3455. Huge Numbers (Small)

Professor Shekhu has another problem for Akki today. He has given him three positive integers $A$, $N$ and $P$ and wants him to calculate the remainder when $A^{N!}$ is divided by $P$. As usual, $N!$ denotes the product of the first $N$ positive integers.

输入格式

The first line of the input gives the number of test cases, $T$. $T$ lines follow. Each line contains three integers $A$, $N$ and $P$, as described above.

• Limits: $1 \le T \le 100$.
• Small dataset: $1 \le A \le 10, 1 \le N \le 10, 1 \le P \le 10$.
• Large dataset: $1 \le A \le 10^5, 1 \le N \le 10^5, 1 \le P \le 10^5$.

输出格式

For each test case, output one line containing Case #x: y, where $x$ is the test case number (starting from 1) and $y$ is the answer.

样例

Input
2
2 1 2
3 3 2

Output
Case #1: 0
Case #2: 1


提示

In Sample Case #1, the answer is the remainder when $2^{1!} = 2$ is divided by 2, which is 0.

In Sample Case #2, the answer is the remainder when $3^{3!} = 36 = 729$ is divided by 2, which is 1.

68 人解决，91 人已尝试。

113 份提交通过，共有 402 份提交。

4.0 EMB 奖励。