题目描述

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.

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.

2
2 1 2
3 3 2

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 $3^{3!} = 3^6 = 729$ is divided by $2$, which is $1$.

Limits

$1 \le T \le 100$.

Small dataset (Test set 1 - Visible)

$1 \le A \le 10$.

$1 \le N \le 10$.

$1 \le P \le 10$.

Large dataset (Test set 2 - Hidden)

$1 \le A \le 10^5$.

$1 \le N \le 10^5$.

$1 \le P \le 10^5$.