DIV + MOD

题意翻译

定义函数 $f_a(x)=\lfloor\frac{x}{a}\rfloor+x\bmod a$，其中 $a$ 为系数。 给定系数 $a$，给定 $x$ 范围 $l\le x\le r$，求 $f_a(x)$ 在范围内值的最大值。 其中 $1\le l\le r\le 10^9$，$1\le a\le 10^9$。

题目描述

Not so long ago, Vlad came up with an interesting function: - $ f_a(x)=\left\lfloor\frac{x}{a}\right\rfloor + x \bmod a $ , where $ \left\lfloor\frac{x}{a}\right\rfloor $ is $ \frac{x}{a} $ , rounded down, $ x \bmod a $ — the remainder of the integer division of $ x $ by $ a $ . For example, with $ a=3 $ and $ x=11 $ , the value $ f_3(11) = \left\lfloor\frac{11}{3}\right\rfloor + 11 \bmod 3 = 3 + 2 = 5 $ . The number $ a $ is fixed and known to Vlad. Help Vlad find the maximum value of $ f_a(x) $ if $ x $ can take any integer value from $ l $ to $ r $ inclusive ( $ l \le x \le r $ ).

输入输出格式

输入格式

The first line of input data contains an integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of input test cases. This is followed by $ t $ lines, each of which contains three integers $ l_i $ , $ r_i $ and $ a_i $ ( $ 1 \le l_i \le r_i \le 10^9, 1 \le a_i \le 10^9 $ ) — the left and right boundaries of the segment and the fixed value of $ a $ .

输出格式

For each test case, output one number on a separate line — the maximum value of the function on a given segment for a given $ a $ .

输入输出样例

输入样例 #1

5
1 4 3
5 8 4
6 10 6
1 1000000000 1000000000
10 12 8

输出样例 #1

2
4
5
999999999
5

说明

In the first sample: - $ f_3(1) = \left\lfloor\frac{1}{3}\right\rfloor + 1 \bmod 3 = 0 + 1 = 1 $ , - $ f_3(2) = \left\lfloor\frac{2}{3}\right\rfloor + 2 \bmod 3 = 0 + 2 = 2 $ , - $ f_3(3) = \left\lfloor\frac{3}{3}\right\rfloor + 3 \bmod 3 = 1 + 0 = 1 $ , - $ f_3(4) = \left\lfloor\frac{4}{3}\right\rfloor + 4 \bmod 3 = 1 + 1 = 2 $ As an answer, obviously, $ f_3(2) $ and $ f_3(4) $ are suitable.

题意翻译

定义函数 $f_a(x)=\lfloor\frac{x}{a}\rfloor+x\bmod a$，其中 $a$ 为系数。 给定系数 $a$，给定 $x$ 范围 $l\le x\le r$，求 $f_a(x)$ 在范围内值的最大值。 其中 $1\le l\le r\le 10^9$，$1\le a\le 10^9$。