In M Country, there are cities and these cities are placed in one line, where the cities are labeled one by one. Citizens in M Country all use MI-phones, and there are totally m network modes among the MI-phones. For better management, MI-phones in i-th city can only use -th mode.

As a MI fan, you want to experience all kind of network modes. So for each , you want to find a shortest subinterval in M Country that all network modes from to are used at least once among the cities whose labels are in interval , and we denote as the length of the shortest subinterval. In this problem, you need to determine .

The first line contains two integers .

The second line contains  integers .

It's guaranteed that for each integer  between  and , it appears in sequence  at least once.

Only one line containing  integers .

5 3
1 3 2 3 1

1 3 3

For ,  contains all network modes from  to .

For ,  contains all network modes from  to .

For ,  contains all network modes from  to .