/* cerberus97 - Hanit Banga */

#include <iostream>
#include <iomanip>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <algorithm>

using namespace std;

#define pb push_back
#define fast_cin() ios_base::sync_with_stdio(false); cin.tie(NULL)

typedef long long ll;
typedef long double ld;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;

const int N = 2e5 + 10;
const ll inf = 1e18 + 42;

struct jewel {
	int c; ll val; int type;
	bool operator<(const jewel &o) const {
		return tie(o.val, o.type) < tie(val, type);
	}
};

vector<jewel> all_jewels;
vector<ll> jewels[N];
multiset<ll> used_pairs, used_singles;
multiset<ll, greater<ll>> avail_singles, triplets;
ll res[N];

int main() {
	fast_cin();
	int n, k;
	cin >> n >> k;
	for (int i = 1; i <= n; ++i) {
		int c, v;
		cin >> c >> v;
		jewels[c].pb(v);
	}
	for (int c = 1; c <= k; ++c) {
		sort(jewels[c].begin(), jewels[c].end(), greater<int>());
		int t = jewels[c].size();
		if (t >= 3) {
			triplets.insert(jewels[c][0] + jewels[c][1] + jewels[c][2]);
		}
		all_jewels.pb({c, jewels[c][0] + jewels[c][1], 2});
		for (int j = 2; j < t; ++j) {
			all_jewels.pb({c, 2 * jewels[c][j], 1});
		}
	}
	sort(all_jewels.begin(), all_jewels.end());
	avail_singles.insert(-inf);
	triplets.insert(-inf);
	used_pairs.insert(inf);
	used_singles.insert(inf);
	ll sum = 0, x = 0;
	for (auto &j : all_jewels) {
		int c = j.c;
		if (j.type == 2) {
			ll ans = -1;
			ans = max(ans, sum + *avail_singles.begin());
			ans = max(ans, sum - *used_pairs.begin() + *triplets.begin());
			ans = max(ans, sum - *used_singles.begin() + j.val);
			res[x + 1] = ans;
			sum += j.val;
			x += 2;
			int t = jewels[c].size();
			for (int i = 2; i < t; ++i) {
				avail_singles.insert(jewels[c][i]);
			}
			if (t >= 3) {
				triplets.erase(triplets.find(jewels[c][0] + jewels[c][1] + jewels[c][2]));
			}
			used_pairs.insert(j.val);
		} else {
			j.val /= 2;
			sum += j.val;
			++x;
			avail_singles.erase(avail_singles.find(j.val));
			used_singles.insert(j.val);
		}
		res[x] = sum;
	}
	for (int i = 1; i <= n; ++i) {
		cout << res[i] << '\n';
	}
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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
/* cerberus97 - Hanit Banga */

#include <iostream>
#include <iomanip>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <algorithm>

using namespace std;

#define pb push_back
#define fast_cin() ios_base::sync_with_stdio(false); cin.tie(NULL)

typedef long long ll;
typedef long double ld;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;

const int N = 2e5 + 10;
const ll inf = 1e18 + 42;

struct jewel {
	int c; ll val; int type;
	bool operator<(const jewel &o) const {
		return tie(o.val, o.type) < tie(val, type);
	}
};

vector<jewel> all_jewels;
vector<ll> jewels[N];
multiset<ll> used_pairs, used_singles;
multiset<ll, greater<ll>> avail_singles, triplets;
ll res[N];

int main() {
	fast_cin();
	int n, k;
	cin >> n >> k;
	for (int i = 1; i <= n; ++i) {
		int c, v;
		cin >> c >> v;
		jewels[c].pb(v);
	}
	for (int c = 1; c <= k; ++c) {
		sort(jewels[c].begin(), jewels[c].end(), greater<int>());
		int t = jewels[c].size();
		if (t >= 3) {
			triplets.insert(jewels[c][0] + jewels[c][1] + jewels[c][2]);
		}
		all_jewels.pb({c, jewels[c][0] + jewels[c][1], 2});
		for (int j = 2; j < t; ++j) {
			all_jewels.pb({c, 2 * jewels[c][j], 1});
		}
	}
	sort(all_jewels.begin(), all_jewels.end());
	avail_singles.insert(-inf);
	triplets.insert(-inf);
	used_pairs.insert(inf);
	used_singles.insert(inf);
	ll sum = 0, x = 0;
	for (auto &j : all_jewels) {
		int c = j.c;
		if (j.type == 2) {
			ll ans = -1;
			ans = max(ans, sum + *avail_singles.begin());
			ans = max(ans, sum - *used_pairs.begin() + *triplets.begin());
			ans = max(ans, sum - *used_singles.begin() + j.val);
			res[x + 1] = ans;
			sum += j.val;
			x += 2;
			int t = jewels[c].size();
			for (int i = 2; i < t; ++i) {
				avail_singles.insert(jewels[c][i]);
			}
			if (t >= 3) {
				triplets.erase(triplets.find(jewels[c][0] + jewels[c][1] + jewels[c][2]));
			}
			used_pairs.insert(j.val);
		} else {
			j.val /= 2;
			sum += j.val;
			++x;
			avail_singles.erase(avail_singles.find(j.val));
			used_singles.insert(j.val);
		}
		res[x] = sum;
	}
	for (int i = 1; i <= n; ++i) {
		cout << res[i] << '\n';
	}
}
```