#include <bits/stdc++.h>

using namespace std;

inline void read() {}
template <class S>
inline void read(S &arg) {
  cin >> arg;
}
template <class S>
inline void readA(S Lptr, S Rptr) {
  while (Lptr != Rptr) {
    read(*Lptr);
    Lptr++;
  }
}
template <class S, class... T>
inline void read(S &arg, T &... rest) {
  read(arg);
  read(rest...);
}

inline void write() {}
template <class S>
inline void write(S arg) {
  cout << arg;
}
template <class S>
inline void writeA(S Lptr, S Rptr) {
  if (Lptr != Rptr) {
    write(*Lptr);
    Lptr++;
  }
  while (Lptr != Rptr) {
    write('\n');
    write(*Lptr);
    Lptr++;
  }
}
template <class S, class... T>
inline void write(S arg, T... rest) {
  write(arg);
  write(' ');
  write(rest...);
}

#define int long long
#define rep(i, j, k) for (int i = j; i < (int)k; i++)
#define pb push_back
#define mt make_tuple
#define all(x) x.begin(), x.end()

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;

template <class T, class S>
inline bool smin(T &a, S b) {
  return (T)b < a ? a = b, 1 : 0;
}
template <class T, class S>
inline bool smax(T &a, S b) {
  return a < (T)b ? a = b, 1 : 0;
}

constexpr int MOD = 1e9 + 7;
constexpr int N = 1e6 + 10;

template <typename T>
inline T mod(T &v) {
  return v = (v % MOD + MOD) % MOD;
}
template <typename S, typename T>
inline S add(S &l, T r) {
  return mod(l += r);
}

ll po(ll v, ll u) {
  return u ? po(v * v % MOD, u >> 1) * (u & 1 ? v : 1) % MOD : 1;
}

int n, k;
vi vec[N];
ll res[N];
vector<pair<int, pii>> st;
ll shiti[N];

int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);

  memset(res, -1, sizeof(res));

  read(n, k);
  rep(i, 0, n) {
    int c, v;
    read(c, v);
    vec[c].pb(v);
  }

  rep(i, 1, k + 1) {
    sort(all(vec[i]), greater<int>());
    st.pb({-1 * (vec[i][0] + vec[i][1]), {0, i}});
    rep(j, 2, vec[i].size()) st.pb({-2 * vec[i][j], {j, i}});
  }
  sort(all(st));

  int sz = 0;
  ll sum = 0;
  ll last = 0;
  multiset<int> ms;

  for (int i = st.size() - 1; ~i; i--) {
    shiti[i] = shiti[i + 1];
    if (st[i].second.first == 0 && vec[st[i].second.second].size() > 2)
      smax(shiti[i], vec[st[i].second.second][2] - st[i].first);
  }

  rep(i, 0, st.size()) {
    smax(res[sz], sum);
    if (!ms.empty()) smax(res[sz + 1], sum + *ms.rbegin());
    if (shiti[i]) smax(res[sz + 3], sum + shiti[i]);
    if (last) smax(res[sz - 1], sum - last);
    if (st[i].second.first == 0) {
      sum -= st[i].first;
      sz += 2;
      if (vec[st[i].second.second].size() > 2)
        ms.insert(vec[st[i].second.second][2]);
    } else {
      sum -= st[i].first / 2;
      last = -st[i].first / 2;
      sz++;
      ms.erase(ms.find(vec[st[i].second.second][st[i].second.first]));
      if (vec[st[i].second.second].size() > st[i].second.first + 1)
        ms.insert(vec[st[i].second.second][st[i].second.first + 1]);
    }
  }
  smax(res[sz], sum);
  if (last) smax(res[sz - 1], sum - last);
  writeA(res + 1, res + n + 1);

  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;

inline void read() {}
template <class S>
inline void read(S &arg) {
  cin >> arg;
}
template <class S>
inline void readA(S Lptr, S Rptr) {
  while (Lptr != Rptr) {
    read(*Lptr);
    Lptr++;
  }
}
template <class S, class... T>
inline void read(S &arg, T &... rest) {
  read(arg);
  read(rest...);
}

inline void write() {}
template <class S>
inline void write(S arg) {
  cout << arg;
}
template <class S>
inline void writeA(S Lptr, S Rptr) {
  if (Lptr != Rptr) {
    write(*Lptr);
    Lptr++;
  }
  while (Lptr != Rptr) {
    write('\n');
    write(*Lptr);
    Lptr++;
  }
}
template <class S, class... T>
inline void write(S arg, T... rest) {
  write(arg);
  write(' ');
  write(rest...);
}

#define int long long
#define rep(i, j, k) for (int i = j; i < (int)k; i++)
#define pb push_back
#define mt make_tuple
#define all(x) x.begin(), x.end()

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;

template <class T, class S>
inline bool smin(T &a, S b) {
  return (T)b < a ? a = b, 1 : 0;
}
template <class T, class S>
inline bool smax(T &a, S b) {
  return a < (T)b ? a = b, 1 : 0;
}

constexpr int MOD = 1e9 + 7;
constexpr int N = 1e6 + 10;

template <typename T>
inline T mod(T &v) {
  return v = (v % MOD + MOD) % MOD;
}
template <typename S, typename T>
inline S add(S &l, T r) {
  return mod(l += r);
}

ll po(ll v, ll u) {
  return u ? po(v * v % MOD, u >> 1) * (u & 1 ? v : 1) % MOD : 1;
}

int n, k;
vi vec[N];
ll res[N];
vector<pair<int, pii>> st;
ll shiti[N];

int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);

  memset(res, -1, sizeof(res));

  read(n, k);
  rep(i, 0, n) {
    int c, v;
    read(c, v);
    vec[c].pb(v);
  }

  rep(i, 1, k + 1) {
    sort(all(vec[i]), greater<int>());
    st.pb({-1 * (vec[i][0] + vec[i][1]), {0, i}});
    rep(j, 2, vec[i].size()) st.pb({-2 * vec[i][j], {j, i}});
  }
  sort(all(st));

  int sz = 0;
  ll sum = 0;
  ll last = 0;
  multiset<int> ms;

  for (int i = st.size() - 1; ~i; i--) {
    shiti[i] = shiti[i + 1];
    if (st[i].second.first == 0 && vec[st[i].second.second].size() > 2)
      smax(shiti[i], vec[st[i].second.second][2] - st[i].first);
  }

  rep(i, 0, st.size()) {
    smax(res[sz], sum);
    if (!ms.empty()) smax(res[sz + 1], sum + *ms.rbegin());
    if (shiti[i]) smax(res[sz + 3], sum + shiti[i]);
    if (last) smax(res[sz - 1], sum - last);
    if (st[i].second.first == 0) {
      sum -= st[i].first;
      sz += 2;
      if (vec[st[i].second.second].size() > 2)
        ms.insert(vec[st[i].second.second][2]);
    } else {
      sum -= st[i].first / 2;
      last = -st[i].first / 2;
      sz++;
      ms.erase(ms.find(vec[st[i].second.second][st[i].second.first]));
      if (vec[st[i].second.second].size() > st[i].second.first + 1)
        ms.insert(vec[st[i].second.second][st[i].second.first + 1]);
    }
  }
  smax(res[sz], sum);
  if (last) smax(res[sz - 1], sum - last);
  writeA(res + 1, res + n + 1);

  return 0;
}

```