#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
typedef pair<int,int> pii;
const int MAXSIZE=10000020;
const ll INF=0x3f3f3f3f3f3f3f3fLL;
int bufpos;
char buf[MAXSIZE];
#define NEG 0
void init(){
	#ifdef LOCAL
		freopen("F.txt","r",stdin);
		freopen("F.out","w",stdout);
	#endif
	buf[fread(buf,1,MAXSIZE,stdin)]='\0';
	bufpos=0;
}
#if NEG
int readint(){
	bool isneg;
	int val=0;
	for(;!isdigit(buf[bufpos]) && buf[bufpos]!='-';bufpos++);
	bufpos+=(isneg=buf[bufpos]=='-');
	for(;isdigit(buf[bufpos]);bufpos++)
		val=val*10+buf[bufpos]-'0';
	return isneg?-val:val;
}
#else
int readint(){
	int val=0;
	for(;!isdigit(buf[bufpos]);bufpos++);
	for(;isdigit(buf[bufpos]);bufpos++)
		val=val*10+buf[bufpos]-'0';
	return val;
}
#endif
char readchar(){
	for(;isspace(buf[bufpos]);bufpos++);
	return buf[bufpos++];
}
int readstr(char* s){
	int cur=0;
	for(;isspace(buf[bufpos]);bufpos++);
	for(;!isspace(buf[bufpos]);bufpos++)
		s[cur++]=buf[bufpos];
	s[cur]='\0';
	return cur;
}
const int maxn=200002;
vector<int> v[maxn];
int id[maxn];
set<pii> s,s2,s3,d,d2;
signed main(){
	init();
	int n=readint(),k=readint();
	for(int i=1;i<=n;i++){
		int c=readint();
		v[c].push_back(readint());
	}
	for(int i=1;i<=k;i++){
		sort(v[i].begin(),v[i].end(),greater<ll>());
		s2.insert(make_pair(v[i][0]+v[i][1],i));
		if (v[i].size()>2)
			s3.insert(make_pair(v[i][0]+v[i][1]+v[i][2],i));
	}
	puts("-1");
	if (n==1)
		return 0;
	pii qwq=*s2.rbegin();
	s2.erase(qwq);
	if (v[qwq.second].size()>2)
		s3.erase(make_pair(qwq.first+v[qwq.second][2],qwq.second));
	d2.insert(qwq);
	ll now=qwq.first;
	id[qwq.second]=2;
	if (v[qwq.second].size()!=2)
		s.insert(make_pair(v[qwq.second][2],qwq.second));
	bool flag=false;
	printf("%lld\n",now);
	for(int i=3;i<=n;i++){
		if (flag){
			ll x=s2.rbegin()->first,y=(s3.empty() || d.empty())?-INF:s3.rbegin()->first-d.begin()->first;
			if (x>=y){
				// fprintf(stderr,"WTF\n");
				now+=x;
				pii qwq=*s2.rbegin();
				s2.erase(qwq);
				if (v[qwq.second].size()>2)
					s3.erase(make_pair(qwq.first+v[qwq.second][2],qwq.second));
				d2.insert(qwq);
				id[qwq.second]=2;
				if (v[qwq.second].size()!=2)
					s.insert(make_pair(v[qwq.second][2],qwq.second));
				printf("%lld\n",now);
			}else{
				// fprintf(stderr,"WTF\n");
				now+=y;
				pii qwq=*s3.rbegin(),lol=*d.begin();
				d.erase(d.begin());
				id[lol.second]--;
				if (id[lol.second]>2)
					d.insert(make_pair(v[lol.second][id[lol.second]-1],lol.second));
				else d2.insert(make_pair(v[lol.second][0]+v[lol.second][1],lol.second));
				s.insert(lol);
				s3.erase(qwq);
				s2.erase(make_pair(qwq.first-v[qwq.second][2],qwq.second));
				id[qwq.second]=3;
				if (v[qwq.second].size()>3)
