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;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int n = cin.Int();
			int m = cin.Int();
			int k = cin.Int();

			var uf = new UnionFindTree(n);

			var to = new List<int>[n];
			for (int i = 0; i < n; i++) {
				to[i] = new List<int>();
			
			}

			for (int i = 0; i < m; i++) {
				int a = cin.Int() - 1;
				int b = cin.Int() - 1;
				to[a].Add(b);
				to[b].Add(a);
				uf.TryUnite(a, b);
			}

			var block = new int[n];
			for (int i = 0; i < k; i++) {
				int c = cin.Int() - 1;
				int d = cin.Int() - 1;
				if (uf.IsUnited(c, d)) {
					block[c]++;
					block[d]++;
				}
			}

			var sb = new StringBuilder();
			for (int i = 0; i < n; i++) {
				int ans = uf.GetSize(i) - to[i].Count() - block[i] - 1;
				sb.Append($"{ans} ");
			}

			Console.WriteLine(sb.ToString());
		}
	}

	public class UnionFindTree
	{
		private readonly List<int> sizes_;
		private readonly List<int> parents_;

		public int Count { get; private set; }
		public int GroupCount { get; private set; }

		public UnionFindTree(int count)
		{
			parents_ = new List<int>(count);
			sizes_ = new List<int>(count);

			Count = 0;
			GroupCount = 0;

			ExtendSize(count);
		}

		public bool IsUnited(int x, int y)
		{
			int xRoot = Find(x);
			int yRoot = Find(y);

			return xRoot == yRoot;
		}

		public bool TryUnite(int x, int y)
		{
			int xRoot = Find(x);
			int yRoot = Find(y);
			if (yRoot == xRoot) {
				return false;
			}

			int parent = sizes_[xRoot] < sizes_[yRoot] ? yRoot : xRoot;
			int child = sizes_[xRoot] < sizes_[yRoot] ? xRoot : yRoot;

			GroupCount--;
			parents_[child] = parent;
			sizes_[parent] += sizes_[child];

			return true;
		}
		public IEnumerable<int> AllRepresents => parents_.Where(x => x == parents_[x]);
		public int GetSize(int x) => sizes_[Find(x)];

		public int Find(int x)
		{
			while (x != parents_[x]) {
				parents_[x] = parents_[parents_[x]];
				x = parents_[x];
			}

			return x;
		}

		public void ExtendSize(int treeSize)
		{
			if (treeSize <= Count) {
				return;
			}

			parents_.Capacity = treeSize;
			sizes_.Capacity = treeSize;
			while (Count < treeSize) {
				parents_.Add(Count);
				sizes_.Add(1);
				Count++;
				GroupCount++;
			}
		}
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private readonly Func<string> reader_;
		private string[] buf_;
		private int index_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}