#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define all(c) c.begin(),c.end()
#define pb push_back
#define fs first
#define sc second
#define show(x) cout << #x << " = " << (x) << endl
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
using namespace std;
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
using ll = long long;
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;

int N,K;
VV<ll> vs;

struct S{
	int w;
	ll v;
	int c;
	S(int w,ll v,int c):w(w),v(v),c(c){}
	bool operator<(const S& r) const {
		return v*2/w > r.v*2/r.w;
	}
};

int main(){
	cin>>N>>K;
	vs.resize(K);
	rep(i,N){
		int c,v;
		cin>>c>>v;
		c--;
		vs[c].pb(v);
	}
	V<S> g;
	rep(c,K){
		sort(all(vs[c]),greater<ll>());
		int n = vs[c].size();
		g.push_back(S(2,vs[c][0]+vs[c][1],c));
		rep(i,n-2){
			g.push_back(S(1,vs[c][i+2],c));
		}
	}
	sort(all(g));
	V<ll> ans(N+1,-1);
	int sz = 0;
	ll V = 0;

	ll inf = 1e18;
	ll bestoL = inf;
	ll bestL2 = inf;

	multiset<ll> oR;

	multiset<ll> R3;
	rep(c,K){
		int n = vs[c].size();
		if(n>=3){
			R3.insert(vs[c][0]+vs[c][1]+vs[c][2]);
		}
	}

	for(S x: g){
		int w = x.w;
		ll v = x.v;
		int c = x.c;
		
		if(w==2){
			//sz+1 ?
			if(bestoL != inf){
				chmax(ans[sz+1],V+v-bestoL);
			}
			if(!oR.empty()){
				chmax(ans[sz+1],V + *oR.rbegin());
			}
			if(bestL2 != inf && !R3.empty()){
				chmax(ans[sz+1], V - bestL2 + *R3.rbegin() );
			}
		}

		sz += w;
		V += v;
		ans[sz] = V;

		if(w==1){
			chmin(bestoL,v);
		}

		if(w==2){
			int n = vs[c].size();
			rep(i,n-2) oR.insert(vs[c][i+2]);
		}else{
			auto it = oR.lower_bound(v);
			assert(*it == v);
			oR.erase(it);
		}

		if(w==2){
			int n = vs[c].size();
			if(n>=3){
				auto it = R3.lower_bound(vs[c][0]+vs[c][1]+vs[c][2]);
				R3.erase(it);
			}
			chmin(bestL2,v);
		}
	}
	rep1(i,N) cout<<ans[i]<<endl;
}
### 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 <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define all(c) c.begin(),c.end()
#define pb push_back
#define fs first
#define sc second
#define show(x) cout << #x << " = " << (x) << endl
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
using namespace std;
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
using ll = long long;
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;

int N,K;
VV<ll> vs;

struct S{
	int w;
	ll v;
	int c;
	S(int w,ll v,int c):w(w),v(v),c(c){}
	bool operator<(const S& r) const {
		return v*2/w > r.v*2/r.w;
	}
};

int main(){
	cin>>N>>K;
	vs.resize(K);
	rep(i,N){
		int c,v;
		cin>>c>>v;
		c--;
		vs[c].pb(v);
	}
	V<S> g;
	rep(c,K){
		sort(all(vs[c]),greater<ll>());
		int n = vs[c].size();
		g.push_back(S(2,vs[c][0]+vs[c][1],c));
		rep(i,n-2){
			g.push_back(S(1,vs[c][i+2],c));
		}
	}
	sort(all(g));
	V<ll> ans(N+1,-1);
	int sz = 0;
	ll V = 0;

	ll inf = 1e18;
	ll bestoL = inf;
	ll bestL2 = inf;

	multiset<ll> oR;

	multiset<ll> R3;
	rep(c,K){
		int n = vs[c].size();
		if(n>=3){
			R3.insert(vs[c][0]+vs[c][1]+vs[c][2]);
		}
	}

	for(S x: g){
		int w = x.w;
		ll v = x.v;
		int c = x.c;
		
		if(w==2){
			//sz+1 ?
			if(bestoL != inf){
				chmax(ans[sz+1],V+v-bestoL);
			}
			if(!oR.empty()){
				chmax(ans[sz+1],V + *oR.rbegin());
			}
			if(bestL2 != inf && !R3.empty()){
				chmax(ans[sz+1], V - bestL2 + *R3.rbegin() );
			}
		}

		sz += w;
		V += v;
		ans[sz] = V;

		if(w==1){
			chmin(bestoL,v);
		}

		if(w==2){
			int n = vs[c].size();
			rep(i,n-2) oR.insert(vs[c][i+2]);
		}else{
			auto it = oR.lower_bound(v);
			assert(*it == v);
			oR.erase(it);
		}

		if(w==2){
			int n = vs[c].size();
			if(n>=3){
				auto it = R3.lower_bound(vs[c][0]+vs[c][1]+vs[c][2]);
				R3.erase(it);
			}
			chmin(bestL2,v);
		}
	}
	rep1(i,N) cout<<ans[i]<<endl;
}
```