#ifndef KOMAKI_LOCAL
#define NDEBUG
#endif

#include <bits/stdc++.h>
#include <sys/time.h>
#include <unistd.h>
using namespace std;
#define i64         int64_t
#define rep(i, n)   for(i64 i = 0; i < ((i64)(n)); ++i)
#define sz(v)       ((i64)((v).size()))
#define bit(n)      (((i64)1)<<((i64)(n)))
#define all(v)      (v).begin(), (v).end()

std::string dbgDelim(int &i){ return (i++ == 0 ? "" : ", "); }
#define dbgEmbrace(exp) { int i = 0; os << "{"; { exp; } os << "}"; return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::vector<T> v);
template <class T> std::ostream& operator<<(std::ostream &os, std::set<T> v);
template <class T> std::ostream& operator<<(std::ostream &os, std::queue<T> q);
template <class T> std::ostream& operator<<(std::ostream &os, std::priority_queue<T> q);
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::pair<T, K> p);
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::map<T, K> mp);
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::unordered_map<T, K> mp);
template <int INDEX, class TUPLE> void dbgDeploy(std::ostream &os, TUPLE tuple){}
template <int INDEX, class TUPLE, class H, class ...Ts> void dbgDeploy(std::ostream &os, TUPLE t)
{ os << (INDEX == 0 ? "" : ", ") << get<INDEX>(t); dbgDeploy<INDEX + 1, TUPLE, Ts...>(os, t); }
template <class T, class K> void dbgDeploy(std::ostream &os, std::pair<T, K> p, std::string delim)
{ os << "(" << p.first << delim << p.second << ")"; }
template <class ...Ts> std::ostream& operator<<(std::ostream &os, std::tuple<Ts...> t)
{ os << "("; dbgDeploy<0, std::tuple<Ts...>, Ts...>(os, t); os << ")"; return os; }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::pair<T, K> p)
{ dbgDeploy(os, p, ", "); return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::vector<T> v)
{ dbgEmbrace( for(T t: v){ os << dbgDelim(i) << t; }); }
template <class T> std::ostream& operator<<(std::ostream &os, std::set<T> s)
{ dbgEmbrace( for(T t: s){ os << dbgDelim(i) << t; }); }
template <class T> std::ostream& operator<<(std::ostream &os, std::queue<T> q)
{ dbgEmbrace( for(; q.size(); q.pop()){ os << dbgDelim(i) << q.front(); }); }
template <class T> std::ostream& operator<<(std::ostream &os, std::priority_queue<T> q)
{ dbgEmbrace( for(; q.size(); q.pop()){ os << dbgDelim(i) << q.top();   }); }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::map<T, K> mp)
{ dbgEmbrace( for(auto p: mp){ os << dbgDelim(i); dbgDeploy(os, p, "->"); }); }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::unordered_map<T, K> mp)
{ dbgEmbrace( for(auto p: mp){ os << dbgDelim(i); dbgDeploy(os, p, "->"); }); }
#define DBG_OUT std::cerr
#define DBG_OVERLOAD(_1, _2, _3, _4, _5, _6, macro_name, ...) macro_name
#define DBG_LINE() { char s[99]; sprintf(s, "line:%3d | ", __LINE__); DBG_OUT << s; }
#define DBG_OUTPUT(v) { DBG_OUT << (#v) << "=" << (v); }
#define DBG1(v, ...) { DBG_OUTPUT(v); }
#define DBG2(v, ...) { DBG_OUTPUT(v); DBG_OUT << ", "; DBG1(__VA_ARGS__); }
#define DBG3(v, ...) { DBG_OUTPUT(v); DBG_OUT << ", "; DBG2(__VA_ARGS__); }
#define DBG4(v, ...) { DBG_OUTPUT(v); DBG_OUT << ", "; DBG3(__VA_ARGS__); }
#define DBG5(v, ...) { DBG_OUTPUT(v); DBG_OUT << ", "; DBG4(__VA_ARGS__); }
#define DBG6(v, ...) { DBG_OUTPUT(v); DBG_OUT << ", "; DBG5(__VA_ARGS__); }

#define DEBUG0() { DBG_LINE(); DBG_OUT << std::endl; }
#define DEBUG(...)                                                      \
  {                                                                     \
    DBG_LINE();                                                         \
    DBG_OVERLOAD(__VA_ARGS__, DBG6, DBG5, DBG4, DBG3, DBG2, DBG1)(__VA_ARGS__); \
    DBG_OUT << std::endl;                                               \
  }







int main()
{
  i64 n, k;
  cin >> n >> k;
  vector<i64> counts(k, 0);
  unordered_map<i64, i64> uni_counts;
  unordered_map<i64, unordered_set<i64>> hoge;
  rep(i, n){
    i64 t;
    cin >> t;
    counts[t % k] += 1;
    uni_counts[t] += 1;
    hoge[t % k].insert(t);
  }
  i64 res = 0;
  res += counts[0] / 2;
  if(k % 2 == 0) res += counts[k / 2] / 2;
  for(int i = 1; i * 2 < k; ++i){
    i64 j = k - i;
    i64 mini = min(counts[i], counts[j]);
    i64 count0 = 0;
    i64 count1 = 0;
    for(i64 t: hoge[i]) count0 += uni_counts[t] / 2;
    for(i64 t: hoge[j]) count1 += uni_counts[t] / 2;
    res += mini;
    res += min((counts[i] - mini) / 2, count0);
    res += min((counts[j] - mini) / 2, count1);
  }
  cout << res << endl;
}














### Prompt

Create a solution in Cpp for the following problem:

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.

