Printer#7828

Printer

1 second
64 megabytes
Medium

Marichka has printers and needs to print reports as quickly as possible. Each printer takes a specific time A_i to print one report. Your task is to determine the minimum time required for Marichka to print all the reports. All printers can operate simultaneously and in any sequence, and only the printing time is relevant.

Input

The first line contains two integers and (1 \le N \le 10^5;\ 1 \le X \le 10^9).The following lines each contain one integer A_i (1 \le A_i \le 10^6).

Output

Output a single integer — the minimum time needed to print all the reports.

Examples

Example 1

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Note

In the first test case, within units of time, you can print report using the first printer, reports using the second printer, and reports using the third printer.