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: Accepted)

from collections import defaultdict, Counter
N, M = map(int, input().split())
X = list(map(int, input().split()))
C = Counter(X)
D = defaultdict(int)
E = defaultdict(int)
for k, v in C.items():
    D[k%M] += v
    E[k%M] += v//2

ans = D[0] // 2

for i in range(1, M):
    j = M - i
    if i < j:
        x = min(D[i], D[j])
        y = min((D[i] - x)//2, E[i]) + min((D[j] - x)//2, E[j])
        ans += x + y
    elif i == j:
        ans += D[i] //2
    else:
        break

print(ans)