Buggy python submission (verdict: Runtime Error):
import sys
sys.setrecursionlimit(100000000)
class UnionFind:
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return {i for i in range(self.n) if self.find(i) == root}

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

n,m,k=map(int,input().split())
path = dict()
block = [set() for _ in range(n)]
for _ in range(m):
  a,b=map(int,input().split())
  if a-1 in path:
    path[a-1].add(b-1)
  else:
    path[a-1] = {b-1}
  if b-1 in path:
    path[b-1].add(a-1)
  else:
    path[b-1] = {a-1}
    
for _ in range(k):
  c,d=map(int,input().split())
  block[c-1].add(d-1)
  block[d-1].add(c-1)

uf = UnionFind(n)
for i, x in path.items():
  for j in x:
    uf.union(i,j)

uf.find(0)

ans = [0]*n
for i in range(n):
  ans[i] = len(uf.members(i) - path[i] - block[i]) -1
print(*ans)

Fixed submission:
import sys
sys.setrecursionlimit(100000000)
class UnionFind:
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return {i for i in range(self.n) if self.find(i) == root}

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

n,m,k=map(int,input().split())
block = [0]*n
uf = UnionFind(n)
for _ in range(m):
  a,b=map(int,input().split())
  block[a-1] += 1
  block[b-1] += 1
  uf.union(a-1,b-1)

uf.find(0)
for _ in range(k):
  c,d=map(int,input().split())
  if uf.same(c-1,d-1):
    block[c-1] += 1
    block[d-1] += 1

ans = [uf.size(i) - block[i] - 1 for i in range(n)]
print(*ans)

Buggy python submission (verdict: Runtime Error):
import sys
sys.setrecursionlimit(100000000)

"""
方針
1. つながってるやつ全員candにぶちこむ
2. 各iについて所属candからblock[i]を差し引く
"""
n,m,k=map(int,input().split())
group = list()
path = dict()
block = [set() for i in range(n+1)]
for _ in range(m):
  a,b = map(int,input().split())
  if a in path:
    path[a].add(b)
  else:
    path[a] = {b}
  if b in path:
    path[b].add(a)
  else:
    path[b] = {a}
for _ in range(k):
  c,d = map(int,input().split())
  block[c].add(d)
  block[d].add(c)

group = list()
memo = [-1]*(n+1)

def rec(g, i):
  res = set()
  memo[i] = g
  #print('call', g, i)
  for p in path[i]:
    if memo[p] < 0:
      res |= rec(g, p)
      memo[p] = g
  #print(g,i,path[i], res)
  if len(res) > 0:
    return res | {i}
  else:
    return {i}
  
for i in range(1,n+1):
  if memo[i] < 0:
    group.append(rec(len(group), i))

ans = list()
for i in range(1,n+1):
  candi = group[memo[i]] - path[i] - block[i] - {i}
  ans.append(len(candi))
#print(*group)
#print(*[[i,b] for i,b in enumerate(block) if len(b) > 0])
print(*ans)

Fixed submission:
import sys
sys.setrecursionlimit(100000000)
class UnionFind:
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return {i for i in range(self.n) if self.find(i) == root}

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

n,m,k=map(int,input().split())
block = [0]*n
uf = UnionFind(n)
for _ in range(m):
  a,b=map(int,input().split())
  block[a-1] += 1
  block[b-1] += 1
  uf.union(a-1,b-1)

uf.find(0)
for _ in range(k):
  c,d=map(int,input().split())
  if uf.same(c-1,d-1):
    block[c-1] += 1
    block[d-1] += 1

ans = [uf.size(i) - block[i] - 1 for i in range(n)]
print(*ans)