#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
const int maxn = 2e5 + 10;
pair<int, int> edge[maxn];
map<pair<int, int>, int> mp;
vector<int> g[maxn];
int vis[maxn];
queue<int> q;
int du[maxn];
int ans[maxn];
int main() {
  std::ios::sync_with_stdio(false);
  int n, m, k;
  cin >> n >> m >> k;
  for (int i = 1; i <= m; i++) {
    int u, v;
    cin >> u >> v;
    edge[i].first = u;
    edge[i].second = v;
    du[u]++;
    du[v]++;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  for (int i = 1; i <= n; i++) {
    if (du[i] < k) {
      vis[i] = 1;
      q.push(i);
    }
  }
  while (!q.empty()) {
    int u = q.front();
    du[u]--;
    q.pop();
    for (int i = 0; i < g[u].size(); i++) {
      int v = g[u][i];
      mp[make_pair(u, v)] = 1;
      mp[make_pair(v, u)] = 1;
      du[v]--;
      if (vis[v] == 0 && du[v] < k) {
        q.push(v);
        vis[v] = 1;
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    if (vis[i] == 0) ans[m]++;
  }
  for (int i = m - 1; i >= 1; i--) {
    ans[i] = ans[i + 1];
    int x = edge[i + 1].first;
    int y = edge[i + 1].second;
    if (mp[make_pair(x, y)] == 1 || mp[make_pair(x, y)] == 1) {
      continue;
    }
    mp[make_pair(x, y)] = 1;
    mp[make_pair(x, y)] = 1;
    du[x]--;
    du[y]--;
    if (vis[x] == 0 && du[x] < k) {
      q.push(x);
      vis[x] = 1;
      ans[i]--;
    }
    if (vis[y] == 0 && du[y] < k) {
      q.push(y);
      vis[y] = 1;
      ans[i]--;
    }
    while (!q.empty()) {
      int u = q.front();
      q.pop();
      for (int t = 0; t < g[u].size(); t++) {
        int v = g[u][t];
        if (mp[make_pair(u, v)] == 1 || mp[make_pair(v, u)] == 1) {
          continue;
        }
        mp[make_pair(u, v)] = 1;
        mp[make_pair(v, u)] = 1;
        du[v]--;
        du[u]--;
        if (vis[v] == 0 && du[v] < k) {
          q.push(v);
          vis[v] = 1;
          ans[i]--;
        }
      }
    }
  }
  for (int i = 1; i <= m; i++) {
    cout << ans[i] << endl;
  }
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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;
const int mod = 1e9 + 7;
const int maxn = 2e5 + 10;
pair<int, int> edge[maxn];
map<pair<int, int>, int> mp;
vector<int> g[maxn];
int vis[maxn];
queue<int> q;
int du[maxn];
int ans[maxn];
int main() {
  std::ios::sync_with_stdio(false);
  int n, m, k;
  cin >> n >> m >> k;
  for (int i = 1; i <= m; i++) {
    int u, v;
    cin >> u >> v;
    edge[i].first = u;
    edge[i].second = v;
    du[u]++;
    du[v]++;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  for (int i = 1; i <= n; i++) {
    if (du[i] < k) {
      vis[i] = 1;
      q.push(i);
    }
  }
  while (!q.empty()) {
    int u = q.front();
    du[u]--;
    q.pop();
    for (int i = 0; i < g[u].size(); i++) {
      int v = g[u][i];
      mp[make_pair(u, v)] = 1;
      mp[make_pair(v, u)] = 1;
      du[v]--;
      if (vis[v] == 0 && du[v] < k) {
        q.push(v);
        vis[v] = 1;
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    if (vis[i] == 0) ans[m]++;
  }
  for (int i = m - 1; i >= 1; i--) {
    ans[i] = ans[i + 1];
    int x = edge[i + 1].first;
    int y = edge[i + 1].second;
    if (mp[make_pair(x, y)] == 1 || mp[make_pair(x, y)] == 1) {
      continue;
    }
    mp[make_pair(x, y)] = 1;
    mp[make_pair(x, y)] = 1;
    du[x]--;
    du[y]--;
    if (vis[x] == 0 && du[x] < k) {
      q.push(x);
      vis[x] = 1;
      ans[i]--;
    }
    if (vis[y] == 0 && du[y] < k) {
      q.push(y);
      vis[y] = 1;
      ans[i]--;
    }
    while (!q.empty()) {
      int u = q.front();
      q.pop();
      for (int t = 0; t < g[u].size(); t++) {
        int v = g[u][t];
        if (mp[make_pair(u, v)] == 1 || mp[make_pair(v, u)] == 1) {
          continue;
        }
        mp[make_pair(u, v)] = 1;
        mp[make_pair(v, u)] = 1;
        du[v]--;
        du[u]--;
        if (vis[v] == 0 && du[v] < k) {
          q.push(v);
          vis[v] = 1;
          ans[i]--;
        }
      }
    }
  }
  for (int i = 1; i <= m; i++) {
    cout << ans[i] << endl;
  }
  return 0;
}

```