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 Julia (0.5.0) (judge verdict: Accepted)

function index(Vec, Num)
  
  N = length(Vec)
  left = 1
  right = N+1
  mid = div(right + left, 2)
  
  while left < right
    if Vec[mid] == Num
      return mid
    elseif Vec[mid] > Num
      right = mid
      mid = div(right + left, 2)
    else
      left = mid + 1
      mid = div(right + left, 2)
    end
  end
  
end

function main()
  
  (N, M) = map(x -> parse(Int, x), split(readline()))
  
  checks = [[] for i in 1:N]
  
  P = zeros(Int, M)
  Y = zeros(Int, M)
  for i in 1:M
    (P[i], Y[i]) = map(x -> parse(Int, x), split(readline()))
    push!(checks[P[i]], Y[i])
  end
  
  for i in 1:N
    sort!(checks[i])
  end
  
  for i in 1:M
    print(lpad(P[i], 6, 0))
    println(lpad(index(checks[P[i]], Y[i]), 6, 0))
  end
  
end

main()