Problem:
Problem A: The Balance

Ms. Iyo Kiffa-Australis has a balance and only two kinds of weights to measure a dose of medicine.

For example, to measure 200mg of aspirin using 300mg weights and 700mg weights, she can put
one 700mg weight on the side of the medicine and three 300mg weights on the opposite side
(Figure 1). Although she could put four 300mg weights on the medicine side and two 700mg
weights on the other (Figure 2), she would not choose this solution because it is less convenient
to use more weights.

You are asked to help her by calculating how many weights are required.

Figure 1: To measure 200mg of aspirin using three 300mg weights and one 700mg weight

Figure 2: To measure 200mg of aspirin using four 300mg weights and two 700mg weights

Input

The input is a sequence of datasets. A dataset is a line containing three positive integers a, b,
and d separated by a space. The following relations hold: a ≠ b, a ≤ 10000, b ≤ 10000, and
d ≤ 50000. You may assume that it is possible to measure d mg using a combination of a mg
and b mg weights. In other words, you need not consider “no solution” cases.

The end of the input is indicated by a line containing three zeros separated by a space. It is not
a dataset.

Output

The output should be composed of lines, each corresponding to an input dataset (a, b, d). An
output line should contain two nonnegative integers x and y separated by a space. They should
satisfy the following three conditions.

You can measure d mg using x many a mg weights and y many b mg weights.

The total number of weights (x + y) is the smallest among those pairs of nonnegative
integers satisfying the previous condition.

The total mass of weights (ax + by) is the smallest among those pairs of nonnegative
integers satisfying the previous two conditions.

No extra characters (e.g. extra spaces) should appear in the output.

Sample Input

700 300 200
500 200 300
500 200 500
275 110 330
275 110 385
648 375 4002
3 1 10000
0 0 0

Output for the Sample Input

1 3
1 1
1 0
0 3
1 1
49 74
3333 1

Solution in Ruby (judge verdict: Accepted)

### constant

INF = 1 << 30
MAX_X = 25000

### subroutines

def check(a, b, x, y)
  xy = x + y
  abxy = a * x + b * y
  if $min_xy > xy
    $min_xy = xy
    $min_abxy = abxy
    $min_x = x
    $min_y = y
  elsif $min_xy == xy
    if $min_abxy > abxy
      $min_abxy = abxy
      $min_x = x
      $min_y = y
    end
  end
end

### main

loop do
  a, b, d = gets.split.map(&:to_i)
  break if (a | b | d) == 0
  #p [a, b, d]

  $min_xy = INF
  $min_axby = INF
  $min_x = $min_y = nil

  for x in (0..MAX_X)
    # ax+d = by
    r = a * x + d
    if r % b == 0
      y = r / b
      check(a, b, x, y)
    end

    # ax = by+d
    r = a * x - d
    if r >= 0 && r % b == 0
      y = r / b
      check(a, b, x, y)
    end

    # ax + by = d
    r = d - a * x
    if r >= 0 && r % b == 0
      y = r / b
      check(a, b, x, y)
    end
  end

  puts [$min_x, $min_y].join(' ')
end