#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <cstring>
#include <queue>
#include <functional>
#include <set>
#include <map>
#define SIZE 200005
#define INF 100000000000000000LL
 
using namespace std;
typedef long long int ll;
typedef pair <ll,int> P;
 
vector <ll> vec[SIZE];
ll mx[SIZE];
ll ans[SIZE];
 
int main()
{
	int n,m;
	scanf("%d %d",&n,&m);
	for(int i=0;i<n;i++)
	{
		int c,v;
		scanf("%d %d",&c,&v);c--;
		vec[c].push_back(v);
	}
	vector <P> vx;
	for(int i=0;i<m;i++)
	{
		sort(vec[i].begin(),vec[i].end(),greater <ll>());
		vx.push_back(P(vec[i][0]+vec[i][1],i));
	}
	sort(vx.begin(),vx.end(),greater <P>());
	for(int i=m-1;i>=0;i--)
	{
		int t=vx[i].second;
		mx[i]=-INF;
		if(vec[t].size()>=3) mx[i]=vec[t][0]+vec[t][1]+vec[t][2];
		if(i+1<m) mx[i]=max(mx[i],mx[i+1]);
	}
	priority_queue <ll> que;
	int to=0,cnt=0;
	ll sum=0,last=INF;
	for(int i=1;i<=n;i++) ans[i]=-INF;
	while(1)
	{
		if(last<INF)
		{
			sum-=last;
			que.push(last);
			last=que.top();
			sum+=last;
			que.pop();
			ans[cnt]=max(ans[cnt],sum);
		}
		if(que.size()>0) ans[cnt+1]=max(ans[cnt+1],sum+que.top());
		if(to<m) ans[cnt+3]=max(ans[cnt+3],sum+mx[to]);
		if(que.size()>0&&to<m)
		{
			ans[cnt+3]=max(ans[cnt+3],sum+que.top()+vx[to].first);
			ans[cnt+4]=max(ans[cnt+4],sum+mx[to]+que.top());
		}
		if(last<INF)
		{
			ans[cnt-1]=max(ans[cnt-1],sum-last);
			if(to<m) ans[cnt+2]=max(ans[cnt+2],sum-last+mx[to]);
		}
		if(que.size()<2)
		{
			if(to==m) break;
			int t=vx[to++].second;
			sum+=vec[t][0]+vec[t][1];
			for(int i=2;i<vec[t].size();i++) que.push(vec[t][i]);
		}
		else
		{
			ll a=que.top();que.pop();
			ll b=que.top();que.pop();
			if(to==m||a+b>vx[to].first)
			{
				sum+=a+b;
				last=min(last,b);
			}
			else
			{
				que.push(a);que.push(b);
				int t=vx[to++].second;
				sum+=vec[t][0]+vec[t][1];
				for(int i=2;i<vec[t].size();i++) que.push(vec[t][i]);
			}
		}
		cnt+=2;
		ans[cnt]=max(ans[cnt],sum);
	}
	for(int i=1;i<=n;i++)
	{
		if(ans[i]<0) puts("-1");
		else printf("%lld\n",ans[i]);
	}
	return 0;
}
### Prompt

Your task is to create a CPP solution to the following problem:

There are N jewels, numbered 1 to N. The color of these jewels are represented by integers between 1 and K (inclusive), and the color of Jewel i is C_i. Also, these jewels have specified values, and the value of Jewel i is V_i.

Snuke would like to choose some of these jewels to exhibit. Here, the set of the chosen jewels must satisfy the following condition:

* For each chosen jewel, there is at least one more jewel of the same color that is chosen.



For each integer x such that 1 \leq x \leq N, determine if it is possible to choose exactly x jewels, and if it is possible, find the maximum possible sum of the values of chosen jewels in that case.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \lfloor N/2 \rfloor
* 1 \leq C_i \leq K
* 1 \leq V_i \leq 10^9
* For each of the colors, there are at least two jewels of that color.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
C_1 V_1
C_2 V_2
:
C_N V_N


Output

Print N lines. In the i-th line, if it is possible to choose exactly i jewels, print the maximum possible sum of the values of chosen jewels in that case, and print -1 otherwise.

