codeforces#P2205B. Simons and Cakes for Success
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ID: 42016
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Simons and Cakes for Success
Problem Description
Simons has $n$ friends and a huge amount of cakes. To divide the cakes fairly, you are asked to help him solve the following problem:
- Find the minimum positive integer $k$ such that $n$ is a divisor of $k^n$.
It can be proved that the answer always exists under the given constraints.
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). The description of the test cases follows.
The only line of each test case contains a single integer $n$ ($2\le n\le 10^9$) — the number of friends Simons has.
For each test case, output a single integer — the minimum $k$ you found.
Input Format
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). The description of the test cases follows.
The only line of each test case contains a single integer $n$ ($2\le n\le 10^9$) — the number of friends Simons has.
Output Format
For each test case, output a single integer — the minimum $k$ you found.
4
8
12
369
55635800
,
2
6
123
2090
Hint
In the first test case:
- $1^8=1$, and $8$ is not a divisor of $1$;
- $2^8=256$, and $8$ is a divisor of $256$, because $256 = 8\cdot 32$.
Thus, the minimum possible $k$ is $2$.
In the second test case, $12$ is a divisor of $6^{12}=2\,176\,782\,336$, because $2\,176\,782\,336=12\cdot 181\,398\,528$.