#include <bits/stdc++.h>
#include <type_traits>
using namespace std;

using ll=int64_t;
#define int ll

#define FOR(i,a,b) for(int i=int(a);i<int(b);i++)
#define REP(i,b) FOR(i,0,b)
#define MP make_pair
#define PB push_back
#define EB emplace_back
#define ALL(x) x.begin(),x.end()
auto& errStream=cerr;
#ifdef LOCAL
#define cerr (cerr<<"-- line "<<__LINE__<<" -- ")
#else
class CerrDummy{}cerrDummy;
template<class T>
CerrDummy& operator<<(CerrDummy&cd,const T&){
	return cd;
}
using charTDummy=char;
using traitsDummy=char_traits<charTDummy>;
CerrDummy& operator<<(CerrDummy&cd,basic_ostream<charTDummy,traitsDummy>&(basic_ostream<charTDummy,traitsDummy>&)){
	return cd;
}
#define cerr cerrDummy
#endif
#define REACH cerr<<"reached"<<endl
#define DMP(x) cerr<<#x<<":"<<x<<endl
#define ZERO(x) memset(x,0,sizeof(x))
#define ONE(x) memset(x,-1,sizeof(x))

using pi=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"{";
	REP(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"}";
	return os;
}

ll read(){
	ll i;
	scanf("%"  SCNd64,&i);
	return i;
}

void printSpace(){
	printf(" ");
}

void printEoln(){
	printf("\n");
}

void print(ll x,int suc=1){
	printf("%" PRId64,x);
	if(suc==1)
		printEoln();
	if(suc==2)
		printSpace();
}

string readString(){
	static char buf[3341000];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341000];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

template<class T,class U>
void chmax(T& a,U b){
	if(a<b)
		a=b;
}

template<class T,class U>
void chmin(T& a,U b){
	if(b<a)
		a=b;
}

template<class T>
T Sq(const T& t){
	return t*t;
}

#define CAPITAL
void Yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void No(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

signed main(){
	int n=read(),k=read();
	vector<vi> vals(k);
	REP(i,n){
		int c=read()-1,v=read();
		vals[c].PB(v);
	}
	vector<pi> wi;
	REP(i,k){
		sort(ALL(vals[i]),greater<int>());
		vals[i][0]=vals[i][1]=vals[i][0]+vals[i][1];
		FOR(j,2,vals[i].size())
			vals[i][j]*=2;
		for(auto v:vals[i])
			wi.EB(v,i);
	}
	sort(ALL(wi),greater<pi>());
	
	const auto GetMax=[&](const multiset<int>& s){
		if(s.empty())return -inf;
		return *prev(s.end());
	};
	
	const auto GetMin=[&](const multiset<int>& s){
		if(s.empty())return inf;
		return *s.begin();
	};
	
	multiset<int> p,q,r,s,t;
	REP(i,k){
		s.insert(vals[i][0]+vals[i][1]);
		if(vals[i].size()>=3)
			t.insert(vals[i][0]+vals[i][1]+vals[i][2]);
	}
	
	vi cnt(k);
	vi ans(n,-1);
	int cur=0;
	REP(i,n){
		int v=wi[i].first,c=wi[i].second;
		if(cnt[c]==0){
			int dif=-inf;
			chmax(dif,GetMax(q));
			chmax(dif,-GetMin(p)+GetMax(s));
			chmax(dif,-GetMin(r)+GetMax(t));
			chmax(ans[i],cur+dif);
		}else{
			ans[i]=cur+v;
			if(cnt[c]==1){
				s.erase(s.find(vals[c][0]+vals[c][1]));
				r.insert(vals[c][0]+vals[c][1]);
				if(vals[c].size()>=3)
					t.erase(t.find(vals[c][0]+vals[c][1]+vals[c][2]));
				FOR(j,2,vals[c].size())
					q.insert(vals[c][j]);
			}else{
				q.erase(q.find(v));
				p.insert(v);
			}
		}
		cnt[c]++;
		cur+=v;
	}
	REP(i,n)
		print(ans[i]==-1?-1:ans[i]/2);
}

