// #pragma GCC target("avx")  // CPU 処理並列化
// #pragma GCC optimize("O3")  // CPU 処理並列化
// #pragma GCC optimize("unroll-loops")  // 条件処理の呼び出しを減らす
// #define BEGIN_STACK_EXTEND(size) void * stack_extend_memory_ = malloc(size);void * stack_extend_origin_memory_;char * stack_extend_dummy_memory_ = (char*)alloca((1+(int)(((long long)stack_extend_memory_)&127))*16);*stack_extend_dummy_memory_ = 0;asm volatile("mov %%rsp, %%rbx\nmov %%rax, %%rsp":"=b"(stack_extend_origin_memory_):"a"((char*)stack_extend_memory_+(size)-1024));
// #define END_STACK_EXTEND asm volatile("mov %%rax, %%rsp"::"a"(stack_extend_origin_memory_));free(stack_extend_memory_);

#include<stdio.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<deque>
#include<stack>
#include<string>
#include<string.h>
#include<vector>
#include<set>
#include<map>
#include<bitset>
#include<stdlib.h>
#include<cassert>
#include<time.h>
#include<bitset>
#include<numeric>
#include<unordered_set>
#include<unordered_map>
#include<complex>
using namespace std;
const long long mod=1000000007;
const long long inf=mod*mod;
const long long d2=(mod+1)/2;
const double EPS=1e-11;
const double INF=1e+10;
const double PI=acos(-1.0);
const int C_SIZE = 3100000;
const int UF_SIZE = 3100000;
namespace{
	long long fact[C_SIZE];
	long long finv[C_SIZE];
	long long inv[C_SIZE];
	inline long long Comb(int a,int b){
	 	if(a<b||b<0)return 0;
	 	return fact[a]*finv[b]%mod*finv[a-b]%mod;
	}
	void init_C(int n){
		fact[0]=finv[0]=inv[1]=1;
		for(int i=2;i<n;i++){
			inv[i]=(mod-(mod/i)*inv[mod%i]%mod)%mod;
		}
		for(int i=1;i<n;i++){
			fact[i]=fact[i-1]*i%mod;
			finv[i]=finv[i-1]*inv[i]%mod;
		}
	}
	long long pw(long long a,long long b){
		if(a<0LL)return 0;
		if(b<0LL)return 0;
		long long ret=1;
		while(b){
			if(b%2)ret=ret*a%mod;
			a=a*a%mod;
			b/=2;
		}
		return ret;
	}
	long long pw_mod(long long a,long long b,long long M){
		if(a<0LL)return 0;
		if(b<0LL)return 0;
		long long ret=1;
		while(b){
			if(b%2)ret=ret*a%M;
			a=a*a%M;
			b/=2;
		}
		return ret;
	}
	int pw_mod_int(int a,int b,int M){
		if(a<0)return 0;
		if(b<0)return 0;
		int ret=1;
		while(b){
			if(b%2)ret=(long long)ret*a%M;
			a=(long long)a*a%M;
			b/=2;
		}
		return ret;
	}
	int ABS(int a){return max(a,-a);}
	long long ABS(long long a){return max(a,-a);}
	double ABS(double a){return max(a,-a);}
	int sig(double r) { return (r < -EPS) ? -1 : (r > +EPS) ? +1 : 0; }
	int UF[UF_SIZE];
	void init_UF(int n){
		for(int i=0;i<n;i++)UF[i]=-1;
	}
	int FIND(int a){
		if(UF[a]<0)return a;
		return UF[a]=FIND(UF[a]);
	}
	void UNION(int a,int b){
		a=FIND(a);b=FIND(b);if(a==b)return;
		if(UF[a]>UF[b])swap(a,b);
		UF[a]+=UF[b];UF[b]=a;
	}
}
// ここから編集しろ
int p[210000];
long long q[210000];
pair<long long,int>t[210000];
vector<long long>v[210000];
long long ans[210000];
int cnt[210000];
int main(){
	int a,b;scanf("%d%d",&a,&b);
	for(int i=0;i<a;i++){
		scanf("%d%lld",p+i,q+i);
		p[i]--;
		v[p[i]].push_back(q[i]);
	}
	int sz=0;
	for(int i=0;i<b;i++){
		std::sort(v[i].begin(),v[i].end());
		reverse(v[i].begin(),v[i].end());
		for(int j=2;j<v[i].size();j++){
			t[sz++]=make_pair(v[i][j]*2,i);
		}
		t[sz++]=make_pair(v[i][0]+v[i][1],i);
