#include <bits/stdc++.h>
using namespace std;
template <class X, class Y>
void amax(X& x, const Y& y) {
  if (x < y) x = y;
}
template <class X, class Y>
void amin(X& x, const Y& y) {
  if (x > y) x = y;
}
const int INF = 1e9 + 10;
const long long INFL = (long long)1e18 + 10;
const int MAX = 2e5 + 10;
int n, m, k;
int cnt[MAX];
pair<int, int> ed[MAX];
bool mark[MAX], removed[MAX];
vector<pair<int, int> > es[MAX];
stack<int> st;
void invalid_push(int v) {
  if (!mark[v] && cnt[v] < k) {
    mark[v] = true;
    st.push(v);
  }
}
void process() {
  cin >> n >> m >> k;
  for (int i = 1; i <= m; i++) {
    cin >> ed[i].first >> ed[i].second;
    cnt[ed[i].first]++;
    cnt[ed[i].second]++;
    es[ed[i].first].push_back(make_pair(ed[i].second, i));
    es[ed[i].second].push_back(make_pair(ed[i].first, i));
  }
  for (int i = 1; i <= n; i++) invalid_push(i);
  vector<int> ans;
  int res = n;
  for (int i = m; i >= 1; i--) {
    while (!st.empty()) {
      int u = st.top();
      st.pop();
      res--;
      for (auto e : es[u])
        if (!mark[e.first] && !removed[e.second]) {
          removed[e.second] = true;
          cnt[e.first]--;
          invalid_push(e.first);
        }
    }
    ans.push_back(res);
    if (!removed[i]) {
      removed[i] = true;
      cnt[ed[i].first]--;
      cnt[ed[i].second]--;
      invalid_push(ed[i].first);
      invalid_push(ed[i].second);
    }
  }
  for (int i = int(ans.size()) - 1; i >= 0; i--) cout << ans[i] << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  process();
}

### Prompt

Please create a solution in CPP 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;
template <class X, class Y>
void amax(X& x, const Y& y) {
  if (x < y) x = y;
}
template <class X, class Y>
void amin(X& x, const Y& y) {
  if (x > y) x = y;
}
const int INF = 1e9 + 10;
const long long INFL = (long long)1e18 + 10;
const int MAX = 2e5 + 10;
int n, m, k;
int cnt[MAX];
pair<int, int> ed[MAX];
bool mark[MAX], removed[MAX];
vector<pair<int, int> > es[MAX];
stack<int> st;
void invalid_push(int v) {
  if (!mark[v] && cnt[v] < k) {
    mark[v] = true;
    st.push(v);
  }
}
void process() {
  cin >> n >> m >> k;
  for (int i = 1; i <= m; i++) {
    cin >> ed[i].first >> ed[i].second;
    cnt[ed[i].first]++;
    cnt[ed[i].second]++;
    es[ed[i].first].push_back(make_pair(ed[i].second, i));
    es[ed[i].second].push_back(make_pair(ed[i].first, i));
  }
  for (int i = 1; i <= n; i++) invalid_push(i);
  vector<int> ans;
  int res = n;
  for (int i = m; i >= 1; i--) {
    while (!st.empty()) {
      int u = st.top();
      st.pop();
      res--;
      for (auto e : es[u])
        if (!mark[e.first] && !removed[e.second]) {
          removed[e.second] = true;
          cnt[e.first]--;
          invalid_push(e.first);
        }
    }
    ans.push_back(res);
    if (!removed[i]) {
      removed[i] = true;
      cnt[ed[i].first]--;
      cnt[ed[i].second]--;
      invalid_push(ed[i].first);
      invalid_push(ed[i].second);
    }
  }
  for (int i = int(ans.size()) - 1; i >= 0; i--) cout << ans[i] << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  process();
}

```