#include <bits/stdc++.h>
using namespace std;
const int maxn = 200005;
set<int> adj[maxn];
int K;
queue<int> Q;
bool deleted[maxn];
int delc;
void del_edge(int u, int v) {
  if (adj[u].count(v) != 0) {
    adj[u].erase(v);
    if (!deleted[u] && (int)adj[u].size() < K) {
      deleted[u] = 1;
      delc++;
      Q.push(u);
    }
  }
  if (adj[v].count(u) != 0) {
    adj[v].erase(u);
    if (!deleted[v] && (int)adj[v].size() < K) {
      deleted[v] = 1;
      delc++;
      Q.push(v);
    }
  }
}
void del_vert(int u) {
  vector<int> todel;
  for (int v : adj[u]) {
    todel.push_back(v);
  }
  for (int v : todel) {
    del_edge(u, v);
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int vertexc, queryc;
  cin >> vertexc >> queryc >> K;
  vector<pair<int, int>> edges;
  for (int i = 0; i < queryc; i++) {
    int u, v;
    cin >> u >> v;
    adj[u].insert(v);
    adj[v].insert(u);
    edges.push_back(make_pair(u, v));
  }
  for (int i = 1; i <= vertexc; i++) {
    if ((int)adj[i].size() < K) {
      deleted[i] = 1;
      delc++;
      Q.push(i);
    }
  }
  deque<int> ans;
  for (int i = 0; i < queryc; i++) {
    while (!Q.empty()) {
      int qtop = Q.front();
      Q.pop();
      del_vert(qtop);
    }
    ans.push_front(vertexc - delc);
    pair<int, int> uv = edges.back();
    edges.pop_back();
    if (!deleted[uv.first] && !deleted[uv.second]) {
      del_edge(uv.first, uv.second);
    }
  }
  for (int i = 0; i < (int)ans.size(); i++) {
    cout << ans[i] << '\n';
  }
}

### Prompt

In cpp, your task is to solve 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;
const int maxn = 200005;
set<int> adj[maxn];
int K;
queue<int> Q;
bool deleted[maxn];
int delc;
void del_edge(int u, int v) {
  if (adj[u].count(v) != 0) {
    adj[u].erase(v);
    if (!deleted[u] && (int)adj[u].size() < K) {
      deleted[u] = 1;
      delc++;
      Q.push(u);
    }
  }
  if (adj[v].count(u) != 0) {
    adj[v].erase(u);
    if (!deleted[v] && (int)adj[v].size() < K) {
      deleted[v] = 1;
      delc++;
      Q.push(v);
    }
  }
}
void del_vert(int u) {
  vector<int> todel;
  for (int v : adj[u]) {
    todel.push_back(v);
  }
  for (int v : todel) {
    del_edge(u, v);
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int vertexc, queryc;
  cin >> vertexc >> queryc >> K;
  vector<pair<int, int>> edges;
  for (int i = 0; i < queryc; i++) {
    int u, v;
    cin >> u >> v;
    adj[u].insert(v);
    adj[v].insert(u);
    edges.push_back(make_pair(u, v));
  }
  for (int i = 1; i <= vertexc; i++) {
    if ((int)adj[i].size() < K) {
      deleted[i] = 1;
      delc++;
      Q.push(i);
    }
  }
  deque<int> ans;
  for (int i = 0; i < queryc; i++) {
    while (!Q.empty()) {
      int qtop = Q.front();
      Q.pop();
      del_vert(qtop);
    }
    ans.push_front(vertexc - delc);
    pair<int, int> uv = edges.back();
    edges.pop_back();
    if (!deleted[uv.first] && !deleted[uv.second]) {
      del_edge(uv.first, uv.second);
    }
  }
  for (int i = 0; i < (int)ans.size(); i++) {
    cout << ans[i] << '\n';
  }
}

```