Spring is interesting season of year. Chef is thinking about different things, but last time he thinks about interesting game - "Strange Matrix". 
Chef has a matrix that consists of n rows, each contains m elements. Initially, the element aij of matrix equals j. (1 ≤ i ≤ n, 1 ≤ j ≤ m). 
Then p times some element aij is increased by 1. 
Then Chef needs to calculate the following: 

- For each row he tries to move from the last element (with number m) to the first one (with the number 1). 
- While staying in aij Chef can only move to aij - 1 only if aij - 1 ≤ aij. 
- The cost of such a movement is aij - aij - 1.
- Otherwise Chef can't move and lose (in this row).
- If Chef can move from the last element of the row to the first one, then the answer is the total cost of all the movements. 
- If Chef can't move from the last element of the row to the first one, then the answer is -1. 

Help Chef to find answers for all the rows after P commands of increasing. 

-----Input-----

- The first line contains three integers n, m and p denoting the number of rows, the number of elements a single row and the number of increasing commands. 
- Each of next p lines contains two integers i and j denoting that the element aij  is increased by one. 

-----Output-----
- For each row in a single line print the answer after the P increasing commands.

-----Constraints-----
- 1 ≤ n, m, p ≤ 10 ^ 5
- 1 ≤ i ≤ n
- 1 ≤ j ≤ m

-----Example-----
Input:
4 4 6
2 2
3 2 
3 2 
4 3
4 4
4 3

Output:
3
3
-1
4


-----Explanation-----

Here is the whole matrix after P commands:
1 2 3 4
1 3 3 4
1 4 3 4
1 2 5 5

Explanations to the answer: 
- The first line is without changes: 4-3=1, 3-2=1, 2-1=1. answer = 3. 
- The second line: 4-3=1, 3-3=0, 3-1=2. The answer is 3. 
- The third line: 4-3=1, 3-4=-1, Chef can't move to the first number here. Therefore, the answer is -1. 
- The fourth line: 5-5=0, 5-2=3, 2-1=1. The answer is 4.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '#!/usr/bin/env python2\n# -*- coding: utf-8 -*-\n\n## Codechef May Challenge 2014\n## Chef and Strange Matrix\n\ntry:\n import psyco\n psyco.full()\nexcept ImportError:\n pass\n\n\ndef main(N, M, P, tab):\n """Evolved solution"""\n # make a dictionnary with rows and cols increased\n dtab = dict()\n for ii, jj in tab:\n  i, j = ii-1, jj-1\n  if i in dtab:\n   dtab[i].append(j)\n  else:\n   dtab[i] = [j]\n\n # move along each row\n for i in range(N):\n  sol = M-1\n  if i in dtab:\n   line = sorted(dtab[i])\n   # only the first and the last col give points\n   sol += line.count(M-1) - line.count(0)\n   # check for unsolvable cases\n   prev = -1 # don\'t repeat k\n   for k in line:\n    if k > prev and k < (M - 1):\n     inc_k = line.count(k)\n     inc_kp = line.count(k+1)\n     if inc_k > (inc_kp + 1):\n      sol = -1\n      break\n     prev = k\n\n  print(sol)\n\n\ndef __starting_point():\n N, M, P = list(map(int, input().split())) # rows, cols, increasing cmds\n tab = [list(map(int, input().split())) for _ in range(P)]\n main(N, M, P, tab)\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 20973