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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class D
{
	public static void Main() => (new Solver()).Solve();
}

public class Solver
{
	public void Solve()
	{
		int N = GetInt();
		int M = GetInt();
		int K = GetInt();

		var uf = new UnionFind(N);
		int[] deg = new int[N];
		for(int i = 0; i < M; i++)
		{
			int A = GetInt() - 1;
			int B = GetInt() - 1;
			if(!uf.IsSame(A, B))
				uf.Merge(A, B);

			deg[A]++;
			deg[B]++;			
		}
		int[] ans = new int[N];
		for(int i = 0; i < N; i++)
			ans[i] = uf.Size(i) - deg[i] - 1;

		for(int i = 0; i < K; i++)
		{
			int C = GetInt() - 1;
			int D = GetInt() - 1;
			if(uf.IsSame(C, D))
			{
				ans[C]--;
				ans[D]--;
			}
		}
		WriteLine(string.Join(" ", ans));
	}
}

public class UnionFind
{
	private int[] par = null;
	private int[] rank = null;
	private int[] ccSize = null;
	
	public UnionFind(int n)
	{
		par = new int[n];
		rank = new int[n];
		ccSize = new int[n];
		for(int i = 0; i < n; i++)
		{
			par[i] = i;
			rank[i] = 0;
			ccSize[i] = 1;
		}
	}

	public bool IsSame(int x, int y)
	{
		return (Root(x) == Root(y));
	}

	public int Root(int x)
	{
		if(par[x] == x)
			return x;

		int r = Root(par[x]);
		par[x] = r;
		return r;
	}
	
	public bool Merge(int x, int y)
	{
		int rx = Root(x);
		int ry = Root(y);
		if(rx == ry)
			return false;
		
		if(rank[rx] < rank[ry])
		{
			int tmp = rx;
			rx = ry;
			ry = tmp;
		}
		else if(rank[rx] == rank[ry])
			rank[rx]++;

		par[ry] = rx;
		ccSize[rx] = ccSize[rx] + ccSize[ry];
		return true;
	}

	public int Size(int x)
	{
		return ccSize[Root(x)];
	}
}

public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => Enumerable.Range(0, (int)N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(long N) => Enumerable.Range(0, (int)N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(long N) => Enumerable.Range(0, (int)N).Select(_ => GetDouble()).ToArray();
	public static decimal[] GetDecimals(long N) => Enumerable.Range(0, (int)N).Select(_ => GetDecimal()).ToArray();
	public static string[] GetStrings(long N) => Enumerable.Range(0, (int)N).Select(_ => GetString()).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) < 0)
			x = y;
	}

	public static void chmin<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) > 0)
			x = y;
	}

	public static void swap<T>(ref T x, ref T y)
	{
		T tmp = x;
		x = y;
		y = tmp;
	}
}