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حد الوقت: 3 s حد الذاكرة: 1024 MB مجموع النقاط: 100

#3004. 这是一个模,模,模,模世界

الإحصائيات

给定多个包含三个整数 $p$、$q$ 和 $n$ 的问题。求 $\sum^n_{i=1}[(pi) \bmod q]$ 的值。即求 $p$ 的前 $n$ 个倍数对 $q$ 取模后的总和。注意,总和进行取模运算。

输入格式

输入的第一行包含一个整数 $W$ ($1 \leq W \leq 10^5$),表示需要解决的测试用例数量。

接下来的 $W$ 行,每行包含三个空格分隔的整数 $p$、$q$ 和 $n$ ($1\leq p, q, n \leq 10^6$),即上述问题的参数。

输出格式

输出 $W$ 行,每行对应一个问题的答案,顺序与输入顺序一致。

样例

样例输入

3
2 7 2
1 4 5
3 8 10

样例输出

6
7
37

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