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 Scala (2.13.1) (judge verdict: Accepted)

object Main extends App {
	val pw = new java.io.PrintWriter(System.out)

	@scala.annotation.tailrec
	def loop(start: Int, end: Int)(f: Int => Unit): Unit =
		if (start < end) {
			f(start)
			loop(start + 1, end)(f)
		}

	val n, m, k = Scanner.nextInt()

	val linked = Array.fill(n)(0)
	val friend = UnionFind(0 until n)
	loop(0, m) { _ =>
		val a, b = Scanner.nextInt() - 1
		friend.unite(a, b)
		linked(a) += 1
		linked(b) += 1
	}

	val blocked = Array.fill(n)(0)
	loop(0, k) { _ =>
		val c, d = Scanner.nextInt() - 1
		if (friend.same(c, d)) {
			blocked(c) += 1
			blocked(d) += 1
		}
	}

	loop(0, n) { i =>
		pw.println(friend.size(i) - blocked(i) - linked(i) - 1)
	}
	pw.flush()
}

case class UnionFind[T](seq: Seq[T]) {
	import scala.collection.mutable.Map
	private[this] val par: Map[T, T] = Map[T,T](seq.map(elem => elem -> elem): _*)
	private[this] val sz: Map[T, Int] = Map[T, Int](seq.map(elem => elem -> 1): _*)

	@scala.annotation.tailrec
	private[this] def find(t: T, acc: Seq[T] = Nil): T = {
		val p = par(t)
		if (p == t) {acc foreach { par(_) = t }; t} else find(p, p +: acc)
	}

	def unite(a: T, b: T): Unit = {
		val pa = find(a)
		val pb = find(b)

		if (pa == pb) return

		if (sz(pa) <= sz(pb)) {
			par(pa) = pb
			sz(pb)  = sz(pa) + sz(pb)
		} else {
			par(pb) = pa
			sz(pa)  = sz(pa) + sz(pb)
		}
	}

	def same(a: T, b: T) = find(a) == find(b)

	def size(a: T) = sz(find(a))
}

object Scanner {
	private val buf = new Array[Byte](1024); private var ptr = 0; private var len = 0

	@inline private def isPrintableChar(c: Int): Boolean = 33 <= c && c <= 126
	@inline private def hasNextByte(): Boolean = if (ptr >= len) { ptr = 0; len = System.in.read(buf); len > 0 } else true
	@inline private def hasNext(): Boolean = {
		while (hasNextByte() && !isPrintableChar(buf(ptr))) ptr += 1
		hasNextByte()
	}
	@inline private def readByte(): Byte = if (hasNextByte()) { val res = buf(ptr); ptr += 1; res } else -1

	def next(): String = {
		if(!hasNext()) ???
		val sb = new StringBuilder; var b = readByte()
		while (isPrintableChar(b)) { sb.append(b.toChar); b = readByte() }
		sb.toString
	}

	def nextInt(): Int = {
		val n = nextLong()
		if (n < Int.MinValue || Int.MaxValue < n) ???
		n.toInt
	}

	def nextLong(): Long = {
		if(!hasNext()) ???
		var minus = false; var b = readByte()
		if (b == '-') { minus = true; b = readByte() }

		@scala.annotation.tailrec
		def go (b: Byte, n: Long = 0): Long = if ('0' <= b && b <= '9') go(readByte(), n * 10 + b - '0') else if (minus) -n else n

		go(b)
	}

	def nextDouble(): Double = next().toDouble
}