#include <bits/stdc++.h>
using namespace std;
const int MAXN = 200100;
int n, m, k;
vector<pair<int, int> > veze;
vector<pair<int, int> > graf[MAXN];
void load() {
  scanf("%d%d%d", &n, &m, &k);
  for (int i = 0; i < m; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    a--;
    b--;
    veze.push_back(pair<int, int>(a, b));
    graf[a].push_back(pair<int, int>(b, i));
    graf[b].push_back(pair<int, int>(a, i));
  }
}
int deg[MAXN];
set<pair<int, int> > S;
void printSet() {
  for (auto it = S.begin(); it != S.end(); it++) {
    printf("%d : %d\n", it->second, it->first);
  }
  printf("\n");
}
void solve() {
  for (int i = 0; i < m; i++) {
    deg[veze[i].first]++;
    deg[veze[i].second]++;
  }
  for (int i = 0; i < n; i++) S.insert(pair<int, int>(deg[i], i));
  while (!S.empty() && S.begin()->first < k) {
    int v = S.begin()->second;
    S.erase(pair<int, int>(deg[v], v));
    for (pair<int, int> p : graf[v]) {
      int u = p.first;
      if (S.find(pair<int, int>(deg[u], u)) == S.end()) continue;
      S.erase(pair<int, int>(deg[u], u));
      deg[u]--;
      S.insert(pair<int, int>(deg[u], u));
    }
  }
  vector<int> sol;
  for (int i = m - 1; i >= 0; i--) {
    sol.push_back(S.size());
    int a = veze[i].first;
    int b = veze[i].second;
    if (S.find(pair<int, int>(deg[a], a)) != S.end() &&
        S.find(pair<int, int>(deg[b], b)) != S.end()) {
      S.erase(pair<int, int>(deg[a], a));
      S.erase(pair<int, int>(deg[b], b));
      deg[a]--;
      deg[b]--;
      S.insert(pair<int, int>(deg[a], a));
      S.insert(pair<int, int>(deg[b], b));
      while (!S.empty() && S.begin()->first < k) {
        int v = S.begin()->second;
        S.erase(pair<int, int>(deg[v], v));
        for (pair<int, int> p : graf[v]) {
          if (p.second >= i) continue;
          int u = p.first;
          if (S.find(pair<int, int>(deg[u], u)) == S.end()) continue;
          S.erase(pair<int, int>(deg[u], u));
          deg[u]--;
          S.insert(pair<int, int>(deg[u], u));
        }
      }
    }
  }
  for (int i = m - 1; i >= 0; i--) printf("%d\n", sol[i]);
}
int main() {
  load();
  solve();
  return 0;
}

### Prompt

Your challenge is to write 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>
using namespace std;
const int MAXN = 200100;
int n, m, k;
vector<pair<int, int> > veze;
vector<pair<int, int> > graf[MAXN];
void load() {
  scanf("%d%d%d", &n, &m, &k);
  for (int i = 0; i < m; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    a--;
    b--;
    veze.push_back(pair<int, int>(a, b));
    graf[a].push_back(pair<int, int>(b, i));
    graf[b].push_back(pair<int, int>(a, i));
  }
}
int deg[MAXN];
set<pair<int, int> > S;
void printSet() {
  for (auto it = S.begin(); it != S.end(); it++) {
    printf("%d : %d\n", it->second, it->first);
  }
  printf("\n");
}
void solve() {
  for (int i = 0; i < m; i++) {
    deg[veze[i].first]++;
    deg[veze[i].second]++;
  }
  for (int i = 0; i < n; i++) S.insert(pair<int, int>(deg[i], i));
  while (!S.empty() && S.begin()->first < k) {
    int v = S.begin()->second;
    S.erase(pair<int, int>(deg[v], v));
    for (pair<int, int> p : graf[v]) {
      int u = p.first;
      if (S.find(pair<int, int>(deg[u], u)) == S.end()) continue;
      S.erase(pair<int, int>(deg[u], u));
      deg[u]--;
      S.insert(pair<int, int>(deg[u], u));
    }
  }
  vector<int> sol;
  for (int i = m - 1; i >= 0; i--) {
    sol.push_back(S.size());
    int a = veze[i].first;
    int b = veze[i].second;
    if (S.find(pair<int, int>(deg[a], a)) != S.end() &&
        S.find(pair<int, int>(deg[b], b)) != S.end()) {
      S.erase(pair<int, int>(deg[a], a));
      S.erase(pair<int, int>(deg[b], b));
      deg[a]--;
      deg[b]--;
      S.insert(pair<int, int>(deg[a], a));
      S.insert(pair<int, int>(deg[b], b));
      while (!S.empty() && S.begin()->first < k) {
        int v = S.begin()->second;
        S.erase(pair<int, int>(deg[v], v));
        for (pair<int, int> p : graf[v]) {
          if (p.second >= i) continue;
          int u = p.first;
          if (S.find(pair<int, int>(deg[u], u)) == S.end()) continue;
          S.erase(pair<int, int>(deg[u], u));
          deg[u]--;
          S.insert(pair<int, int>(deg[u], u));
        }
      }
    }
  }
  for (int i = m - 1; i >= 0; i--) printf("%d\n", sol[i]);
}
int main() {
  load();
  solve();
  return 0;
}

```