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 C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

int find(int y, vector<int> v) {
  int i = 0, j = v.size()-1;
  while (i <= j) {
    int idx = (i + j) / 2;
    if (v[idx] == y) {
      return idx + 1;
    }
    if (y < v[idx]) {
      j = idx - 1;
    } else {
      i = idx + 1;
    }
  }
}

int main() {
  int N, M;
  cin >> N >> M;
  vector<int> P(M), Y(M);
  for (int i = 0; i < M; i++) {
    cin >> P[i] >> Y[i];
  }
  map<int, vector<int>> X;
  for (int i = 0; i < M; i++) {
    X[P[i]].push_back(Y[i]);
  }

  for (auto i = X.begin(); i != X.end(); i++) {
    sort(i->second.begin(), i->second.end());
  }

  for (int i = 0; i < M; i++) {
    int p = P[i];
    int y = find(Y[i], X[p]);
    printf("%06d%06d\n", p, y);
  }
}