Building Teams

import sys
# print(sys.getrecursionlimit())
sys.setrecursionlimit(10**5)

inp1 = input().split()
numPupils = int(inp1[0])
numFriendships = int(inp1[1])

friendshipList = []

def whetherValid(group1, group2):
  for friendship in friendshipList:
    if friendship[0] in group1 and friendship[1] in group1:
      return False
    if friendship[0] in group2 and friendship[1] in group2:
      return False
    
  return True

def get_combinations(index, group1, group2):
  # base case
  # if index reaches total number of pupils, then no more pupils to sort. Check if both group1 and group2 are valid. If yes then print out
  if possibleGroup != []:
    return
  if index == numPupils + 1:
    if whetherValid(group1, group2):
      # print("group1:", group1)
      # print("group2:", group2)
      possibleGroup.append(group1)
      possibleGroup.append(group2)

      whetherPossible[0] = True
    return
    
  # print(f"index: {index}, group1: {group1}, group2: {group2}")

  # reduction step
  # 2 choices
  # 1. don't add the pupil to group1, add to group2 and increment index
  # 2. add the pupil to group1, don't add to group2, increment index
  get_combinations(index + 1, group1, group2 + [index])
  get_combinations(index + 1, group1 + [index], group2)

if numPupils == 1:
  print("1")
else:
  for i in range(numFriendships):
    inp2 = input().split()
    friendshipList.append([int(inp2[0]), int(inp2[1])])

  whetherPossible = [False]
  possibleGroup = []

  get_combinations(1, [], [])
  # print(possibleGroup)
  if whetherPossible[0]:
    # print("YAY")
    group1 = possibleGroup[0]
    group2 = possibleGroup[1]
    solution = ""

    for i in range(1, numPupils + 1):
      if i in group1:
        solution += "1 "
      else:
        solution += "2 "

    print(solution[:-1])

  else:
    print("IMPOSSIBLE")

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: TIME LIMIT EXCEEDED

Test 7

Verdict: TIME LIMIT EXCEEDED

Test 8

Verdict: TIME LIMIT EXCEEDED

Test 9

Verdict: TIME LIMIT EXCEEDED

Test 10

Verdict: TIME LIMIT EXCEEDED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED