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 Python (3.4.3) (judge verdict: Wrong Answer)

from collections import Counter

N, M = map(int, input().split())
X = list(map(int, input().split()))
cntX = Counter(X)

X.sort(reverse=True)
maxX = X[0]

ans = 0
for x in X:
    for mul in range(1, N):
        if not cntX[x]:
            continue
        y = mul * M - x
        if y > maxX:
            break
        if cntX[y]:
            ans += 1
            cntX[y] -= 1
            cntX[x] -= 1

for x in X:
    ans += cntX[x] // 2

print(ans)