Problem:
Score : 400 points

Problem Statement

An SNS has N users - User 1, User 2, \cdots, User N.

Between these N users, there are some relationships - M friendships and K blockships.

For each i = 1, 2, \cdots, M, there is a bidirectional friendship between User A_i and User B_i.

For each i = 1, 2, \cdots, K, there is a bidirectional blockship between User C_i and User D_i.

We define User a to be a friend candidate for User b when all of the following four conditions are satisfied:

a \neq b.

There is not a friendship between User a and User b.

There is not a blockship between User a and User b.

There exists a sequence c_0, c_1, c_2, \cdots, c_L consisting of integers between 1 and N (inclusive) such that c_0 = a, c_L = b, and there is a friendship between User c_i and c_{i+1} for each i = 0, 1, \cdots, L - 1.

For each user i = 1, 2, ... N, how many friend candidates does it have?

Constraints

All values in input are integers.

2 ≤ N ≤ 10^5

0 \leq M \leq 10^5

0 \leq K \leq 10^5

1 \leq A_i, B_i \leq N

A_i \neq B_i

1 \leq C_i, D_i \leq N

C_i \neq D_i

(A_i, B_i) \neq (A_j, B_j) (i \neq j)

(A_i, B_i) \neq (B_j, A_j)

(C_i, D_i) \neq (C_j, D_j) (i \neq j)

(C_i, D_i) \neq (D_j, C_j)

(A_i, B_i) \neq (C_j, D_j)

(A_i, B_i) \neq (D_j, C_j)

Input

Input is given from Standard Input in the following format:

N M K
A_1 B_1
\vdots
A_M B_M
C_1 D_1
\vdots
C_K D_K

Output

Print the answers in order, with space in between.

Sample Input 1

4 4 1
2 1
1 3
3 2
3 4
4 1

Sample Output 1

0 1 0 1

There is a friendship between User 2 and 3, and between 3 and 4. Also, there is no friendship or blockship between User 2 and 4. Thus, User 4 is a friend candidate for User 2.

However, neither User 1 or 3 is a friend candidate for User 2, so User 2 has one friend candidate.

Sample Input 2

5 10 0
1 2
1 3
1 4
1 5
3 2
2 4
2 5
4 3
5 3
4 5

Sample Output 2

0 0 0 0 0

Everyone is a friend of everyone else and has no friend candidate.

Sample Input 3

10 9 3
10 1
6 7
8 2
2 5
8 4
7 3
10 9
6 4
5 8
2 6
7 5
3 1

Sample Output 3

1 3 5 4 3 3 3 3 1 0

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#pragma GCC optimize ("-O2")
#include <bits/stdc++.h>
using namespace std;

// ============union_find_tree===============
int MAX_N = 100000;
vector<int> par(MAX_N);//MAX_N == num of node
vector<int> tree_rank(MAX_N);

void init(int n)
{
  for (int i = 0; i < n; ++i)
  {
    par.at(i) = i;
    tree_rank.at(i) = 0;
  }
}

int find(int x)
{
  if (par.at(x) == x)
  {
    return x;
  }
  else
  {
    return par.at(x) = find(par.at(x));
  }
}

void unite(int x, int y)
{
  x = find(x);
  y = find(y);
  if (x == y)
  {
    return;
  }
  if (tree_rank.at(x) < tree_rank.at(y))
  {
    par.at(x) = y;
  }
  else
  {
    par.at(y) = x;
    if (tree_rank.at(x) == tree_rank.at(y))
    {
      tree_rank.at(x)++;
    }
  }
}

bool same(int x, int y)
{
  return find(x) == find(y);
}

int main()
{
  int N, M, K;
  cin >> N >> M >> K;
  init(N);
  int A, B, C, D;
  vector<vector<int>> friend_or_block(N, vector<int>(0));
  for (int i = 0; i < M; ++i)
  {
    cin >> A >> B;
    friend_or_block.at(A - 1).push_back(B - 1);
    friend_or_block.at(B - 1).push_back(A - 1);
    unite(A - 1, B - 1);
  }
  for (int i = 0; i < K; ++i)
  {
    cin >> C >> D;
    if (same(C - 1, D - 1))
    {
      friend_or_block.at(C - 1).push_back(D - 1);
      friend_or_block.at(D - 1).push_back(C - 1);
    }
  }
  vector<int> connected_num(N, 0);
  for (int i = 0; i < N; ++i)
  {
    connected_num.at(find(i)) += 1;
  }

  for (int i = 0; i < N; ++i)
  {
    cout << connected_num.at(find(i)) - friend_or_block.at(i).size() - 1 << ' ';
  }
  cout << endl;
}