#include <bits/stdc++.h>
using namespace std;
int deg[200010];
vector<vector<int> > graph(200010);
map<pair<int, int>, int> edgeNum;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int tt = 1;
  while (tt--) {
    int n, m, k;
    cin >> n >> m >> k;
    int x[m], y[m];
    for (int i = 0; i < m; i++) {
      cin >> x[i] >> y[i];
      edgeNum[{x[i], y[i]}] = i;
      edgeNum[{y[i], x[i]}] = i;
      graph[x[i]].push_back(y[i]);
      graph[y[i]].push_back(x[i]);
      deg[x[i]]++;
      deg[y[i]]++;
    }
    set<pair<int, int> > s;
    for (int i = 1; i <= n; i++) {
      s.insert({deg[i], i});
    }
    set<int> removed;
    while (!s.empty()) {
      pair<int, int> tmp = *s.begin();
      s.erase(tmp);
      int ver = tmp.second;
      if (tmp.first >= k) {
        s.insert(tmp);
        break;
      }
      for (int i = 0; i < graph[ver].size(); i++) {
        if (removed.count(edgeNum[{graph[ver][i], ver}]) == 1) continue;
        removed.insert(edgeNum[{graph[ver][i], ver}]);
        s.erase({deg[graph[ver][i]], graph[ver][i]});
        deg[graph[ver][i]]--;
        s.insert({deg[graph[ver][i]], graph[ver][i]});
      }
    }
    int ans[m];
    for (int ii = m - 1; ii >= 0; --ii) {
      ans[ii] = s.size();
      if (s.count({deg[x[ii]], x[ii]}) == 0 ||
          s.count({deg[y[ii]], y[ii]}) == 0)
        continue;
      s.erase({deg[x[ii]], x[ii]});
      s.erase({deg[y[ii]], y[ii]});
      deg[x[ii]]--;
      deg[y[ii]]--;
      removed.insert(edgeNum[{x[ii], y[ii]}]);
      s.insert({deg[x[ii]], x[ii]});
      s.insert({deg[y[ii]], y[ii]});
      while (!s.empty() && ((*s.begin()).first) < k) {
        pair<int, int> tmp = *s.begin();
        s.erase(tmp);
        int ver = tmp.second;
        if (tmp.first >= k) {
          s.insert(tmp);
          break;
        }
        for (int i = 0; i < graph[ver].size(); i++) {
          if (removed.count(edgeNum[{graph[ver][i], ver}]) == 1) continue;
          s.erase({deg[graph[ver][i]], graph[ver][i]});
          removed.insert(edgeNum[{graph[ver][i], ver}]);
          deg[graph[ver][i]]--;
          s.insert({deg[graph[ver][i]], graph[ver][i]});
        }
      }
    }
    for (int i = 0; i < m; i++) {
      cout << ans[i] << '\n';
    }
  }
}

### Prompt

Create a solution in Cpp for 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;
int deg[200010];
vector<vector<int> > graph(200010);
map<pair<int, int>, int> edgeNum;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int tt = 1;
  while (tt--) {
    int n, m, k;
    cin >> n >> m >> k;
    int x[m], y[m];
    for (int i = 0; i < m; i++) {
      cin >> x[i] >> y[i];
      edgeNum[{x[i], y[i]}] = i;
      edgeNum[{y[i], x[i]}] = i;
      graph[x[i]].push_back(y[i]);
      graph[y[i]].push_back(x[i]);
      deg[x[i]]++;
      deg[y[i]]++;
    }
    set<pair<int, int> > s;
    for (int i = 1; i <= n; i++) {
      s.insert({deg[i], i});
    }
    set<int> removed;
    while (!s.empty()) {
      pair<int, int> tmp = *s.begin();
      s.erase(tmp);
      int ver = tmp.second;
      if (tmp.first >= k) {
        s.insert(tmp);
        break;
      }
      for (int i = 0; i < graph[ver].size(); i++) {
        if (removed.count(edgeNum[{graph[ver][i], ver}]) == 1) continue;
        removed.insert(edgeNum[{graph[ver][i], ver}]);
        s.erase({deg[graph[ver][i]], graph[ver][i]});
        deg[graph[ver][i]]--;
        s.insert({deg[graph[ver][i]], graph[ver][i]});
      }
    }
    int ans[m];
    for (int ii = m - 1; ii >= 0; --ii) {
      ans[ii] = s.size();
      if (s.count({deg[x[ii]], x[ii]}) == 0 ||
          s.count({deg[y[ii]], y[ii]}) == 0)
        continue;
      s.erase({deg[x[ii]], x[ii]});
      s.erase({deg[y[ii]], y[ii]});
      deg[x[ii]]--;
      deg[y[ii]]--;
      removed.insert(edgeNum[{x[ii], y[ii]}]);
      s.insert({deg[x[ii]], x[ii]});
      s.insert({deg[y[ii]], y[ii]});
      while (!s.empty() && ((*s.begin()).first) < k) {
        pair<int, int> tmp = *s.begin();
        s.erase(tmp);
        int ver = tmp.second;
        if (tmp.first >= k) {
          s.insert(tmp);
          break;
        }
        for (int i = 0; i < graph[ver].size(); i++) {
          if (removed.count(edgeNum[{graph[ver][i], ver}]) == 1) continue;
          s.erase({deg[graph[ver][i]], graph[ver][i]});
          removed.insert(edgeNum[{graph[ver][i], ver}]);
          deg[graph[ver][i]]--;
          s.insert({deg[graph[ver][i]], graph[ver][i]});
        }
      }
    }
    for (int i = 0; i < m; i++) {
      cout << ans[i] << '\n';
    }
  }
}

```