### Prompt

Please formulate 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 <bits/stdc++.h>
#include <type_traits>
using namespace std;

using ll=int64_t;
#define int ll

#define FOR(i,a,b) for(int i=int(a);i<int(b);i++)
#define REP(i,b) FOR(i,0,b)
#define MP make_pair
#define PB push_back
#define EB emplace_back
#define ALL(x) x.begin(),x.end()
auto& errStream=cerr;
#ifdef LOCAL
#define cerr (cerr<<"-- line "<<__LINE__<<" -- ")
#else
class CerrDummy{}cerrDummy;
template<class T>
CerrDummy& operator<<(CerrDummy&cd,const T&){
	return cd;
}
using charTDummy=char;
using traitsDummy=char_traits<charTDummy>;
CerrDummy& operator<<(CerrDummy&cd,basic_ostream<charTDummy,traitsDummy>&(basic_ostream<charTDummy,traitsDummy>&)){
	return cd;
}
#define cerr cerrDummy
#endif
#define REACH cerr<<"reached"<<endl
#define DMP(x) cerr<<#x<<":"<<x<<endl
#define ZERO(x) memset(x,0,sizeof(x))
#define ONE(x) memset(x,-1,sizeof(x))

using pi=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"{";
	REP(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"}";
	return os;
}

ll read(){
	ll i;
	scanf("%"  SCNd64,&i);
	return i;
}

void printSpace(){
	printf(" ");
}

void printEoln(){
	printf("\n");
}

void print(ll x,int suc=1){
	printf("%" PRId64,x);
	if(suc==1)
		printEoln();
	if(suc==2)
		printSpace();
}

string readString(){
	static char buf[3341000];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341000];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

template<class T,class U>
void chmax(T& a,U b){
	if(a<b)
		a=b;
}

template<class T,class U>
void chmin(T& a,U b){
	if(b<a)
		a=b;
}

template<class T>
T Sq(const T& t){
	return t*t;
}

#define CAPITAL
void Yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void No(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

signed main(){
	int n=read(),k=read();
	vector<vi> vals(k);
	REP(i,n){
		int c=read()-1,v=read();
		vals[c].PB(v);
	}
	vector<pi> wi;
	REP(i,k){
		sort(ALL(vals[i]),greater<int>());
		vals[i][0]=vals[i][1]=vals[i][0]+vals[i][1];
		FOR(j,2,vals[i].size())
			vals[i][j]*=2;
		for(auto v:vals[i])
			wi.EB(v,i);
	}
	sort(ALL(wi),greater<pi>());
	
	const auto GetMax=[&](const multiset<int>& s){
		if(s.empty())return -inf;
		return *prev(s.end());
	};
	
	const auto GetMin=[&](const multiset<int>& s){
		if(s.empty())return inf;
		return *s.begin();
	};
	
	multiset<int> p,q,r,s,t;
	REP(i,k){
		s.insert(vals[i][0]+vals[i][1]);
		if(vals[i].size()>=3)
			t.insert(vals[i][0]+vals[i][1]+vals[i][2]);
	}
	
	vi cnt(k);
	vi ans(n,-1);
	int cur=0;
	REP(i,n){
		int v=wi[i].first,c=wi[i].second;
		if(cnt[c]==0){
			int dif=-inf;
			chmax(dif,GetMax(q));
			chmax(dif,-GetMin(p)+GetMax(s));
			chmax(dif,-GetMin(r)+GetMax(t));
			chmax(ans[i],cur+dif);
		}else{
			ans[i]=cur+v;
			if(cnt[c]==1){
				s.erase(s.find(vals[c][0]+vals[c][1]));
				r.insert(vals[c][0]+vals[c][1]);
				if(vals[c].size()>=3)
					t.erase(t.find(vals[c][0]+vals[c][1]+vals[c][2]));
				FOR(j,2,vals[c].size())
					q.insert(vals[c][j]);
			}else{
				q.erase(q.find(v));
				p.insert(v);
			}
		}
		cnt[c]++;
		cur+=v;
	}
	REP(i,n)
		print(ans[i]==-1?-1:ans[i]/2);
}

```