#include<bits/stdc++.h>
using namespace std;
int num[100010],r[100010],same[100010];
int main(){
	ios::sync_with_stdio(false);
	int n,m;
	cin>>n>>m;
	for(int i=1;i<=n;i++){
		int x;
		cin>>x;
		num[x]++;
	}
	for(int i=1;i<=100000;i++){
		r[i%m]+=num[i];
		same[i%m]+=num[i]/2;
	}
	if(m%2){
		int ans=r[0]/2;
		for(int i=1;2*i<=m;i++){
			if(r[i]>=r[m-i]){
				ans+=r[m-i];
				r[i]-=r[m-i];
				ans+=min(r[i]/2,same[i]);
			}
			else{
				ans+=r[i];
				r[m-i]-=r[i];
				ans+=min(r[m-i]/2,same[m-i]);
			}
		}
		cout<<ans;
	}
	else{
		int ans=r[0]/2;
		for(int i=1;2*i<m;i++){
			//cout<<i<<" "<<r[i]<<" "<<r[m-i]<<endl;
			if(r[i]>=r[m-i]){
				ans+=r[m-i];
				r[i]-=r[m-i];
				ans+=min(r[i]/2,same[i]);
			}
			else{
				
				ans+=r[i];
				r[m-i]-=r[i];
				ans+=min(r[m-i]/2,same[m-i]);
			}
			//cout<<ans<<endl;
		}
		ans+=r[m/2]/2;
		cout<<ans;
	}
	
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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
#include<bits/stdc++.h>
using namespace std;
int num[100010],r[100010],same[100010];
int main(){
	ios::sync_with_stdio(false);
	int n,m;
	cin>>n>>m;
	for(int i=1;i<=n;i++){
		int x;
		cin>>x;
		num[x]++;
	}
	for(int i=1;i<=100000;i++){
		r[i%m]+=num[i];
		same[i%m]+=num[i]/2;
	}
	if(m%2){
		int ans=r[0]/2;
		for(int i=1;2*i<=m;i++){
			if(r[i]>=r[m-i]){
				ans+=r[m-i];
				r[i]-=r[m-i];
				ans+=min(r[i]/2,same[i]);
			}
			else{
				ans+=r[i];
				r[m-i]-=r[i];
				ans+=min(r[m-i]/2,same[m-i]);
			}
		}
		cout<<ans;
	}
	else{
		int ans=r[0]/2;
		for(int i=1;2*i<m;i++){
			//cout<<i<<" "<<r[i]<<" "<<r[m-i]<<endl;
			if(r[i]>=r[m-i]){
				ans+=r[m-i];
				r[i]-=r[m-i];
				ans+=min(r[i]/2,same[i]);
			}
			else{
				
				ans+=r[i];
				r[m-i]-=r[i];
				ans+=min(r[m-i]/2,same[m-i]);
			}
			//cout<<ans<<endl;
		}
		ans+=r[m/2]/2;
		cout<<ans;
	}
	
}

```