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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.util.*;

public class Main {


    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
        HashMap<Integer,HashSet<Integer>[]> relation = new HashMap<>();
        for (int i=1;i<=n;i++){
            relation.put(i,new HashSet[2]);
            relation.get(i)[0] = new HashSet<>();
            relation.get(i)[1] = new HashSet<>();
        }
        for (int i=0;i<m;i++){
            int a = sc.nextInt();
            int b = sc.nextInt();
            relation.get(a)[0].add(b);
            relation.get(b)[0].add(a);
        }
        for (int i=0;i<k;i++){
            int c = sc.nextInt();
            int d = sc.nextInt();
            relation.get(c)[1].add(d);
            relation.get(d)[1].add(c);
        }
        boolean[] done = new boolean[n+1];
        HashSet<Integer>[] con = new HashSet[n+1];
        Arrays.fill(done,false);
        Stack stack = new Stack();
        for (int i=1;i<=n;i++){
            stack.init();
            if (!done[i]){
                HashSet<Integer> hash = new HashSet<>();
                hash.add(i);
                boolean[] seen = new boolean[n+1];
                for (int j=1;j<=n;j++)seen[i]=false;
                stack.push(i);
                seen[i]=true;
                while (!stack.isEmpty()){
                    int v = stack.pop();
                    for (int l : relation.get(v)[0]){
                        if (!seen[l]){
                            seen[l]=true;
                            stack.push(l);
                            hash.add(l);
                        }
                    }
                }
                for (int a : hash){
                    con[a]= new HashSet<>();
                    con[a].addAll(hash);
                    done[a]=true;
                }
            }
            con[i].removeAll(relation.get(i)[1]);
            System.out.print((con[i].size()-relation.get(i)[0].size()-1)+" ");
        }
        System.out.println();
    }
    public static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            }else{
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while(true){
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                }else if(b == -1 || !isPrintableChar(b)){
                    return minus ? -n : n;
                }else{
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }
        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }
        public double nextDouble() { return Double.parseDouble(next());}
    }
    public static class Queue{
        private final int max = 1000000;
        private final int[] queue = new int[max];
        private int tail = 0; private int head = 0;
        public void init(){this.head = 0; tail = 0;}
        public boolean isEmpty(){return (head==tail);}
        public boolean isFull(){return (head == (tail+1)%max);}
        public void enqueue(int v){
            if (isFull()){
                System.out.println("error: queue is full.");
                return;
            }
            queue[tail++] = v;
            if (tail == max) tail = 0;
        }
        public int dequeue(){
            if (isEmpty()){
                System.out.println("error: queue is empty");
                return -1;
            }
            int res = queue[head];
            ++head;
            if (head == max) head = 0;
            return res;
        }
    }
    public static class Stack{
        private final int max = 100000;
        private final int[] stack = new int[max];
        private int top = 0;
        public boolean isEmpty(){return (top==0);}
        public boolean isFull(){return (top==max);}
        public void init(){top=0;}
        public void push(int v){
            if (isFull()){
                System.out.println("error: stack is full.");
                return;
            }
            stack[top++] = v;
        }
        public int pop(){
            if (isEmpty()){
                System.out.println("error: stack is empty");
                return -1;
            }
            return stack[--top];
        }
    }
    public static class BasicMath {
        private final int MAX = 510000;
        private final int MOD = 1000000007;
        private final long[] fac = new long[MAX];
        private final long[] finv= new long[MAX];
        private final long[] inv = new long[MAX];
        public long factorial(long num){
            if (num<2)return 1;
            else return num*factorial(num-1);
        }
        public int arraySum(int[] array){
            int ans = 0;
            for (int value : array) ans += value;
            return ans;
        }
        public double log(double base,double antilogarithm){
            return Math.log(antilogarithm)/Math.log(base);
        }
        public long gcd(long x,long y){
            if (y==0)return x;
            else return gcd(y,x%y);
        }
        public long lcm(long x,long y){
            return x/gcd(x,y)*y;
        }
        public HashMap<Long,Long> factorization(long num){
            HashMap<Long,Long> hash = new HashMap<>();
            long n = num;
            long count = 2;
            while (n>1){
                while (n%count==0){
                    n/=count;
                    if (hash.containsKey(count))hash.put(count,hash.get(count)+1);
                    else hash.put(count,1L);
                }
                count++;
            }
            return hash;
        }
        public int sum(int[] num){
            int ans = 0;
            for (int i = 0; i < num.length;i++){
                ans += num[i];
            }
            return ans;
        }
        public int[] reduce(int small, int big){
            int ins = 2;
            while (ins<=small){
                if (small%ins==0&&big%ins==0){
                    small/=ins;
                    big/=ins;
                    ins = 2;
                }else {
                    ins++;
                }
            }
            return new int[]{small, big};
        }
        public int reduceCount(int small, int big){
            int ins = 2;
            int ans = 0;
            while (ins<=small){
                if (small%ins==0&&big%ins==0){
                    small/=ins;
                    big/=ins;
                    ins = 2;
                    ans++;
                }else {
                    ins++;
                }
            }
            return ans;
        }
        public int binarySearch(int[] array, int target){
            int pos = -1;
            int left = 0;
            int right = array.length-1;
            int middle;
            while (pos==-1&&left<=right){
                middle = (left+right)/2;
                if (array[middle]==target)pos=middle;
                else if (array[middle]>target)right=middle-1;
                else left=middle+1;
            }
            return pos;
        }
        public long modPow(long a, long n, long mod){
            long res = 1;
            while (n>0){
                if ((n&1)!=0)res = res*a%mod;
                a=a*a%mod;
                n >>= 1;
            }
            return res;
        }
        public long modinv(long a, long mod){return modPow(a,mod-2,mod);}
        public void COMinit(){
            fac[0]=1;
            fac[1]=1;
            finv[0]=1;
            finv[1]=1;
            inv[1]=1;
            for (int i=2;i<MAX;i++){
                fac[i]=fac[i-1]*i%MOD;
                inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
                finv[i]=finv[i-1]*inv[i]%MOD;
            }
        }
        public long COM(int n, int k){
            if (n<k)return 0;
            if (n<0||k<0)return 0;
            return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
        }
        public long HCOM(int n, int k){
            return COM(n+k-1,k);
        }
    }
}