#include <bits/stdc++.h>
using namespace std;
map<long long int, long long int> m1, m2;
const long long int N = 3 * 1e5;
vector<long long int>::iterator itr, itr1;
int main() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<pair<int, int> > Edges(m);
  vector<int> Ans(m);
  vector<int> degree(n);
  vector<vector<pair<int, int> > > adj(n);
  set<pair<int, int> > Good_set;
  vector<int> in_good_set(n, true);
  for (int i = 0; i < m; i++) {
    cin >> Edges[i].first >> Edges[i].second;
    Edges[i].first--;
    Edges[i].second--;
    adj[Edges[i].first].push_back({Edges[i].second, i});
    adj[Edges[i].second].push_back({Edges[i].first, i});
    degree[Edges[i].first]++;
    degree[Edges[i].second]++;
  }
  for (int i = 0; i < n; i++) {
    Good_set.insert({degree[i], i});
  }
  while (!Good_set.empty() && Good_set.begin()->first < k) {
    int node = Good_set.begin()->second;
    for (auto &y : adj[node]) {
      int x = y.first;
      if (in_good_set[x]) {
        Good_set.erase({degree[x], x});
        --degree[x];
        Good_set.insert({degree[x], x});
      }
    }
    Good_set.erase({degree[node], node});
    in_good_set[node] = false;
  }
  for (int i = m - 1; i >= 0; i--) {
    Ans[i] = Good_set.size();
    int u = Edges[i].first, v = Edges[i].second;
    if (in_good_set[u] && in_good_set[v]) {
      Good_set.erase({degree[u], u});
      --degree[u];
      Good_set.insert({degree[u], u});
      Good_set.erase({degree[v], v});
      --degree[v];
      Good_set.insert({degree[v], v});
      while (!Good_set.empty() && Good_set.begin()->first < k) {
        int node = Good_set.begin()->second;
        for (auto &y : adj[node]) {
          int x = y.first;
          if (y.second >= i) continue;
          if (in_good_set[x]) {
            Good_set.erase({degree[x], x});
            --degree[x];
            Good_set.insert({degree[x], x});
          }
        }
        Good_set.erase({degree[node], node});
        in_good_set[node] = false;
      }
    }
  }
  for (int i = 0; i < m; i++) {
    cout << Ans[i] << "\n";
  }
  return 0;
}

### Prompt

Generate a Cpp solution to the following problem:

There are n persons who initially don't know each other. On each morning, two of them, who were not friends before, become friends.

We want to plan a trip for every evening of m days. On each trip, you have to select a group of people that will go on the trip. For every person, one of the following should hold: 

  * Either this person does not go on the trip, 
  * Or at least k of his friends also go on the trip. 



Note that the friendship is not transitive. That is, if a and b are friends and b and c are friends, it does not necessarily imply that a and c are friends.

For each day, find the maximum number of people that can go on the trip on that day.

Input

The first line contains three integers n, m, and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ m ≤ 2 ⋅ 10^5, 1 ≤ k < n) — the number of people, the number of days and the number of friends each person on the trip should have in the group.

The i-th (1 ≤ i ≤ m) of the next m lines contains two integers x and y (1≤ x, y≤ n, x≠ y), meaning that persons x and y become friends on the morning of day i. It is guaranteed that x and y were not friends before.

Output

Print exactly m lines, where the i-th of them (1≤ i≤ m) contains the maximum number of people that can go on the trip on the evening of the day i.

Examples

Input

4 4 2
2 3
1 2
1 3
1 4


Output

0
0
3
3


Input

5 8 2
2 1
4 2
5 4
5 2
4 3
5 1
4 1
3 2


Output

0
0
0
3
3
4
4
5


Input

5 7 2
1 5
3 2
2 5
3 4
1 2
5 3
1 3


Output

0
0
0
0
3
4
4

Note

In the first example, 

  * 1,2,3 can go on day 3 and 4. 



In the second example, 

  * 2,4,5 can go on day 4 and 5. 
  * 1,2,4,5 can go on day 6 and 7. 
  * 1,2,3,4,5 can go on day 8. 



In the third example, 

  * 1,2,5 can go on day 5. 
  * 1,2,3,5 can go on day 6 and 7. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
map<long long int, long long int> m1, m2;
const long long int N = 3 * 1e5;
vector<long long int>::iterator itr, itr1;
int main() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<pair<int, int> > Edges(m);
  vector<int> Ans(m);
  vector<int> degree(n);
  vector<vector<pair<int, int> > > adj(n);
  set<pair<int, int> > Good_set;
  vector<int> in_good_set(n, true);
  for (int i = 0; i < m; i++) {
    cin >> Edges[i].first >> Edges[i].second;
    Edges[i].first--;
    Edges[i].second--;
    adj[Edges[i].first].push_back({Edges[i].second, i});
    adj[Edges[i].second].push_back({Edges[i].first, i});
    degree[Edges[i].first]++;
    degree[Edges[i].second]++;
  }
  for (int i = 0; i < n; i++) {
    Good_set.insert({degree[i], i});
  }
  while (!Good_set.empty() && Good_set.begin()->first < k) {
    int node = Good_set.begin()->second;
    for (auto &y : adj[node]) {
      int x = y.first;
      if (in_good_set[x]) {
        Good_set.erase({degree[x], x});
        --degree[x];
        Good_set.insert({degree[x], x});
      }
    }
    Good_set.erase({degree[node], node});
    in_good_set[node] = false;
  }
  for (int i = m - 1; i >= 0; i--) {
    Ans[i] = Good_set.size();
    int u = Edges[i].first, v = Edges[i].second;
    if (in_good_set[u] && in_good_set[v]) {
      Good_set.erase({degree[u], u});
      --degree[u];
      Good_set.insert({degree[u], u});
      Good_set.erase({degree[v], v});
      --degree[v];
      Good_set.insert({degree[v], v});
      while (!Good_set.empty() && Good_set.begin()->first < k) {
        int node = Good_set.begin()->second;
        for (auto &y : adj[node]) {
          int x = y.first;
          if (y.second >= i) continue;
          if (in_good_set[x]) {
            Good_set.erase({degree[x], x});
            --degree[x];
            Good_set.insert({degree[x], x});
          }
        }
        Good_set.erase({degree[node], node});
        in_good_set[node] = false;
      }
    }
  }
  for (int i = 0; i < m; i++) {
    cout << Ans[i] << "\n";
  }
  return 0;
}

```