and the name of i-th problem is P_i.
However, since they proposed too many problems, they decided to divide them into some sets for several contests.

They decided to divide this year's KUPC into several KUPCs by dividing problems under the following conditions.

One KUPC provides K problems.

Each problem appears at most once among all the KUPCs.

All the first letters of the problem names in one KUPC must be different.

You, one of the committee members, want to hold as many KUPCs as possible.
Write a program to find the maximum number of KUPCs that can be held this year.

Constraints

1 \leq N \leq 10^4

1 \leq K \leq 26

1 \leq |P_i| \leq 10

All characters in P_i are capital letters.

Note that, for each i and j (1 \leq i < j \leq N),
P_i \neq P_j are not necessarily satisfied.

Input

The input is given from Standard Input in the following format:

N K
P_1
:
P_N

Output

Print the maximum number of KUPCs that can be held on one line.

Sample Input 1

9 3
APPLE
ANT
ATCODER
BLOCK
BULL
BOSS
CAT
DOG
EGG

For example, three KUPCs can be held by dividing the problems as follows.

First: APPLE, BLOCK, CAT

Second: ANT, BULL, DOG

Third: ATCODER, BOSS, EGG

Sample Output 1

3

Sample Input 2

3 2
KU
KYOUDAI
KYOTOUNIV

Sample Output 2

0

No KUPC can be held.

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

n,k = gets.split.map(&:to_i)

alf = Array.new(26,0)
count = 0
dp = Array.new(k)
cont = true

for i in 0 .. n-1
	c = gets.chomp[0]
	alf[c.ord - 'A'.ord] += 1
end

p alf

for i in 0 .. 26-k
	dp[0] = i
	while alf[i] > 0
		for l in 0 .. k-2
			for j in dp[l]+1 .. 25
				if !cont
					break
				end
				if alf[j] > 0
					dp[l+1] = j
					break
				end
				if j == 25
					cont = false
				end
			end
		end
		if !cont
			break
		end
		for j in 0 .. k-1
			alf[dp[j]] -= 1
		end
		count += 1
	end
	if !cont
		break
	end
end

puts count