#include <bits/stdc++.h>
using namespace std;
int main(int argc, char const *argv[]) {
  int n, m, k;
  cin >> n >> m >> k;
  vector<vector<int> > edges(m, vector<int>(2));
  vector<vector<int> > graph(n + 1);
  vector<int> degrees(n + 1, 0);
  for (int i = 0; i < m; ++i) {
    scanf("%d %d", &edges[i][0], &edges[i][1]);
    degrees[edges[i][0]]++;
    degrees[edges[i][1]]++;
    graph[edges[i][0]].push_back(edges[i][1]);
    graph[edges[i][1]].push_back(edges[i][0]);
  }
  map<pair<int, int>, bool> sorted;
  for (int i = 0; i < n; ++i)
    sorted.insert(make_pair(make_pair(degrees[i + 1], i + 1), 1));
  vector<int> ans(m);
  for (int i = m - 1; i >= 0; --i) {
    while ((!sorted.empty()) and sorted.begin()->first.first < k) {
      int temp = sorted.begin()->first.second;
      sorted.erase(sorted.begin());
      degrees[temp] = 0;
      for (int i = 0; i < graph[temp].size(); ++i) {
        auto it =
            sorted.find(make_pair(degrees[graph[temp][i]], graph[temp][i]));
        degrees[graph[temp][i]]--;
        if (it != sorted.end()) {
          sorted.erase(it);
          if (degrees[graph[temp][i]] >= 0)
            sorted.insert(make_pair(
                make_pair(degrees[graph[temp][i]], graph[temp][i]), 1));
        }
      }
    }
    ans[i] = sorted.size();
    graph[edges[i][0]].pop_back();
    graph[edges[i][1]].pop_back();
    if (degrees[edges[i][0]] >= k and degrees[edges[i][1]] >= k) {
      auto it1 = sorted.find(make_pair(degrees[edges[i][0]], edges[i][0]));
      auto it2 = sorted.find(make_pair(degrees[edges[i][1]], edges[i][1]));
      degrees[edges[i][0]]--;
      degrees[edges[i][1]]--;
      if (it1 != sorted.end()) {
        sorted.erase(it1);
        sorted.insert(
            make_pair(make_pair(degrees[edges[i][0]], edges[i][0]), 1));
      }
      if (it2 != sorted.end()) {
        sorted.erase(it2);
        sorted.insert(
            make_pair(make_pair(degrees[edges[i][1]], edges[i][1]), 1));
      }
    }
  }
  for (int i = 0; i < m; ++i) printf("%d\n", ans[i]);
  return 0;
}

### Prompt

Please formulate 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;
int main(int argc, char const *argv[]) {
  int n, m, k;
  cin >> n >> m >> k;
  vector<vector<int> > edges(m, vector<int>(2));
  vector<vector<int> > graph(n + 1);
  vector<int> degrees(n + 1, 0);
  for (int i = 0; i < m; ++i) {
    scanf("%d %d", &edges[i][0], &edges[i][1]);
    degrees[edges[i][0]]++;
    degrees[edges[i][1]]++;
    graph[edges[i][0]].push_back(edges[i][1]);
    graph[edges[i][1]].push_back(edges[i][0]);
  }
  map<pair<int, int>, bool> sorted;
  for (int i = 0; i < n; ++i)
    sorted.insert(make_pair(make_pair(degrees[i + 1], i + 1), 1));
  vector<int> ans(m);
  for (int i = m - 1; i >= 0; --i) {
    while ((!sorted.empty()) and sorted.begin()->first.first < k) {
      int temp = sorted.begin()->first.second;
      sorted.erase(sorted.begin());
      degrees[temp] = 0;
      for (int i = 0; i < graph[temp].size(); ++i) {
        auto it =
            sorted.find(make_pair(degrees[graph[temp][i]], graph[temp][i]));
        degrees[graph[temp][i]]--;
        if (it != sorted.end()) {
          sorted.erase(it);
          if (degrees[graph[temp][i]] >= 0)
            sorted.insert(make_pair(
                make_pair(degrees[graph[temp][i]], graph[temp][i]), 1));
        }
      }
    }
    ans[i] = sorted.size();
    graph[edges[i][0]].pop_back();
    graph[edges[i][1]].pop_back();
    if (degrees[edges[i][0]] >= k and degrees[edges[i][1]] >= k) {
      auto it1 = sorted.find(make_pair(degrees[edges[i][0]], edges[i][0]));
      auto it2 = sorted.find(make_pair(degrees[edges[i][1]], edges[i][1]));
      degrees[edges[i][0]]--;
      degrees[edges[i][1]]--;
      if (it1 != sorted.end()) {
        sorted.erase(it1);
        sorted.insert(
            make_pair(make_pair(degrees[edges[i][0]], edges[i][0]), 1));
      }
      if (it2 != sorted.end()) {
        sorted.erase(it2);
        sorted.insert(
            make_pair(make_pair(degrees[edges[i][1]], edges[i][1]), 1));
      }
    }
  }
  for (int i = 0; i < m; ++i) printf("%d\n", ans[i]);
  return 0;
}

```