#include <bits/stdc++.h>
template <class C, class E>
inline bool contains(const C& container, const E& element) {
  return container.find(element) != container.end();
}
template <class T>
inline void checkmin(T& a, T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkmax(T& a, T b) {
  if (b > a) a = b;
}
using namespace std;
vector<pair<int, int> > fr;
vector<set<int> > gr;
int n, m, k;
vector<bool> inTrip;
int inTripCount;
void Remove(int a, int b) {
  gr[a].erase(b);
  gr[b].erase(a);
}
int Deg(int a) { return gr[a].size(); }
vector<bool> InQueue;
void RemAll(queue<int>& toRemove) {
  while (!toRemove.empty()) {
    int iRem = toRemove.front();
    inTrip[iRem] = false;
    InQueue[iRem] = false;
    --inTripCount;
    toRemove.pop();
    for (int br : gr[iRem]) {
      gr[br].erase(iRem);
      if (Deg(br) < k && !InQueue[br]) {
        InQueue[br] = true;
        toRemove.push(br);
      }
    }
    gr[iRem].clear();
  }
}
void Process(pair<int, int> p) {
  if (!contains(gr[p.first], p.second)) return;
  Remove(p.first, p.second);
  queue<int> toRemove;
  if (inTrip[p.first] && Deg(p.first) < k) {
    InQueue[p.first] = true;
    toRemove.push(p.first);
  }
  if (inTrip[p.second] && Deg(p.second) < k) {
    InQueue[p.second] = true;
    toRemove.push(p.second);
  }
  RemAll(toRemove);
}
void Init() {
  queue<int> toRemove;
  for (int i = (0), _b = ((n)-1); i <= _b; i++) {
    if (Deg(i) < k) {
      InQueue[i] = true;
      toRemove.push(i);
    }
  }
  RemAll(toRemove);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << std::setprecision(15);
  cout << std::fixed;
  cin >> n >> m >> k;
  fr.resize(m);
  gr.resize(n);
  InQueue.resize(n);
  inTrip.resize(n, true);
  inTripCount = n;
  for (int i = (0), _b = ((m)-1); i <= _b; i++) {
    int a, b;
    cin >> a >> b;
    --a;
    --b;
    fr[i] = make_pair(a, b);
    gr[a].insert(b);
    gr[b].insert(a);
  }
  Init();
  vector<int> res;
  for (int i = (m - 1), _b = (0); i >= _b; i--) {
    res.push_back(inTripCount);
    if (i != 0) Process(fr[i]);
  }
  for (int i = (m - 1), _b = (0); i >= _b; i--) {
    cout << res[i] << endl;
  }
  return 0;
}

### Prompt

Generate 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>
template <class C, class E>
inline bool contains(const C& container, const E& element) {
  return container.find(element) != container.end();
}
template <class T>
inline void checkmin(T& a, T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkmax(T& a, T b) {
  if (b > a) a = b;
}
using namespace std;
vector<pair<int, int> > fr;
vector<set<int> > gr;
int n, m, k;
vector<bool> inTrip;
int inTripCount;
void Remove(int a, int b) {
  gr[a].erase(b);
  gr[b].erase(a);
}
int Deg(int a) { return gr[a].size(); }
vector<bool> InQueue;
void RemAll(queue<int>& toRemove) {
  while (!toRemove.empty()) {
    int iRem = toRemove.front();
    inTrip[iRem] = false;
    InQueue[iRem] = false;
    --inTripCount;
    toRemove.pop();
    for (int br : gr[iRem]) {
      gr[br].erase(iRem);
      if (Deg(br) < k && !InQueue[br]) {
        InQueue[br] = true;
        toRemove.push(br);
      }
    }
    gr[iRem].clear();
  }
}
void Process(pair<int, int> p) {
  if (!contains(gr[p.first], p.second)) return;
  Remove(p.first, p.second);
  queue<int> toRemove;
  if (inTrip[p.first] && Deg(p.first) < k) {
    InQueue[p.first] = true;
    toRemove.push(p.first);
  }
  if (inTrip[p.second] && Deg(p.second) < k) {
    InQueue[p.second] = true;
    toRemove.push(p.second);
  }
  RemAll(toRemove);
}
void Init() {
  queue<int> toRemove;
  for (int i = (0), _b = ((n)-1); i <= _b; i++) {
    if (Deg(i) < k) {
      InQueue[i] = true;
      toRemove.push(i);
    }
  }
  RemAll(toRemove);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << std::setprecision(15);
  cout << std::fixed;
  cin >> n >> m >> k;
  fr.resize(m);
  gr.resize(n);
  InQueue.resize(n);
  inTrip.resize(n, true);
  inTripCount = n;
  for (int i = (0), _b = ((m)-1); i <= _b; i++) {
    int a, b;
    cin >> a >> b;
    --a;
    --b;
    fr[i] = make_pair(a, b);
    gr[a].insert(b);
    gr[b].insert(a);
  }
  Init();
  vector<int> res;
  for (int i = (m - 1), _b = (0); i >= _b; i--) {
    res.push_back(inTripCount);
    if (i != 0) Process(fr[i]);
  }
  for (int i = (m - 1), _b = (0); i >= _b; i--) {
    cout << res[i] << endl;
  }
  return 0;
}

```