#include <bits/stdc++.h>
using namespace std;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) cout << #v << "=" << endl; REP(i_debug, v.size()){ cout << v[i_debug] << ","; } cout << endl;
#define mdebug(m) cout << #m << "=" << endl; REP(i_debug, m.size()){ REP(j_debug, m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;}
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; }
template<typename T> ostream &operator<<(ostream &os, vector<T> &v){ for(int i = 0; i < v.size(); i++) { cout << v[i]; if(i != v.size() - 1) cout << endl; }; return os; }
template<typename T> void Out(T x) { cout << x << endl; }
template<typename T1, typename T2> void Ans(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); }

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};
//char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
//const int mod = 998244353;
//#define Add(x, y) x = (x + (y)) % mod
//#define Mult(x, y) x = (x * (y)) % mod

struct SegmentTree
{
    using T = int;

    int N;
    vector<T> dat;

    T id = -INF;
    T F(T &a, T &b) { return max(a, b); }
    
    SegmentTree(int n){
        N = 1;
        while(n > N) N = N << 1;
        dat = vector<T>(2 * N - 1, id);
    }

    SegmentTree(int n, vector<T> &v){
        N = 1;
        while(n > N) N = N << 1;
        dat = vector<T>(2 * N - 1, id);
        for(int i = 0; i < n; i++) dat[i + N - 1] = v[i];
        for(int i = N - 2; i >= 0; i--) dat[i] = F(dat[i * 2 + 1], dat[i * 2 + 2]); 
    }

    SegmentTree(){}


    void update(int k, T a){
        k += N - 1;
        dat[k] = a;
        while(k > 0){
            k = (k - 1) / 2;
            dat[k] = F(dat[k * 2 + 1], dat[k * 2 + 2]);
        }
    }

    void reset() { fill(dat.begin(), dat.end(), id); }

    T get(int a, int b, int k, int l, int r){
        if(r <= a || b <= l) return id;
        if(a <= l && r <= b) return dat[k];
        else{
            T vl = get(a, b, k * 2 + 1, l, (l + r) / 2);
            T vr = get(a, b, k * 2 + 2, (l + r) / 2, r);
            return F(vl, vr);
        }
    }
    T get(int a, int b) { return get(a, b, 0, 0, N); }

    T val(int k){ return dat[k + N - 1]; }
};

signed main(){

    int N, K; cin >> N >> K;
    mat val(K);
    REP(i, N){
        int C, V; cin >> C >> V;
        val[C - 1].pb(V);
    }
    REP(i, K){
        Sort(val[i]);
        Reverse(val[i]);
    }
    //mdebug(val);
    SegmentTree ST2(K), ST3(K), STm(K);
    priority_queue<Pii> que1, que2;
    REP(i, K){
        ST2.update(i, val[i][0] + val[i][1]);
        if(SZ(val[i]) >= 3) ST3.update(i, val[i][0] + val[i][1] + val[i][2]);
        que2.push(Pii(val[i][0] + val[i][1], i));
    }
    vec ans(N + 1, -1);
    int n = 0, t = 0;
    int m1 = INF, m2 = INF;
    while(!que1.empty() || !que2.empty()){
        Pii p1 = Pii(-INF, -INF); if(!que1.empty()) p1 = que1.top();
        Pii p2 = Pii(-INF, -INF); if(!que2.empty()) p2 = que2.top();
        if(p1 > p2) que1.pop();
        else{
            que2.pop();
            swap(p1, p2);
        }
        int V = p1.f, i = p1.s;
        if(i >= 0){
            //ans[n + 1]を考える
            if(!que1.empty()) Max(ans[n + 1], t + que1.top().f / 2);
            if(m1 < INF) Max(ans[n + 1], t - m1 + ST2.get(0, K));
            m2 = -STm.get(0, K);
            if(m2 < INF) Max(ans[n + 1], t - m2 + ST3.get(0, K));

            n += 2;
            t += V;
            FOR(j, 2, SZ(val[i])) que1.push(Pii(val[i][j] * 2, -(i + 1)));
            ST2.update(i, -INF);
            ST3.update(i, -INF);
            STm.update(i, -V);
        }else{
            n += 1;
            t += V / 2;
            Min(m1, V / 2);
            STm.update(-i - 1, -INF);
        }
        ans[n] = t;
    }
    FOR(i, 1, N + 1) Out(ans[i]);

    return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) cout << #v << "=" << endl; REP(i_debug, v.size()){ cout << v[i_debug] << ","; } cout << endl;
#define mdebug(m) cout << #m << "=" << endl; REP(i_debug, m.size()){ REP(j_debug, m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;}
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; }
template<typename T> ostream &operator<<(ostream &os, vector<T> &v){ for(int i = 0; i < v.size(); i++) { cout << v[i]; if(i != v.size() - 1) cout << endl; }; return os; }
template<typename T> void Out(T x) { cout << x << endl; }
template<typename T1, typename T2> void Ans(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); }

