Problem:
Score : 300 points

Problem Statement

There is a circular pond with a perimeter of K meters, and N houses around them.

The i-th house is built at a distance of A_i meters from the northmost point of the pond, measured clockwise around the pond.

When traveling between these houses, you can only go around the pond.

Find the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Constraints

2 \leq K \leq 10^6

2 \leq N \leq 2 \times 10^5

0 \leq A_1 < ... < A_N < K

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K N
A_1 A_2 ... A_N

Output

Print the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Sample Input 1

20 3
5 10 15

Sample Output 1

10

If you start at the 1-st house and go to the 2-nd and 3-rd houses in this order, the total distance traveled will be 10.

Sample Input 2

20 3
0 5 15

Sample Output 2

10

If you start at the 2-nd house and go to the 1-st and 3-rd houses in this order, the total distance traveled will be 10.

Solution in Ruby (2.3.3) (judge verdict: Accepted)

# Wrote in Mar 28, 2020 21:13 by reetok
require 'time'
require 'prime'
require 'bigdecimal'
def inp(type=:to_i,spst=" ")
  return eval("gets.chomp.split(#{spst}).map(&:#{type})")
end
def inpf() return self.inp(:to_f," ") end
def inps() return self.inp(:to_s," ") end
def r_up(a, b) (a/b).ceil end
def r_down(a, b) (a/b).floor end
def sum(a) a.inject(:+) end
def big(a,b) return (a>b)? a:b end
def small(a,b) return (a<b)? a:b end
def minp(n,datatype=".to_i")
  t = []
  n.times do
    t.push(eval("gets.chomp#{datatype}"))
  end
  return t
end
def yes() puts "Yes" end
def no() puts "No" end
def ynju(bool,yes="Yes",no="No") puts (bool ? yes : no) end
class Integer
  def divisor_list
    devisors = [1]
    2.upto(self/2) do |i|
      devisors << i if self%i == 0
    end
    devisors << self
    return devisors.uniq.sort
  end
end
class Array
  def upper(a) #aより上
    self.sort.select{|n|n>=a}
  end
  def downer(a) #aより下
    self.sort.select{|n|n<=a}
  end
end
#---------------

k,m = inp
a = inp

sences = []

a.size.times do |n|
  if n==0
    sences.push(k-a[a.size-1]+a[0])
  else
    sences.push(a[n]-a[n-1])
  end
end

puts k-sences.max