Examples

Input

7 5
3 1 4 1 5 9 2


Output

3


Input

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


Output

6

### Response

```cpp
#ifndef KOMAKI_LOCAL
#define NDEBUG
#endif

#include <bits/stdc++.h>
#include <sys/time.h>
#include <unistd.h>
using namespace std;
#define i64         int64_t
#define rep(i, n)   for(i64 i = 0; i < ((i64)(n)); ++i)
#define sz(v)       ((i64)((v).size()))
#define bit(n)      (((i64)1)<<((i64)(n)))
#define all(v)      (v).begin(), (v).end()

std::string dbgDelim(int &i){ return (i++ == 0 ? "" : ", "); }
#define dbgEmbrace(exp) { int i = 0; os << "{"; { exp; } os << "}"; return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::vector<T> v);
template <class T> std::ostream& operator<<(std::ostream &os, std::set<T> v);
template <class T> std::ostream& operator<<(std::ostream &os, std::queue<T> q);
template <class T> std::ostream& operator<<(std::ostream &os, std::priority_queue<T> q);
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::pair<T, K> p);
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::map<T, K> mp);
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::unordered_map<T, K> mp);
template <int INDEX, class TUPLE> void dbgDeploy(std::ostream &os, TUPLE tuple){}
template <int INDEX, class TUPLE, class H, class ...Ts> void dbgDeploy(std::ostream &os, TUPLE t)
{ os << (INDEX == 0 ? "" : ", ") << get<INDEX>(t); dbgDeploy<INDEX + 1, TUPLE, Ts...>(os, t); }
template <class T, class K> void dbgDeploy(std::ostream &os, std::pair<T, K> p, std::string delim)
{ os << "(" << p.first << delim << p.second << ")"; }
template <class ...Ts> std::ostream& operator<<(std::ostream &os, std::tuple<Ts...> t)
{ os << "("; dbgDeploy<0, std::tuple<Ts...>, Ts...>(os, t); os << ")"; return os; }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::pair<T, K> p)
{ dbgDeploy(os, p, ", "); return os; }
template <class T> std::ostream& operator<<(std::ostream &os, std::vector<T> v)
{ dbgEmbrace( for(T t: v){ os << dbgDelim(i) << t; }); }
template <class T> std::ostream& operator<<(std::ostream &os, std::set<T> s)
{ dbgEmbrace( for(T t: s){ os << dbgDelim(i) << t; }); }
template <class T> std::ostream& operator<<(std::ostream &os, std::queue<T> q)
{ dbgEmbrace( for(; q.size(); q.pop()){ os << dbgDelim(i) << q.front(); }); }
template <class T> std::ostream& operator<<(std::ostream &os, std::priority_queue<T> q)
{ dbgEmbrace( for(; q.size(); q.pop()){ os << dbgDelim(i) << q.top();   }); }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::map<T, K> mp)
{ dbgEmbrace( for(auto p: mp){ os << dbgDelim(i); dbgDeploy(os, p, "->"); }); }
template <class T, class K> std::ostream& operator<<(std::ostream &os, std::unordered_map<T, K> mp)
{ dbgEmbrace( for(auto p: mp){ os << dbgDelim(i); dbgDeploy(os, p, "->"); }); }
#define DBG_OUT std::cerr
#define DBG_OVERLOAD(_1, _2, _3, _4, _5, _6, macro_name, ...) macro_name
#define DBG_LINE() { char s[99]; sprintf(s, "line:%3d | ", __LINE__); DBG_OUT << s; }
#define DBG_OUTPUT(v) { DBG_OUT << (#v) << "=" << (v); }
#define DBG1(v, ...) { DBG_OUTPUT(v); }
#define DBG2(v, ...) { DBG_OUTPUT(v); DBG_OUT << ", "; DBG1(__VA_ARGS__); }
#define DBG3(v, ...) { DBG_OUTPUT(v); DBG_OUT << ", "; DBG2(__VA_ARGS__); }
#define DBG4(v, ...) { DBG_OUTPUT(v); DBG_OUT << ", "; DBG3(__VA_ARGS__); }
#define DBG5(v, ...) { DBG_OUTPUT(v); DBG_OUT << ", "; DBG4(__VA_ARGS__); }
#define DBG6(v, ...) { DBG_OUTPUT(v); DBG_OUT << ", "; DBG5(__VA_ARGS__); }

#define DEBUG0() { DBG_LINE(); DBG_OUT << std::endl; }
#define DEBUG(...)                                                      \
  {                                                                     \
    DBG_LINE();                                                         \
    DBG_OVERLOAD(__VA_ARGS__, DBG6, DBG5, DBG4, DBG3, DBG2, DBG1)(__VA_ARGS__); \
    DBG_OUT << std::endl;                                               \
  }







int main()
{
  i64 n, k;
  cin >> n >> k;
  vector<i64> counts(k, 0);
  unordered_map<i64, i64> uni_counts;
  unordered_map<i64, unordered_set<i64>> hoge;
  rep(i, n){
    i64 t;
    cin >> t;
    counts[t % k] += 1;
    uni_counts[t] += 1;
    hoge[t % k].insert(t);
  }
  i64 res = 0;
  res += counts[0] / 2;
  if(k % 2 == 0) res += counts[k / 2] / 2;
  for(int i = 1; i * 2 < k; ++i){
    i64 j = k - i;
    i64 mini = min(counts[i], counts[j]);
    i64 count0 = 0;
    i64 count1 = 0;
    for(i64 t: hoge[i]) count0 += uni_counts[t] / 2;
    for(i64 t: hoge[j]) count1 += uni_counts[t] / 2;
    res += mini;
    res += min((counts[i] - mini) / 2, count0);
    res += min((counts[j] - mini) / 2, count1);
  }
  cout << res << endl;
}














```