시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 16 5 5 71.429%

문제

원웅이는 두 종류의 추와 저울을 이용해서 아스피린의 양을 재려고 한다. 원웅이는 추를 무수히 많이 가지고 있고, 약은 가루로 가지고 있다.

예를 들어, 300mg 추와 700mg 추가 있을 때, 200mg의 아스피린을 재려면, 300mg 추 3개를 왼편에 놓고, 700mg의 추 1개를 반대편에 놓은 뒤, 평형을 이루도록 약을 놓으면 된다. 

또는, 왼쪽에 700mg 추 2개를 놓고, 오른쪽에 300mg추 4개를 놓으면, 오른쪽에 약을 저울이 평형을 이루도록 놓으면 된다.

원웅이가 가지고 있는 추의 종류와 재려고 하는 아스피린의 양이 주어졌을 때, 각각 추를 몇 개 사용하면 아스피린의 양을 잴 수 있는지 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스는 한 줄로 이루어져 있고, a, b, d가 공백으로 구분되어 주어진다.

a와 b는 원웅이가 가지고 있는 추의 무게이고, d는 재려고 하는 약의 양이다. a와 b는 같지 않고, 두 수 모두 10,00보다 작거나 같은 자연수이다. d는 50,000보다 작거나 같은 자연수이다.

정답이 존재하지 않는 경우는 없다.

테스트 케이스는 a, b, d가 0일 때 끝난다.

출력

각 테스트 케이스에 대해서, x와 y를 출력한다. x와 y는 다음 세가지 조건을 만족해야 한다.

1. amg추 x개와 bmg추 y개를 이용해서 dmg의 약을 저울로 잴 수 있어야 한다.

2. 1번 조건을 만족하는 경우가 여러 가지라면, 사용한 추의 개수(x+y)가 가장 작은 것을 출력한다.

3. 2번 조건을 만족하는 경우도 여러 가지라면, 추의 총 질량(ax+by)이 가장 작은 것을 출력한다.

예제 입력 1

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

예제 출력 1

1 3
1 1
1 0
0 3
1 1
49 74
3333 1
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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.<\/p>\r\n\r\n<p>You are asked to help her by calculating how many weights are required.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/b1.png\" style=\"height:119px; width:427px\" \/><\/p>\r\n\r\n<p>Figure 1: To measure 200mg of aspirin using three 300mg weights and one 700mg weight<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/b2.png\" style=\"height:134px; width:426px\" \/><\/p>\r\n\r\n<p>Figure 2: To measure 200mg of aspirin using four 300mg weights and two 700mg weights<\/p>\r\n","input":"<p>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 &ne; b, a &le; 10000, b &le; 10000, and d &le; 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 &quot;no solution&quot; cases.<\/p>\r\n\r\n<p>The end of the input is indicated by a line containing three zeros separated by a space. It is not a dataset.<\/p>\r\n","output":"<p>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.<\/p>\r\n\r\n<ul>\r\n\t<li>You can measure d mg using x many a mg weights and y many b mg weighs.<\/li>\r\n\t<li>The total number of weights (x + y) is the smallest among those pairs of nonnegative integers satisfying the previous condition.<\/li>\r\n\t<li>The total mass of weights (ax + by) is the smallest among those pairs of nonnegative integers satisfying the previous two conditions.<\/li>\r\n<\/ul>\r\n\r\n<p>No extra characters (e.g. extra spaces) should appear in the output.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]