#include<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}

//INSERT ABOVE HERE
signed main(){
  Int n,k;
  cin>>n>>k;
  vector<Int> c(n),v(n);
  for(Int i=0;i<n;i++) cin>>c[i]>>v[i],c[i]--;

  vector<vector<Int> > G(k);
  for(Int i=0;i<n;i++) G[c[i]].emplace_back(v[i]);
  
  vector<Int> ans(n+1,-1);
  struct T{
    Int w,v,c;
    T(Int w,Int v,Int c):w(w),v(v),c(c){}
    bool operator<(const T &a)const{
      //return v/w > a.v/a.w;
      if(v*a.w==a.v*w) return w>a.w;
      return v*a.w > a.v*w;
    }
  };
  
  using P = pair<Int, Int>;
  vector<priority_queue<P> > pq(k);
  priority_queue<P> bs;
  priority_queue<P> ts;
  priority_queue<P, vector<P>, greater<P> > tt;
  vector<T> vt;
  
  for(Int i=0;i<k;i++){
    sort(G[i].rbegin(),G[i].rend());
    vt.emplace_back(2,G[i][0]+G[i][1],i);
    if(G[i].size()>2u){
      ts.emplace(G[i][0]+G[i][1]+G[i][2],i);
    }    
    for(Int j=2;j<(Int)G[i].size();j++){
      vt.emplace_back(1,G[i][j],i);
      pq[i].emplace(G[i][j],(i<<30)|j);
    }
  }
  sort(vt.begin(),vt.end());
  
  Int l=0,s=0,p1=1e17;
  set<P> used;
  set<Int> used2,used3;
  vector<Int> cnt(k,0);
  for(T t:vt){
    //cout<<l<<" "<<s<<":"<<t.w<<" "<<t.v<<" "<<t.c<<endl;
    l+=t.w;
    s+=t.v;
    while(!bs.empty()){
      if(used.count(bs.top())) bs.pop();      
      else break;
    }
    used2.emplace(t.c);
    while(!ts.empty()){
      if(used2.count(ts.top().second)) ts.pop();
      else break;
    }
    while(!tt.empty()){
      if(used3.count(tt.top().second)) tt.pop();
      else break;
    }
    if(t.w==2){
      // remove 1
      chmax(ans[l-1],s-p1);
      
      //remove cur, put 1
      if(!bs.empty()){
        chmax(ans[l-1],s-t.v+bs.top().first);
      }
      if(!tt.empty()){
        Int p2=tt.top().first;

        //remove cur and 2, put 3
        if(!ts.empty()){
          chmax(ans[l-1],s-t.v-p2+ts.top().first);
        }
        //remove 2, put nxt
        if(!pq[t.c].empty()){        
          chmax(ans[l-1],s-p2+pq[t.c].top().first);          
        }
      }
      if(!pq[t.c].empty()) bs.emplace(pq[t.c].top());
      tt.emplace(t.v,t.c);
    }else{
      chmin(p1,t.v);

      used.emplace(pq[t.c].top());pq[t.c].pop();
      if(!pq[t.c].empty()) bs.emplace(pq[t.c].top());
      
      used3.emplace(t.c);
    }
    chmax(ans[l],s);
  }  
  for(Int i=1;i<=n;i++) cout<<ans[i]<<"\n";
  cout<<flush;
  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<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}

//INSERT ABOVE HERE
signed main(){
  Int n,k;
  cin>>n>>k;
  vector<Int> c(n),v(n);
  for(Int i=0;i<n;i++) cin>>c[i]>>v[i],c[i]--;

  vector<vector<Int> > G(k);
  for(Int i=0;i<n;i++) G[c[i]].emplace_back(v[i]);
  
  vector<Int> ans(n+1,-1);
  struct T{
    Int w,v,c;
    T(Int w,Int v,Int c):w(w),v(v),c(c){}
    bool operator<(const T &a)const{
      //return v/w > a.v/a.w;
      if(v*a.w==a.v*w) return w>a.w;
      return v*a.w > a.v*w;
    }
  };
  
  using P = pair<Int, Int>;
  vector<priority_queue<P> > pq(k);
  priority_queue<P> bs;
  priority_queue<P> ts;
  priority_queue<P, vector<P>, greater<P> > tt;
  vector<T> vt;
  
  for(Int i=0;i<k;i++){
    sort(G[i].rbegin(),G[i].rend());
    vt.emplace_back(2,G[i][0]+G[i][1],i);
    if(G[i].size()>2u){
      ts.emplace(G[i][0]+G[i][1]+G[i][2],i);
    }    
    for(Int j=2;j<(Int)G[i].size();j++){
      vt.emplace_back(1,G[i][j],i);
      pq[i].emplace(G[i][j],(i<<30)|j);
    }
  }
  sort(vt.begin(),vt.end());
  
  Int l=0,s=0,p1=1e17;
  set<P> used;
  set<Int> used2,used3;
  vector<Int> cnt(k,0);
  for(T t:vt){
    //cout<<l<<" "<<s<<":"<<t.w<<" "<<t.v<<" "<<t.c<<endl;
    l+=t.w;
    s+=t.v;
    while(!bs.empty()){
      if(used.count(bs.top())) bs.pop();      
      else break;
    }
    used2.emplace(t.c);
    while(!ts.empty()){
      if(used2.count(ts.top().second)) ts.pop();
      else break;
    }
    while(!tt.empty()){
      if(used3.count(tt.top().second)) tt.pop();
      else break;
    }
    if(t.w==2){
      // remove 1
      chmax(ans[l-1],s-p1);
      
      //remove cur, put 1
      if(!bs.empty()){
        chmax(ans[l-1],s-t.v+bs.top().first);
      }
      if(!tt.empty()){
        Int p2=tt.top().first;

        //remove cur and 2, put 3
        if(!ts.empty()){
          chmax(ans[l-1],s-t.v-p2+ts.top().first);
        }
        //remove 2, put nxt
        if(!pq[t.c].empty()){        
          chmax(ans[l-1],s-p2+pq[t.c].top().first);          
        }
      }
      if(!pq[t.c].empty()) bs.emplace(pq[t.c].top());
      tt.emplace(t.v,t.c);
    }else{
      chmin(p1,t.v);

      used.emplace(pq[t.c].top());pq[t.c].pop();
      if(!pq[t.c].empty()) bs.emplace(pq[t.c].top());
      
      used3.emplace(t.c);
    }
    chmax(ans[l],s);
  }  
  for(Int i=1;i<=n;i++) cout<<ans[i]<<"\n";
  cout<<flush;
  return 0;
}

```