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 Python (3.4.3) (judge verdict: Runtime Error)

import math

def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

h, w, k = list(map(int, input().split(" ")))

if(w == 1):
    print(1)
    exit()

ans = 0
for i in range(h+1):
    if((k - 1) <= i and (k - 1 + i) % 2 == 0):
        if(h - i != 0):
            tmp = 0
            for j in range(h-i+1):
                tmp += combinations_count(h, j)
            ans += combinations_count(h, i) * tmp
        else:
            ans += combinations_count(h, i)

    
    if((k - 1) <= i and (k - 1 + i) % 4 == 0 and w >= 4):
        if(h - i != 0):
            tmp = 0
            for j in range(h-i+1):
                tmp += combinations_count(h, j)
                if(j != 0): tmp -= combinations_count(h-1, j-1)
            ans += combinations_count(h, i) * tmp
        else:
            ans += combinations_count(h-1, i)


    if((k - 1) <= i and (k - 1 + i) % 6 == 0 and w >= 6):
        if(h - i != 0):
            tmp = 0
            for j in range(h-i+1):
                tmp += combinations_count(h, j)
                if(j != 0): tmp -= combinations_count(h-1, j-1)
                if(j >= 2): tmp -= combinations_count(h-2, j-2)
            ans += combinations_count(h, i) * tmp
        else:
            ans += combinations_count(h-1, i)

    if((k - 1) <= i and (k - 1 + i) % 8 == 0 and w >= 8):
        if(h - i != 0):
            tmp = 0
            for j in range(h-i+1):
                tmp += combinations_count(h, j)
                if(j != 0): tmp -= combinations_count(h-1, j-1)
                if(j >= 2): tmp -= combinations_count(h-2, j-2)
                if(j >= 3): tmp -= combinations_count(h-3, j-3)
            ans += combinations_count(h, i) * tmp
        else:
            ans += combinations_count(h-1, i)
            

print(ans % 1000000007)