#include <bits/stdc++.h>
using namespace std;
const int INF = 2147483647;
const long long INFL = 9223372036854775807LL;
const double EPSILON = 0.00000001;
const long long MOD = 1000000007;
vector<int> adj[200000 + 5];
unordered_map<int, int> removed[200000 + 5];
int degree[200000 + 5];
bool node_removed[200000 + 5];
int ans = 0;
void remove_edge(int u, int v, int k) {
  degree[u]--;
  degree[v]--;
  removed[u][v] = true;
  removed[v][u] = true;
}
void remove_edges(int start, int k) {
  queue<int> q;
  assert(degree[start] < k);
  assert(not node_removed[start]);
  q.push(start);
  node_removed[start] = true;
  ans--;
  while (!q.empty()) {
    int top = q.front();
    q.pop();
    for (int x : adj[top]) {
      if (not removed[top][x]) {
        remove_edge(top, x, k);
        if (not node_removed[x] and degree[x] < k) {
          node_removed[x] = true;
          ans--;
          q.push(x);
        }
      }
    }
  }
}
int32_t main() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<pair<int, int>> edges;
  memset(node_removed, false, sizeof(node_removed));
  ;
  ans = n;
  for (int i = 0; i < m; i++) {
    int u, v;
    scanf("%d", &u);
    ;
    scanf("%d", &v);
    ;
    u--;
    v--;
    adj[u].push_back(v);
    adj[v].push_back(u);
    edges.push_back({u, v});
    removed[u][v] = false;
    removed[v][u] = false;
  }
  for (int i = 0; i < n; i++) {
    degree[i] = (int)(adj[i]).size();
  }
  for (int i = 0; i < n; i++) {
    if (not node_removed[i] and degree[i] < k) {
      remove_edges(i, k);
    }
  }
  vector<int> out;
  for (int i = (int)(edges).size() - 1; i >= 0; i--) {
    out.push_back(ans);
    int u = edges[i].first, v = edges[i].second;
    if (not removed[u][v]) {
      remove_edge(u, v, k);
      if (not node_removed[u] and degree[u] < k) {
        remove_edges(u, k);
      }
      if (not node_removed[v] and degree[v] < k) {
        remove_edges(v, k);
      }
    }
  }
  for (int i = (int)(out).size() - 1; i >= 0; i--) {
    printf("%d\n", out[i]);
  }
  return 0;
}

### 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;
const int INF = 2147483647;
const long long INFL = 9223372036854775807LL;
const double EPSILON = 0.00000001;
const long long MOD = 1000000007;
vector<int> adj[200000 + 5];
unordered_map<int, int> removed[200000 + 5];
int degree[200000 + 5];
bool node_removed[200000 + 5];
int ans = 0;
void remove_edge(int u, int v, int k) {
  degree[u]--;
  degree[v]--;
  removed[u][v] = true;
  removed[v][u] = true;
}
void remove_edges(int start, int k) {
  queue<int> q;
  assert(degree[start] < k);
  assert(not node_removed[start]);
  q.push(start);
  node_removed[start] = true;
  ans--;
  while (!q.empty()) {
    int top = q.front();
    q.pop();
    for (int x : adj[top]) {
      if (not removed[top][x]) {
        remove_edge(top, x, k);
        if (not node_removed[x] and degree[x] < k) {
          node_removed[x] = true;
          ans--;
          q.push(x);
        }
      }
    }
  }
}
int32_t main() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<pair<int, int>> edges;
  memset(node_removed, false, sizeof(node_removed));
  ;
  ans = n;
  for (int i = 0; i < m; i++) {
    int u, v;
    scanf("%d", &u);
    ;
    scanf("%d", &v);
    ;
    u--;
    v--;
    adj[u].push_back(v);
    adj[v].push_back(u);
    edges.push_back({u, v});
    removed[u][v] = false;
    removed[v][u] = false;
  }
  for (int i = 0; i < n; i++) {
    degree[i] = (int)(adj[i]).size();
  }
  for (int i = 0; i < n; i++) {
    if (not node_removed[i] and degree[i] < k) {
      remove_edges(i, k);
    }
  }
  vector<int> out;
  for (int i = (int)(edges).size() - 1; i >= 0; i--) {
    out.push_back(ans);
    int u = edges[i].first, v = edges[i].second;
    if (not removed[u][v]) {
      remove_edge(u, v, k);
      if (not node_removed[u] and degree[u] < k) {
        remove_edges(u, k);
      }
      if (not node_removed[v] and degree[v] < k) {
        remove_edges(v, k);
      }
    }
  }
  for (int i = (int)(out).size() - 1; i >= 0; i--) {
    printf("%d\n", out[i]);
  }
  return 0;
}

```