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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

public class Hello
{
    private const int MOD_N = 1000000000 + 7;

    public static void Main()
    {
        var nmk = Console.ReadLine().Split(' ');
        var n = int.Parse(nmk[0]);
        var m = int.Parse(nmk[1]);
        var k = int.Parse(nmk[2]);

        var friends = new bool[n][];
        var uf = new UnionFind(n);
        for (int i = 0; i < friends.Length; ++i)
            friends[i] = new bool[n];
        for (int i = 0; i < m; ++i)
        {
            var ab = Console.ReadLine().Split(' ');
            var a = int.Parse(ab[0]) - 1;
            var b = int.Parse(ab[1]) - 1;
            friends[a][b] = friends[b][a] = true;
            uf.Unite(a, b);
        }

        var blocks = new bool[n][];
        for (int i = 0; i < blocks.Length; ++i)
            blocks[i] = new bool[n];
        for (int i = 0; i < k; ++i)
        {
            var cd = Console.ReadLine().Split(' ');
            var c = int.Parse(cd[0]) - 1;
            var d = int.Parse(cd[1]) - 1;
            blocks[c][d] = blocks[d][c] = true;
        }

        var answers = new int[n];
        for (int i = 0; i < answers.Length; ++i)
        {
            int answer = 0;
            var fs = friends[i];
            var bs = blocks[i];
            for (int j = 0; j < n; ++j)
            {
                if (j == i || fs[j] || bs[j])
                    continue;
                if (uf.Same(i, j))
                    ++answer;
            }
            answers[i] = answer;
        }

        Console.WriteLine(string.Join(" ", answers));
    }

    public sealed class UnionFind
    {
        int[] Parent { get; }
        public UnionFind(int n)
        {
            var parent = new int[n];
            for (int i = 0; i < parent.Length; ++i)
                parent[i] = i;
            Parent = parent;
        }

        public int Root(int c)
        {
            if (Parent[c] == c)
                return c;
            return Parent[c] = Root(Parent[c]);
        }

        public void Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);
            if (x != y)
                Parent[y] = x;
        }

        public bool Same(int x, int y) => Root(x) == Root(y);
    }

    private static int GCD(int a, int b) => a > b ? GCD_impl(a, b) : GCD_impl(b, a);
    private static int GCD_impl(int a, int b) => b == 0 ? a : GCD_impl(b, a % b);
    private static long LCM(int a, int b) => (long)a * b / GCD(a, b);

    private static int Comb(int m, int n)
    {
        var t = m - n;
        if (n > t)
            n = t;

        long numerator = 1;
        for (int i = 0; i < n; ++i)
        {
            numerator *= m - i;
            numerator %= MOD_N;
        }
        long denominator = 1;
        for (; n != 0; --n)
        {
            denominator *= n;
            denominator %= MOD_N;
        }

        var inv_denominator = ModInv((int)denominator, MOD_N);
        var ret = (int)(numerator * inv_denominator % MOD_N);

        return ret >= 0 ? ret : ret + MOD_N;
    }

    private static int ModInv(int a, int m)
    {
        int b = m, x = 1, y = 0;
        while (b != 0)
        {
            var t = a / b;
            a -= t * b;
            Swap(ref a, ref b);
            x -= t * y;
            Swap(ref x, ref y);
        }
        x %= m;
        return x >= 0 ? x : x + m;
    }

    private static void Swap<T>(ref T a, ref T b)
    {
        var t = a;
        a = b;
        b = t;
    }
}