#include <bits/stdc++.h>
using namespace std;
template <class T, class U>
bool cmax(T& a, const U& b) {
  return a < b ? a = b, 1 : 0;
}
template <class T, class U>
bool cmin(T& a, const U& b) {
  return b < a ? a = b, 1 : 0;
}
void _BG(const char* s) { cerr << s << endl; };
template <class T, class... TT>
void _BG(const char* s, T a, TT... b) {
  for (int c = 0; *s && (c || *s != ','); ++s) {
    cerr << *s;
    for (char x : "([{") c += *s == x;
    for (char x : ")]}") c -= *s == x;
  }
  cerr << " = " << a;
  if (sizeof...(b)) {
    cerr << ", ";
    ++s;
  }
  _BG(s, b...);
}
bool RD() { return 1; }
bool RD(char& a) { return scanf(" %c", &a) == 1; }
bool RD(char* a) { return scanf("%s", a) == 1; }
bool RD(double& a) { return scanf("%lf", &a) == 1; }
bool RD(int& a) { return scanf("%d", &a) == 1; }
bool RD(long long& a) { return scanf("%lld", &a) == 1; }
template <class T, class... TT>
bool RD(T& a, TT&... b) {
  return RD(a) && RD(b...);
}
void PT(const char& a) { putchar(a); }
void PT(char const* const& a) { fputs(a, stdout); }
void PT(const double& a) { printf("%.16f", a); }
void PT(const int& a) { printf("%d", a); }
void PT(const long long& a) { printf("%lld", a); }
template <char s = ' ', char e = '\n'>
void PL() {
  if (e) PT(e);
}
template <char s = ' ', char e = '\n', class T, class... TT>
void PL(const T& a, const TT&... b) {
  PT(a);
  if (sizeof...(b) && s) PT(s);
  PL<s, e>(b...);
}
const int N = 212345;
int n, m, k;
set<int> g[N];
pair<int, int> e[N];
bool die[N];
int ans, QAQ[N];
vector<int> rm;
void chk(int v) {
  if (((int)(g[v]).size()) < k && !die[v]) {
    rm.push_back(v);
    die[v] = 1;
    --ans;
  }
}
void del(int u, int v) {
  g[u].erase(v);
  g[v].erase(u);
  chk(u);
  chk(v);
}
int main() {
  RD(n, m, k);
  for (int i(0); i < (m); ++i) {
    int u, v;
    RD(u, v);
    --u, --v;
    e[i] = {u, v};
    g[u].insert(v);
    g[v].insert(u);
  }
  ans = n;
  for (int i(0); i < (n); ++i) chk(i);
  for (int i((m)-1); i >= (0); --i) {
    while (((int)(rm).size())) {
      int u = ((rm).back());
      (rm).pop_back();
      while (((int)(g[u]).size())) del(u, *begin(g[u]));
    }
    QAQ[i] = ans;
    del(e[i].first, e[i].second);
  }
  for (int i(0); i < (m); ++i) PL(QAQ[i]);
}

### 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>
using namespace std;
template <class T, class U>
bool cmax(T& a, const U& b) {
  return a < b ? a = b, 1 : 0;
}
template <class T, class U>
bool cmin(T& a, const U& b) {
  return b < a ? a = b, 1 : 0;
}
void _BG(const char* s) { cerr << s << endl; };
template <class T, class... TT>
void _BG(const char* s, T a, TT... b) {
  for (int c = 0; *s && (c || *s != ','); ++s) {
    cerr << *s;
    for (char x : "([{") c += *s == x;
    for (char x : ")]}") c -= *s == x;
  }
  cerr << " = " << a;
  if (sizeof...(b)) {
    cerr << ", ";
    ++s;
  }
  _BG(s, b...);
}
bool RD() { return 1; }
bool RD(char& a) { return scanf(" %c", &a) == 1; }
bool RD(char* a) { return scanf("%s", a) == 1; }
bool RD(double& a) { return scanf("%lf", &a) == 1; }
bool RD(int& a) { return scanf("%d", &a) == 1; }
bool RD(long long& a) { return scanf("%lld", &a) == 1; }
template <class T, class... TT>
bool RD(T& a, TT&... b) {
  return RD(a) && RD(b...);
}
void PT(const char& a) { putchar(a); }
void PT(char const* const& a) { fputs(a, stdout); }
void PT(const double& a) { printf("%.16f", a); }
void PT(const int& a) { printf("%d", a); }
void PT(const long long& a) { printf("%lld", a); }
template <char s = ' ', char e = '\n'>
void PL() {
  if (e) PT(e);
}
template <char s = ' ', char e = '\n', class T, class... TT>
void PL(const T& a, const TT&... b) {
  PT(a);
  if (sizeof...(b) && s) PT(s);
  PL<s, e>(b...);
}
const int N = 212345;
int n, m, k;
set<int> g[N];
pair<int, int> e[N];
bool die[N];
int ans, QAQ[N];
vector<int> rm;
void chk(int v) {
  if (((int)(g[v]).size()) < k && !die[v]) {
    rm.push_back(v);
    die[v] = 1;
    --ans;
  }
}
void del(int u, int v) {
  g[u].erase(v);
  g[v].erase(u);
  chk(u);
  chk(v);
}
int main() {
  RD(n, m, k);
  for (int i(0); i < (m); ++i) {
    int u, v;
    RD(u, v);
    --u, --v;
    e[i] = {u, v};
    g[u].insert(v);
    g[v].insert(u);
  }
  ans = n;
  for (int i(0); i < (n); ++i) chk(i);
  for (int i((m)-1); i >= (0); --i) {
    while (((int)(rm).size())) {
      int u = ((rm).back());
      (rm).pop_back();
      while (((int)(g[u]).size())) del(u, *begin(g[u]));
    }
    QAQ[i] = ans;
    del(e[i].first, e[i].second);
  }
  for (int i(0); i < (m); ++i) PL(QAQ[i]);
}

```