Polycarp's workday lasts exactly n minutes. He loves chocolate bars and can eat one bar in one minute. Today Polycarp has k bars at the beginning of the workday.
In some minutes of the workday Polycarp has important things to do and in such minutes he is not able to eat a chocolate bar. In other minutes he can either eat or not eat one chocolate bar. It is guaranteed, that in the first and in the last minutes of the workday Polycarp has no important things to do and he will always eat bars in this minutes to gladden himself at the begining and at the end of the workday. Also it is guaranteed, that k is strictly greater than 1.
Your task is to determine such an order of eating chocolate bars that the maximum break time between eating bars is as minimum as possible.
Consider that Polycarp eats a bar in the minute x and the next bar in the minute y (x<y). Then the break time is equal to y-x-1 minutes. It is not necessary for Polycarp to eat all bars he has.
Output
Print the minimum possible break in minutes between eating chocolate bars.
Note
In the first example Polycarp can not eat the chocolate bar in the second minute, so the time of the break equals to one minute.
In the second example Polycarp will eat bars in the minutes
1 and
8 anyway, also he needs to eat the chocolate bar in the minute
5, so that the time of the maximum break will be equal to
3 minutes.