		t[sz++]=make_pair(v[i][0]+v[i][1],i);
	}
	std::sort(t,t+sz);
	reverse(t,t+sz);
	set<pair<long long,pair<int,int> > >A;
	set<pair<long long,pair<int,int> > >B;
	set<pair<long long,int> >C;
	set<pair<long long,int> >D;
	set<pair<long long,int> >E;
	for(int i=0;i<b;i++){
		D.insert(make_pair(v[i][0]+v[i][1],i));
		if(v[i].size()>2){
			E.insert(make_pair(v[i][0]+v[i][1]+v[i][2],i));
		}
	}
	long long tmp=0;
	for(int i=0;i<a;i++){
		cnt[t[i].second]++;
		if(cnt[t[i].second]==1){
			long long val=-2;
			if(!B.empty()){
				long long v1=tmp+2*(B.rbegin()->first);
				val=max(val,v1);
			}
			if(!A.empty()&&!D.empty()){
				long long v1=tmp-2*(A.begin()->first)+2*(D.rbegin()->first);
				val=max(val,v1);
			}
			if(!C.empty()&&!E.empty()){
				long long v1=tmp-(C.begin()->first)+2*(E.rbegin()->first);
				val=max(val,v1);
			}
			ans[i]=val;
		}else{
			if(cnt[t[i].second]==2){
				tmp+=t[i].first*2;
				for(int j=2;j<v[t[i].second].size();j++){
					B.insert(make_pair(v[t[i].second][j],make_pair(t[i].second,j)));
				}
				C.insert(make_pair(t[i].first*2,t[i].second));
				D.erase(make_pair(t[i].first,t[i].second));
				if(v[t[i].second].size()>2){
					int I=t[i].second;
					E.erase(make_pair(v[I][0]+v[I][1]+v[I][2],I));
				}
			}else{
				tmp+=t[i].first;
				A.insert(make_pair(t[i].first/2,make_pair(t[i].second,cnt[t[i].second]-1)));
				B.erase(make_pair(t[i].first/2,make_pair(t[i].second,cnt[t[i].second]-1)));
			}
			ans[i]=tmp;
		}
	}
	for(int i=0;i<a;i++){
		printf("%lld\n",ans[i]/2);
	}
}
### Prompt

Your challenge is to write 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
// #pragma GCC target("avx")  // CPU 処理並列化
// #pragma GCC optimize("O3")  // CPU 処理並列化
// #pragma GCC optimize("unroll-loops")  // 条件処理の呼び出しを減らす
// #define BEGIN_STACK_EXTEND(size) void * stack_extend_memory_ = malloc(size);void * stack_extend_origin_memory_;char * stack_extend_dummy_memory_ = (char*)alloca((1+(int)(((long long)stack_extend_memory_)&127))*16);*stack_extend_dummy_memory_ = 0;asm volatile("mov %%rsp, %%rbx\nmov %%rax, %%rsp":"=b"(stack_extend_origin_memory_):"a"((char*)stack_extend_memory_+(size)-1024));
// #define END_STACK_EXTEND asm volatile("mov %%rax, %%rsp"::"a"(stack_extend_origin_memory_));free(stack_extend_memory_);

#include<stdio.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<deque>
#include<stack>
#include<string>
#include<string.h>
#include<vector>
#include<set>
#include<map>
#include<bitset>
#include<stdlib.h>
#include<cassert>
#include<time.h>
#include<bitset>
#include<numeric>
#include<unordered_set>
#include<unordered_map>
#include<complex>
using namespace std;
const long long mod=1000000007;
const long long inf=mod*mod;
const long long d2=(mod+1)/2;
const double EPS=1e-11;
const double INF=1e+10;
const double PI=acos(-1.0);
const int C_SIZE = 3100000;
const int UF_SIZE = 3100000;
namespace{
	long long fact[C_SIZE];
	long long finv[C_SIZE];
	long long inv[C_SIZE];
	inline long long Comb(int a,int b){
	 	if(a<b||b<0)return 0;
	 	return fact[a]*finv[b]%mod*finv[a-b]%mod;
	}
	void init_C(int n){
		fact[0]=finv[0]=inv[1]=1;
		for(int i=2;i<n;i++){
			inv[i]=(mod-(mod/i)*inv[mod%i]%mod)%mod;