Examples

Input

5 2
1 1
1 2
1 3
2 4
2 5


Output

-1
9
6
14
15


Input

5 2
1 1
1 2
2 3
2 4
2 5


Output

-1
9
12
12
15


Input

8 4
3 2
2 3
4 5
1 7
3 11
4 13
1 17
2 19


Output

-1
24
-1
46
-1
64
-1
77


Input

15 5
3 87
1 25
1 27
3 58
2 85
5 19
5 39
1 58
3 12
4 13
5 54
4 100
2 33
5 13
2 55


Output

-1
145
173
285
318
398
431
491
524
576
609
634
653
666
678

### Response

```cpp
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <cstring>
#include <queue>
#include <functional>
#include <set>
#include <map>
#define SIZE 200005
#define INF 100000000000000000LL
 
using namespace std;
typedef long long int ll;
typedef pair <ll,int> P;
 
vector <ll> vec[SIZE];
ll mx[SIZE];
ll ans[SIZE];
 
int main()
{
	int n,m;
	scanf("%d %d",&n,&m);
	for(int i=0;i<n;i++)
	{
		int c,v;
		scanf("%d %d",&c,&v);c--;
		vec[c].push_back(v);
	}
	vector <P> vx;
	for(int i=0;i<m;i++)
	{
		sort(vec[i].begin(),vec[i].end(),greater <ll>());
		vx.push_back(P(vec[i][0]+vec[i][1],i));
	}
	sort(vx.begin(),vx.end(),greater <P>());
	for(int i=m-1;i>=0;i--)
	{
		int t=vx[i].second;
		mx[i]=-INF;
		if(vec[t].size()>=3) mx[i]=vec[t][0]+vec[t][1]+vec[t][2];
		if(i+1<m) mx[i]=max(mx[i],mx[i+1]);
	}
	priority_queue <ll> que;
	int to=0,cnt=0;
	ll sum=0,last=INF;
	for(int i=1;i<=n;i++) ans[i]=-INF;
	while(1)
	{
		if(last<INF)
		{
			sum-=last;
			que.push(last);
			last=que.top();
			sum+=last;
			que.pop();
			ans[cnt]=max(ans[cnt],sum);
		}
		if(que.size()>0) ans[cnt+1]=max(ans[cnt+1],sum+que.top());
		if(to<m) ans[cnt+3]=max(ans[cnt+3],sum+mx[to]);
		if(que.size()>0&&to<m)
		{
			ans[cnt+3]=max(ans[cnt+3],sum+que.top()+vx[to].first);
			ans[cnt+4]=max(ans[cnt+4],sum+mx[to]+que.top());
		}
		if(last<INF)
		{
			ans[cnt-1]=max(ans[cnt-1],sum-last);
			if(to<m) ans[cnt+2]=max(ans[cnt+2],sum-last+mx[to]);
		}
		if(que.size()<2)
		{
			if(to==m) break;
			int t=vx[to++].second;
			sum+=vec[t][0]+vec[t][1];
			for(int i=2;i<vec[t].size();i++) que.push(vec[t][i]);
		}
		else
		{
			ll a=que.top();que.pop();
			ll b=que.top();que.pop();
			if(to==m||a+b>vx[to].first)
			{
				sum+=a+b;
				last=min(last,b);
			}
			else
			{
				que.push(a);que.push(b);
				int t=vx[to++].second;
				sum+=vec[t][0]+vec[t][1];
				for(int i=2;i<vec[t].size();i++) que.push(vec[t][i]);
			}
		}
		cnt+=2;
		ans[cnt]=max(ans[cnt],sum);
	}
	for(int i=1;i<=n;i++)
	{
		if(ans[i]<0) puts("-1");
		else printf("%lld\n",ans[i]);
	}
	return 0;
}
```