Problem:
Score : 700 points

Problem Statement

Takahashi is playing with N cards.

The i-th card has an integer X_i on it.

Takahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:

The integers on the two cards are the same.

The sum of the integers on the two cards is a multiple of M.

Find the maximum number of pairs that can be created.

Note that a card cannot be used in more than one pair.

Constraints

2≦N≦10^5

1≦M≦10^5

1≦X_i≦10^5

Input

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

N M
X_1 X_2 ... X_N

Output

Print the maximum number of pairs that can be created.

Sample Input 1

7 5
3 1 4 1 5 9 2

Sample Output 1

3

Three pairs (3,2), (1,4) and (1,9) can be created.

It is possible to create pairs (3,2) and (1,1), but the number of pairs is not maximized with this.

Sample Input 2

15 10
1 5 6 10 11 11 11 20 21 25 25 26 99 99 99

Sample Output 2

6

Solution in Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
	n,m = readline() |> split |> parseMap
	x = readline() |> split |> parseMap
	z = maximum(x)
	np = zeros(Int,m)
	p = zeros(Int,m)
	ct = zeros(Int,z)
	for i in 1:n
		if ct[x[i]]==1
			np[x[i]%m+1]-=1
			p[x[i]%m+1]+=2
			ct[x[i]]=0
		else
			np[x[i]%m+1]+=1
			ct[x[i]]=1
		end
	end
	ans = 0
	ans += np[1]>>1+p[1]>>1
	for i in 2:(m+1)>>1
		j = m+2-i
		if np[i]>np[j]
			if np[i]>np[j]+p[j]
				ans += np[j]+p[j]
				ans += p[i]>>1
			elseif np[i]+p[i]>np[j]+p[j]
				ans += np[j]+p[j]
				ans += (p[i]-(np[j]+p[j]-np[i]))>>1
			else
				ans += np[i]+p[i]
				ans += (p[j]-(np[i]+p[i]-np[j]))>>1
			end
		else
			if np[j]>np[i]+p[i]
				ans += np[i]+p[i]
				ans += p[j]>>1
			elseif np[i]+p[i]>np[j]+p[j]
				ans += np[j]+p[j]
				ans += (p[i]-(np[j]+p[j]-np[i]))>>1
			else
				ans += np[i]+p[i]
				ans += (p[j]-(np[i]+p[i]-np[j]))>>1
			end
		end	
	end
	if m%2==0
		ans += np[m>>1+1]>>1+p[m>>1+1]>>1
	end
	println(ans)
end

main()