Gathering the Followers

Interview

Time limit2sMemory limit1024 MB

Summary

Given each follower's visit period d_i and the weekday s of the last joint meeting, find the weekday of the next joint meeting.

Level: Easy3 of 10
Topics: Math, Number theory
Solved: No attempts yet

Statement

Grindelwald wants to gather his followers. However, he cannot do it on just any day. Grindelwald has $n$ followers, numbered from 1 to $n$ . Follower $i$ visits the meeting place every $d_i$ days, based on personal beliefs (that is, the interval between two consecutive visits by follower $i$ is $d_i$ days). Grindelwald remembers that the last time all his followers appeared at the meeting place together, it was on day $s$ of the week. Help him find the number of the day of the week on which all followers will next be at the meeting place together.

Input

The first line contains two integers $n$ and $s$ ( $1 \le n \le 10^5$ , $1 \le s \le 7$ ). The second line contains $n$ integers $d_i$ ( $1 \le d_i \le 20$ ).

Output

Print a single integer from 1 to 7: the number of the day of the week on which all followers will next be at the meeting place together. A week has 7 days, which Grindelwald numbered from 1 to 7 in order.

Examples1

Example 1
Input
```
3 1
2 5 10
```
Expected output
```
4
```