Bananas#1408

Bananas

1 second
64 megabytes
Hard

Recently, the company "LLC Sherkhan Tabaki" won a tender to supply bananas to schools for talented Bandar-logs. According to the tender conditions and the ministry program "Equal Access to Quality Nutrition," each Bandar-log in a school must receive the same number of bananas. Unfortunately, the company management does not yet know which school will be selected this summer, so they decided to ship bananas in boxes containing bananas each, while minimizing the total number of bananas shipped.

After extensive calculations, recalculations, and meetings, it was determined that one of the boxes might be shipped to the Jungle not fully packed. The only remaining question is how many bananas should be placed in this last box.

Input

The first line contains the number of Bandar-log schools (1 \leq n \leq 10000) and the number of bananas that fit in one box. The second line contains integers—the number of Bandar-logs in each school. All numbers in the second line do not exceed 10^9.

Output

Output the number of bananas in the last box.

Examples

Example 1

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