					s.insert(make_pair(v[qwq.second][3],qwq.second));
				d.insert(make_pair(v[qwq.second][2],qwq.second));
				printf("%lld\n",now);
			}
			flag=false;
			continue;
		}
		ll x=s.empty()?-INF:s.rbegin()->first,y=(s2.empty() || d.empty())?-INF:(s2.rbegin()->first-d.begin()->first);
		// printf("%d %d\n",s2.rbegin()->first,d.begin()->first);
		ll z=(d2.empty() || s3.empty())?-INF:(s3.rbegin()->first-d2.begin()->first);
		ll mx=max(x,max(y,z));
		if (mx==-INF){
			flag=true;
			puts("-1");
			continue;
		}
		if (mx==x){
			// if (i<=4)
			// fprintf(stderr,"on x\n");
			now+=x;
			printf("%lld\n",now);
			if (s2.size() && x*2<s2.rbegin()->first){
				flag=true;
				now-=x;
			}else{
				pii qwq=*s.rbegin();
				s.erase(qwq);
				if (id[qwq.second]>2)
					d.erase(make_pair(v[qwq.second][id[qwq.second]-1],qwq.second));
				else d2.erase(make_pair(v[qwq.second][0]+v[qwq.second][1],qwq.second));
				d.insert(qwq);
				id[qwq.second]++;
				if (id[qwq.second]!=v[qwq.second].size())
					s.insert(make_pair(v[qwq.second][id[qwq.second]],qwq.second));
			}
		}else if (mx==y){
			// if (i<=4)
			// fprintf(stderr,"on y\n");
			now+=y;
			printf("%lld\n",now);
			now-=y;
			flag=true;
		}else{
			// if (i<=4)
			// fprintf(stderr,"on z\n");
			now+=z;
			printf("%lld\n",now);
			now-=z;
			flag=true;
		}
	}
}

### Prompt

Please create a solution in cpp 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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
typedef pair<int,int> pii;
const int MAXSIZE=10000020;
const ll INF=0x3f3f3f3f3f3f3f3fLL;
int bufpos;
char buf[MAXSIZE];
#define NEG 0
void init(){
	#ifdef LOCAL
		freopen("F.txt","r",stdin);
		freopen("F.out","w",stdout);
	#endif
	buf[fread(buf,1,MAXSIZE,stdin)]='\0';
	bufpos=0;
}
#if NEG
int readint(){
	bool isneg;
	int val=0;
	for(;!isdigit(buf[bufpos]) && buf[bufpos]!='-';bufpos++);
	bufpos+=(isneg=buf[bufpos]=='-');
	for(;isdigit(buf[bufpos]);bufpos++)
		val=val*10+buf[bufpos]-'0';
	return isneg?-val:val;
}
#else
int readint(){
	int val=0;
	for(;!isdigit(buf[bufpos]);bufpos++);
	for(;isdigit(buf[bufpos]);bufpos++)
		val=val*10+buf[bufpos]-'0';
	return val;
}
#endif
char readchar(){
	for(;isspace(buf[bufpos]);bufpos++);
	return buf[bufpos++];
}
int readstr(char* s){
	int cur=0;
	for(;isspace(buf[bufpos]);bufpos++);
	for(;!isspace(buf[bufpos]);bufpos++)
		s[cur++]=buf[bufpos];
	s[cur]='\0';
	return cur;
}
const int maxn=200002;
vector<int> v[maxn];
int id[maxn];
set<pii> s,s2,s3,d,d2;
signed main(){
	init();
	int n=readint(),k=readint();
	for(int i=1;i<=n;i++){
		int c=readint();
		v[c].push_back(readint());
	}
	for(int i=1;i<=k;i++){
		sort(v[i].begin(),v[i].end(),greater<ll>());
		s2.insert(make_pair(v[i][0]+v[i][1],i));
