Problem:
Score: 300 points

Problem Statement

In Republic of Atcoder, there are N prefectures, and a total of M cities that belong to those prefectures.

City i is established in year Y_i and belongs to Prefecture P_i.

You can assume that there are no multiple cities that are established in the same year.

It is decided to allocate a 12-digit ID number to each city.

If City i is the x-th established city among the cities that belong to Prefecture i, the first six digits of the ID number of City i is P_i, and the last six digits of the ID number is x.

Here, if P_i or x (or both) has less than six digits, zeros are added to the left until it has six digits.

Find the ID numbers for all the cities.

Note that there can be a prefecture with no cities.

Constraints

1 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq P_i \leq N

1 \leq Y_i \leq 10^9

Y_i are all different.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
P_1 Y_1
:
P_M Y_M

Output

Print the ID numbers for all the cities, in ascending order of indices (City 1, City 2, ...).

Sample Input 1

2 3
1 32
2 63
1 12

Sample Output 1

000001000002
000002000001
000001000001

As City 1 is the second established city among the cities that belong to Prefecture 1, its ID number is 000001000002.

As City 2 is the first established city among the cities that belong to Prefecture 2, its ID number is 000002000001.

As City 3 is the first established city among the cities that belong to Prefecture 1, its ID number is 000001000001.

Sample Input 2

2 3
2 55
2 77
2 99

Sample Output 2

000002000001
000002000002
000002000003

Solution in Ruby (2.3.3) (judge verdict: Accepted)

class Heap
  attr_reader :size

  def initialize
    @heap = []
    @data = {}
    @size = 0
  end

  def add(n, data)
    i = @size
    while i > 0 do
      parent_index = (i - 1) / 2
      break if n >= @heap[parent_index]

      @heap[i] = @heap[parent_index]
      i = parent_index
    end

    @heap[i] = n
    @data[n] = data.merge(key: n)
    @size += 1
  end

  def pop
    min_n = @heap[0]
    @size -= 1
    n = @heap[@size]
    i = 0
    while i * 2 + 1 < @size do
      child_index1 = i * 2 + 1
      child_index2 = i * 2 + 2
      if child_index2 < @size && @heap[child_index2] < @heap[child_index1]
        child_index1 = child_index2
      end
      break if @heap[child_index1] >= n

      @heap[i] = @heap[child_index1]
      i = child_index1
    end
    @heap[i] = n
    @data.delete(min_n)
  end

  def min; @heap[0] end
  def values; @heap.first(@size) end
  def inspect; "Heap: #{values}" end
end

N, M = gets.split.map(&:to_i)
heaps = {}
cities = []
M.times do |i|
  pref, year = gets.split.map(&:to_i)
  heaps[pref] ||= Heap.new
  heaps[pref].add(year, {n: i})
  cities[i] = {p: pref}
end

# p heaps
heaps.each do |pref, heap|
  o = 1
  while c = heap.pop
    cities[c[:n]][:o] = o
    o += 1
  end
end

cities.each do |city|
  puts "%06d%06d" % [city[:p], city[:o]]
end