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)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
#ifdef ENABLE_DEBUG
#define dump(a) cerr<<#a<<"="<<a<<endl
#define dumparr(a,n) cerr<<#a<<"["<<n<<"]="<<a[n]<<endl
#else
#define dump(a) 
#define dumparr(a,n) 
#endif
#define FOR(i, a, b) for(ll i = a;i < b;i++)
#define For(i, a) FOR(i, 0, a)
#define REV(i, a, b) for(ll i = b-1;i >= a;i--)
#define Rev(i, a) REV(i, 0, a)
#define REP(a) For(i, a)
#define SIGN(a) (a==0?0:(a>0?1:-1))

typedef long long int ll;
typedef unsigned long long ull;
typedef unsigned int uint;
typedef pair<ll, ll> pll;
typedef pair<ll,pll> ppll;
typedef vector<ll> vll;
typedef long double ld;
typedef pair<ld,ld> pdd;

const ll INF=(1LL<<50);
#if __cplusplus<201700L
ll gcd(ll a, ll b) {
  if(a < b) return gcd(b, a);
  ll r;
  while ((r=a%b)) {
    a = b;
    b = r;
  }
  return b;
}
#endif
template<class T>
bool chmax(T& a,const T& b){
  if(a<b){
    a=b;
    return true;
  }
  return false;
}
template<class T>
bool chmin(T& a,const T& b){
  if(a>b){
    a=b;
    return true;
  }
  return false;
}
template<class S,class T>
std::ostream& operator<<(std::ostream& os,pair<S,T> a){
  os << "(" << a.first << "," << a.second << ")";
  return os;
}
template<class T>
std::ostream& operator<<(std::ostream& os,vector<T> a){
  os << "[ ";
  REP(a.size()){
    os<< a[i] << " ";
  }
  os<< " ]";
  return os;
}


class UF{
  vector<long> par,rank,size_uf;
  long _chunk_size;
public:
  UF(long size):_chunk_size(size){
    for (long i = 0; i < size; i++) {
      par.push_back(i);
      rank.push_back(0);
      size_uf.push_back(1);
    }
  }
  long find(long x){
    if(par[x]==x)return x;
    return par[x]=find(par[x]);
  }
  void unite(long x,long y){
    x=find(x);
    y=find(y);
    if(x==y)return;
    --_chunk_size;
    if(rank[x]<rank[y]){
      par[x]=y;
      size_uf[y]+=size_uf[x];
    }
    else{
      par[y]=x;
      size_uf[x]+=size_uf[y];
      if(rank[x]==rank[y])rank[x]++;
    }
  }
  bool same(long x,long y){
    return find(x)==find(y);
  }
  long operator [](long x){
    return this->find(x);
  }
  long size(long x){
    x=find(x);
    return size_uf[x];
  }
  long chunk_size(){
    return this->_chunk_size;
  }
};
void solve(long long N, long long M, long long K, std::vector<long long> A, std::vector<long long> B, std::vector<long long> C, std::vector<long long> D){
  UF friends(N);
  vector<ll> ans(N,-1);
  REP(M){
    friends.unite(A[i]-1,B[i]-1);
    --ans[A[i]-1];
    --ans[B[i]-1];
  }
  REP(N){
    ans[i]+=friends.size(i);
  }
  REP(K){
    if(friends.same(C[i]-1,D[i]-1)){
      --ans[C[i]-1];
      --ans[D[i]-1];
    }
  }
  REP(N){
    cout<<ans[i]<<" ";
  }
  cout<<endl;
}

int main(){
  cout<<setprecision(1000);
    long long N;
    scanf("%lld",&N);
    long long M;
    scanf("%lld",&M);
    long long K;
    scanf("%lld",&K);
    std::vector<long long> A(M);
    std::vector<long long> B(M);
    for(int i = 0 ; i < M ; i++){
        scanf("%lld",&A[i]);
        scanf("%lld",&B[i]);
    }
    std::vector<long long> C(K);
    std::vector<long long> D(K);
    for(int i = 0 ; i < K ; i++){
        scanf("%lld",&C[i]);
        scanf("%lld",&D[i]);
    }
    solve(N, M, K, std::move(A), std::move(B), std::move(C), std::move(D));
    return 0;
}