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No.3186 Big Order

レベル : / AI推定難易度 : 1925 / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 25
作問者 : 蜜蜂 / テスター : Mitarushi
お気に入りにしたユーザー ProblemId : 12327 / 自分の提出
問題文最終更新日: 2025-06-21 18:44:00
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yukicoder contest 471 (順位表) の他の問題:

Problem Statement

You are given positive integers $A, B, C$. Find the number of times $A^B$ is divisible by $C$, modulo $998244353$.
Here, it is guaranteed that $C$ is at least $2$.

You are given $T$ test cases; find the answer for each of them.

Input

$T$
$\mathrm{case}_1$
$\mathrm{case}_2$
$\vdots$
$\mathrm{case}_T$
Here, $\mathrm{case}_i$ denotes the $i$-th test case, and each test case is given in the following format.
$A\ \ B\ \ C$

  • $1 \leq T \leq 100$
  • $1 \leq A, B \leq 10^{40}$
  • $2 \leq C \leq 10^{40}$
  • All input values are integers.

Output

For each test case, print the number of times $A^B$ is divisible by $C$, modulo $998244353$, followed by a newline.

Sample

Sample 1
Input
3
2 3 4
1 2 3
2 1000000000 2
Output
1
0
1755647

  • For the $1$-st test case, the number of times $A^B = 8$ is divisible by $4$ is $1$.
  • For the $2$-nd test case, the number of times $A^B = 1$ is divisible by $3$ is $0$.
  • For the $3$-rd test case, note that you must print the remainder when divided by $998244353$.

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