		}
		for(int i=1;i<n;i++){
			fact[i]=fact[i-1]*i%mod;
			finv[i]=finv[i-1]*inv[i]%mod;
		}
	}
	long long pw(long long a,long long b){
		if(a<0LL)return 0;
		if(b<0LL)return 0;
		long long ret=1;
		while(b){
			if(b%2)ret=ret*a%mod;
			a=a*a%mod;
			b/=2;
		}
		return ret;
	}
	long long pw_mod(long long a,long long b,long long M){
		if(a<0LL)return 0;
		if(b<0LL)return 0;
		long long ret=1;
		while(b){
			if(b%2)ret=ret*a%M;
			a=a*a%M;
			b/=2;
		}
		return ret;
	}
	int pw_mod_int(int a,int b,int M){
		if(a<0)return 0;
		if(b<0)return 0;
		int ret=1;
		while(b){
			if(b%2)ret=(long long)ret*a%M;
			a=(long long)a*a%M;
			b/=2;
		}
		return ret;
	}
	int ABS(int a){return max(a,-a);}
	long long ABS(long long a){return max(a,-a);}
	double ABS(double a){return max(a,-a);}
	int sig(double r) { return (r < -EPS) ? -1 : (r > +EPS) ? +1 : 0; }
	int UF[UF_SIZE];
	void init_UF(int n){
		for(int i=0;i<n;i++)UF[i]=-1;
	}
	int FIND(int a){
		if(UF[a]<0)return a;
		return UF[a]=FIND(UF[a]);
	}
	void UNION(int a,int b){
		a=FIND(a);b=FIND(b);if(a==b)return;
		if(UF[a]>UF[b])swap(a,b);
		UF[a]+=UF[b];UF[b]=a;
	}
}
// ここから編集しろ
int p[210000];
long long q[210000];
pair<long long,int>t[210000];
vector<long long>v[210000];
long long ans[210000];
int cnt[210000];
int main(){
	int a,b;scanf("%d%d",&a,&b);
	for(int i=0;i<a;i++){
		scanf("%d%lld",p+i,q+i);
		p[i]--;
		v[p[i]].push_back(q[i]);
	}
	int sz=0;
	for(int i=0;i<b;i++){
		std::sort(v[i].begin(),v[i].end());
		reverse(v[i].begin(),v[i].end());
		for(int j=2;j<v[i].size();j++){
			t[sz++]=make_pair(v[i][j]*2,i);
		}
		t[sz++]=make_pair(v[i][0]+v[i][1],i);
		t[sz++]=make_pair(v[i][0]+v[i][1],i);
	}
	std::sort(t,t+sz);
	reverse(t,t+sz);
	set<pair<long long,pair<int,int> > >A;
	set<pair<long long,pair<int,int> > >B;
	set<pair<long long,int> >C;
	set<pair<long long,int> >D;
	set<pair<long long,int> >E;
	for(int i=0;i<b;i++){
		D.insert(make_pair(v[i][0]+v[i][1],i));
		if(v[i].size()>2){
			E.insert(make_pair(v[i][0]+v[i][1]+v[i][2],i));
		}
	}
	long long tmp=0;
	for(int i=0;i<a;i++){
		cnt[t[i].second]++;
		if(cnt[t[i].second]==1){
			long long val=-2;
			if(!B.empty()){
				long long v1=tmp+2*(B.rbegin()->first);
				val=max(val,v1);
			}
			if(!A.empty()&&!D.empty()){
				long long v1=tmp-2*(A.begin()->first)+2*(D.rbegin()->first);
				val=max(val,v1);
			}
			if(!C.empty()&&!E.empty()){
				long long v1=tmp-(C.begin()->first)+2*(E.rbegin()->first);
				val=max(val,v1);
			}
			ans[i]=val;
		}else{
			if(cnt[t[i].second]==2){
				tmp+=t[i].first*2;
				for(int j=2;j<v[t[i].second].size();j++){
					B.insert(make_pair(v[t[i].second][j],make_pair(t[i].second,j)));
				}
				C.insert(make_pair(t[i].first*2,t[i].second));
				D.erase(make_pair(t[i].first,t[i].second));
				if(v[t[i].second].size()>2){
					int I=t[i].second;
					E.erase(make_pair(v[I][0]+v[I][1]+v[I][2],I));
				}
			}else{
				tmp+=t[i].first;
				A.insert(make_pair(t[i].first/2,make_pair(t[i].second,cnt[t[i].second]-1)));
				B.erase(make_pair(t[i].first/2,make_pair(t[i].second,cnt[t[i].second]-1)));
			}
			ans[i]=tmp;
		}
	}
	for(int i=0;i<a;i++){
		printf("%lld\n",ans[i]/2);
	}
}
```