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};
//char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
//const int mod = 998244353;
//#define Add(x, y) x = (x + (y)) % mod
//#define Mult(x, y) x = (x * (y)) % mod

struct SegmentTree
{
    using T = int;

    int N;
    vector<T> dat;

    T id = -INF;
    T F(T &a, T &b) { return max(a, b); }
    
    SegmentTree(int n){
        N = 1;
        while(n > N) N = N << 1;
        dat = vector<T>(2 * N - 1, id);
    }

    SegmentTree(int n, vector<T> &v){
        N = 1;
        while(n > N) N = N << 1;
        dat = vector<T>(2 * N - 1, id);
        for(int i = 0; i < n; i++) dat[i + N - 1] = v[i];
        for(int i = N - 2; i >= 0; i--) dat[i] = F(dat[i * 2 + 1], dat[i * 2 + 2]); 
    }

    SegmentTree(){}


    void update(int k, T a){
        k += N - 1;
        dat[k] = a;
        while(k > 0){
            k = (k - 1) / 2;
            dat[k] = F(dat[k * 2 + 1], dat[k * 2 + 2]);
        }
    }

    void reset() { fill(dat.begin(), dat.end(), id); }

    T get(int a, int b, int k, int l, int r){
        if(r <= a || b <= l) return id;
        if(a <= l && r <= b) return dat[k];
        else{
            T vl = get(a, b, k * 2 + 1, l, (l + r) / 2);
            T vr = get(a, b, k * 2 + 2, (l + r) / 2, r);
            return F(vl, vr);
        }
    }
    T get(int a, int b) { return get(a, b, 0, 0, N); }

    T val(int k){ return dat[k + N - 1]; }
};

signed main(){

    int N, K; cin >> N >> K;
    mat val(K);
    REP(i, N){
        int C, V; cin >> C >> V;
        val[C - 1].pb(V);
    }
    REP(i, K){
        Sort(val[i]);
        Reverse(val[i]);
    }
    //mdebug(val);
    SegmentTree ST2(K), ST3(K), STm(K);
    priority_queue<Pii> que1, que2;
    REP(i, K){
        ST2.update(i, val[i][0] + val[i][1]);
        if(SZ(val[i]) >= 3) ST3.update(i, val[i][0] + val[i][1] + val[i][2]);
        que2.push(Pii(val[i][0] + val[i][1], i));
    }
    vec ans(N + 1, -1);
    int n = 0, t = 0;
    int m1 = INF, m2 = INF;
    while(!que1.empty() || !que2.empty()){
        Pii p1 = Pii(-INF, -INF); if(!que1.empty()) p1 = que1.top();
        Pii p2 = Pii(-INF, -INF); if(!que2.empty()) p2 = que2.top();
        if(p1 > p2) que1.pop();
        else{
            que2.pop();
            swap(p1, p2);
        }
        int V = p1.f, i = p1.s;
        if(i >= 0){
            //ans[n + 1]を考える
            if(!que1.empty()) Max(ans[n + 1], t + que1.top().f / 2);
            if(m1 < INF) Max(ans[n + 1], t - m1 + ST2.get(0, K));
            m2 = -STm.get(0, K);
            if(m2 < INF) Max(ans[n + 1], t - m2 + ST3.get(0, K));

            n += 2;
            t += V;
            FOR(j, 2, SZ(val[i])) que1.push(Pii(val[i][j] * 2, -(i + 1)));
            ST2.update(i, -INF);
            ST3.update(i, -INF);
            STm.update(i, -V);
        }else{
            n += 1;
            t += V / 2;
            Min(m1, V / 2);
            STm.update(-i - 1, -INF);
        }
        ans[n] = t;
    }
    FOR(i, 1, N + 1) Out(ans[i]);

    return 0;
}

```