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CF1872A.Two Vessels

普及/提高-

通过率：0%

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题目描述

You have two vessels with water. The first vessel contains aa grams of water, and the second vessel contains bb grams of water. Both vessels are very large and can hold any amount of water.

You also have an empty cup that can hold up to cc grams of water.

In one move, you can scoop up to cc grams of water from any vessel and pour it into the other vessel. Note that the mass of water poured in one move does not have to be an integer.

What is the minimum number of moves required to make the masses of water in the vessels equal? Note that you cannot perform any actions other than the described moves.

输入格式

Each test contains multiple test cases. The first line contains the number of test cases tt ( 1≤t≤10001 \le t \le 1000 ). The description of the test cases follows.

Each test case consists of a single line containing three integers aa , bb , and cc ( 1≤a,b,c≤1001 \le a, b, c \le 100 ) — the mass of water in the vessels and the capacity of the cup, respectively.

输出格式

For each test case, output a single number — the minimum number of moves required to make the masses of water in the vessels equal. It can be shown, that it is always possible.

输入输出样例

  • 输入#1

    6
3 7 2
17 4 3
17 17 1
17 21 100
1 100 1
97 4 3

    输出#1

    1
3
0
1
50
16

说明/提示

In the first test case, only one move is enough: if we pour 22 grams of water from the second vessel into the first one, both vessels will contain 55 grams of water.

In the second example test case, three moves are enough:

  • Pour 33 grams of water from the first vessel into the second one. After this move, the first vessel will contain 17−3=1417 - 3 = 14 grams of water, and the second vessel will contain 4+3=74 + 3 = 7 grams.
  • Pour 22 grams of water from the first vessel into the second one. After this move, the first vessel will contain 14−2=1214 - 2 = 12 grams of water, and the second vessel will contain 7+2=97 + 2 = 9 grams.
  • Finally, pour 1.51.5 grams of water from the first vessel into the second one. After this move, the first vessel will contain 12−1.5=10.512 - 1.5 = 10.5 grams of water, and the second vessel will contain 9+1.5=10.59 + 1.5 = 10.5 grams.

Note that this is not the only way to equalize the vessels in 33 moves, but there is no way to do it in 22 moves.

In the third example test case, the vessels initially contain the same amount of water, so no moves are needed. The answer is 00 .

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