import sys, re

from collections import deque, defaultdict, Counter

from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians

from itertools import accumulate, permutations, combinations, product, groupby

from operator import itemgetter, mul

from copy import deepcopy

from string import ascii_lowercase, ascii_uppercase, digits

from bisect import bisect, bisect_left

from fractions import gcd

from heapq import heappush, heappop

from functools import reduce

def input(): return sys.stdin.readline().strip()

def INT(): return int(eval(input()))

def MAP(): return list(map(int, input().split()))

def LIST(): return list(map(int, input().split()))

def ZIP(n): return list(zip(*(MAP() for _ in range(n))))

sys.setrecursionlimit(10 ** 9)

INF = float('inf')

mod = 10 ** 9 + 7

import numpy as np



K, N = MAP()

A = LIST()

A.append(A[0]+K)



B = np.zeros(N)

for i in range(N):

  		B[i] = A[i+1] - A[i]



print((int(K - max(B))))
import sys, re

from collections import deque, defaultdict, Counter

from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians

from itertools import accumulate, permutations, combinations, product, groupby

from operator import itemgetter, mul

from copy import deepcopy

from string import ascii_lowercase, ascii_uppercase, digits

from bisect import bisect, bisect_left

from fractions import gcd

from heapq import heappush, heappop

from functools import reduce

def input(): return sys.stdin.readline().strip()

def INT(): return int(eval(input()))

def MAP(): return list(map(int, input().split()))

def LIST(): return list(map(int, input().split()))

def ZIP(n): return list(zip(*(MAP() for _ in range(n))))

sys.setrecursionlimit(10 ** 9)

INF = float('inf')

mod = 10 ** 9 + 7



K, N = MAP()

A = LIST()

diff = abs(K - A[-1] + A[0])

d = abs(K - A[-1] + A[0])

if N == 2:

  print((min(d, A[1] - A[0])))

  exit()

for i in range(1, N):

  d += abs(A[i] - A[i-1])

  diff = max(diff, abs(A[i] - A[i-1]))

print((d - diff))
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import accumulate, permutations, combinations, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from fractions import gcd
from heapq import heappush, heappop
from functools import reduce


def input():
    return sys.stdin.readline().strip()


def INT():
    return int(eval(input()))


def MAP():
    return list(map(int, input().split()))


def LIST():
    return list(map(int, input().split()))


def ZIP(n):
    return list(zip(*(MAP() for _ in range(n))))


sys.setrecursionlimit(10**9)
INF = float("inf")
mod = 10**9 + 7
import numpy as np

K, N = MAP()
A = LIST()
A.append(A[0] + K)
B = np.zeros(N)
for i in range(N):
    B[i] = A[i + 1] - A[i]
print((int(K - max(B))))

import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import accumulate, permutations, combinations, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from fractions import gcd
from heapq import heappush, heappop
from functools import reduce


def input():
    return sys.stdin.readline().strip()


def INT():
    return int(eval(input()))


def MAP():
    return list(map(int, input().split()))


def LIST():
    return list(map(int, input().split()))


def ZIP(n):
    return list(zip(*(MAP() for _ in range(n))))


sys.setrecursionlimit(10**9)
INF = float("inf")
mod = 10**9 + 7
K, N = MAP()
A = LIST()
diff = abs(K - A[-1] + A[0])
d = abs(K - A[-1] + A[0])
if N == 2:
    print((min(d, A[1] - A[0])))
    exit()
for i in range(1, N):
    d += abs(A[i] - A[i - 1])
    diff = max(diff, abs(A[i] - A[i - 1]))
print((d - diff))

-import numpy as np - -A.append(A[0] + K) -B = np.zeros(N) -for i in range(N): -    B[i] = A[i + 1] - A[i] -print((int(K - max(B)))) +diff = abs(K - A[-1] + A[0]) +d = abs(K - A[-1] + A[0]) +if N == 2: +    print((min(d, A[1] - A[0]))) +    exit() +for i in range(1, N): +    d += abs(A[i] - A[i - 1]) +    diff = max(diff, abs(A[i] - A[i - 1])) +print((d - diff))