		if (v[i].size()>2)
			s3.insert(make_pair(v[i][0]+v[i][1]+v[i][2],i));
	}
	puts("-1");
	if (n==1)
		return 0;
	pii qwq=*s2.rbegin();
	s2.erase(qwq);
	if (v[qwq.second].size()>2)
		s3.erase(make_pair(qwq.first+v[qwq.second][2],qwq.second));
	d2.insert(qwq);
	ll now=qwq.first;
	id[qwq.second]=2;
	if (v[qwq.second].size()!=2)
		s.insert(make_pair(v[qwq.second][2],qwq.second));
	bool flag=false;
	printf("%lld\n",now);
	for(int i=3;i<=n;i++){
		if (flag){
			ll x=s2.rbegin()->first,y=(s3.empty() || d.empty())?-INF:s3.rbegin()->first-d.begin()->first;
			if (x>=y){
				// fprintf(stderr,"WTF\n");
				now+=x;
				pii qwq=*s2.rbegin();
				s2.erase(qwq);
				if (v[qwq.second].size()>2)
					s3.erase(make_pair(qwq.first+v[qwq.second][2],qwq.second));
				d2.insert(qwq);
				id[qwq.second]=2;
				if (v[qwq.second].size()!=2)
					s.insert(make_pair(v[qwq.second][2],qwq.second));
				printf("%lld\n",now);
			}else{
				// fprintf(stderr,"WTF\n");
				now+=y;
				pii qwq=*s3.rbegin(),lol=*d.begin();
				d.erase(d.begin());
				id[lol.second]--;
				if (id[lol.second]>2)
					d.insert(make_pair(v[lol.second][id[lol.second]-1],lol.second));
				else d2.insert(make_pair(v[lol.second][0]+v[lol.second][1],lol.second));
				s.insert(lol);
				s3.erase(qwq);
				s2.erase(make_pair(qwq.first-v[qwq.second][2],qwq.second));
				id[qwq.second]=3;
				if (v[qwq.second].size()>3)
					s.insert(make_pair(v[qwq.second][3],qwq.second));
				d.insert(make_pair(v[qwq.second][2],qwq.second));
				printf("%lld\n",now);
			}
			flag=false;
			continue;
		}
		ll x=s.empty()?-INF:s.rbegin()->first,y=(s2.empty() || d.empty())?-INF:(s2.rbegin()->first-d.begin()->first);
		// printf("%d %d\n",s2.rbegin()->first,d.begin()->first);
		ll z=(d2.empty() || s3.empty())?-INF:(s3.rbegin()->first-d2.begin()->first);
		ll mx=max(x,max(y,z));
		if (mx==-INF){
			flag=true;
			puts("-1");
			continue;
		}
		if (mx==x){
			// if (i<=4)
			// fprintf(stderr,"on x\n");
			now+=x;
			printf("%lld\n",now);
			if (s2.size() && x*2<s2.rbegin()->first){
				flag=true;
				now-=x;
			}else{
				pii qwq=*s.rbegin();
				s.erase(qwq);
				if (id[qwq.second]>2)
					d.erase(make_pair(v[qwq.second][id[qwq.second]-1],qwq.second));
				else d2.erase(make_pair(v[qwq.second][0]+v[qwq.second][1],qwq.second));
				d.insert(qwq);
				id[qwq.second]++;
				if (id[qwq.second]!=v[qwq.second].size())
					s.insert(make_pair(v[qwq.second][id[qwq.second]],qwq.second));
			}
		}else if (mx==y){
			// if (i<=4)
			// fprintf(stderr,"on y\n");
			now+=y;
			printf("%lld\n",now);
			now-=y;
			flag=true;
		}else{
			// if (i<=4)
			// fprintf(stderr,"on z\n");
			now+=z;
			printf("%lld\n",now);
			now-=z;
			flag=true;
		}
	}
}

```