AtCoder Grand Contest 018
翻译中…
Problem Statement
翻译中…
There is a box containing $N$ balls. The $i$-th ball has the integer $A_i$ written on it. Snuke can perform the following operation any number of times:
翻译中…
- Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
翻译中…
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer $K$ is written.
翻译中…
Constraints
翻译中…
$1 \leq N \leq 10^5$$1 \leq A_i \leq 10^9$$1 \leq K \leq 10^9$- All input values are integers.
翻译中…
Input
翻译中…
Input is given from Standard Input in the following format:
翻译中…
N K
A_1 A_2 ... A_N翻译中…
Output
翻译中…
If it is possible for Snuke to reach the state where the box contains a ball on which the integer $K$ is written, print POSSIBLE; if it is not possible, print IMPOSSIBLE.
翻译中…
样例
Input #1
3 7
9 3 4
Output #1
POSSIBLE
First, take out the two balls $9$ and $4$, and return them back along with a new ball, $abs(9-4)=5$. Next, take out $3$ and $5$, and return them back along with $abs(3-5)=2$. Finally, take out $9$ and $2$, and return them back along with $abs(9-2)=7$. Now we have $7$ in the box, and the answer is therefore `POSSIBLE`.
Input #2
3 5
6 9 3
Output #2
IMPOSSIBLE
No matter what we do, it is not possible to have $5$ in the box. The answer is therefore `IMPOSSIBLE`.
Input #3
4 11
11 3 7 15
Output #3
POSSIBLE
The box already contains $11$ before we do anything. The answer is therefore `POSSIBLE`.
Input #4
5 12
10 2 8 6 4
Output #4
IMPOSSIBLE
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。