Description

The train stations in Upper Bytown and Lower Bytown are connected with a single track rail link. It takes the train minutes to travel between them in either direction. However, the trains departing a station have to be spaced at least one minute apart. Moreover, at all times, all the trains on the rail link have to go in the same direction.

According to the timetable at our disposal, cargo trains destined for Lower Bytown are to pass through the Upper Bytown. They are to be loaded with goods in Lower Bytown and then return to Upper Bytown. For simplicity, we assume that loading the goods on the train takes virtually no time.

We are to determine the minimum possible time of the last train returning to Upper Bytown.

Upper Bytown和Lower Bytown的火车站被一条铁路连接着。火车从一侧到另一侧需要S分钟。然而，每两列车发车时间至少需要间隔一分钟。并且，在每一个时刻，在铁路上的所有列车的行驶方向都必须相同。

按照时间表的顺序，N辆列车将从Upper Bytown出发前往Lower Bytown，到达后又需要回到Upper Bytown。

请计算最迟回到Upper Bytown的列车回到Upper Bytown的时刻的最小值。

Format

Input

The first line of the standard input contains two integers N,S(1<=N<=1 000 000,1<=S<=10^9) , separated by a single space, that specify the number of trains and the one-way travel time respectively. The second line contains integers T1,T2…Tn(0<=T1<=T2..<=Tn<=10^9) , separated by a single space, that specify the arrival times of successive trains at the Upper Bytown station.

Output

Your program should print out a single line with a single integer to the standard output: the minimum possible time of the last train returning to Upper Bytown.

Samples

3 4
1 8 11

20

Limitation