import std.stdio;
import std.string;
import std.format;
import std.conv;
import std.typecons;
import std.algorithm;
import std.functional;
import std.bigint;
import std.numeric;
import std.array;
import std.math;
import std.range;
import std.container;
import std.concurrency;
import std.traits;
import std.uni;
import std.regex;
import core.bitop : popcnt;
alias Generator = std.concurrency.Generator;

enum long INF = long.max/5;

void main() {
  long K, N;
  scanln(K, N);
  long[] as = readln.split.to!(long[]);
  long[] bs = new long[N];
  foreach(i; 0..N-1) {
    bs[i] = (as[i+1] - as[i] + K)%K;
  }
  bs[N-1] = as[0] + (K - as[N-1]);
  long s = bs[0..N-1].sum;
  long ans = s;
  foreach(i; 0..N-1) {
    s = s - bs[i] + bs[(N-1+i)%$];
    ans.ch!min(s);
  }
  ans.writeln;
}

// ----------------------------------------------


void times(alias fun)(long n) {
  // n.iota.each!(i => fun());
  foreach(i; 0..n) fun();
}
auto rep(alias fun, T = typeof(fun()))(long n) {
  // return n.iota.map!(i => fun()).array;
  T[] res = new T[n];
  foreach(ref e; res) e = fun();
  return res;
}

T ceil(T)(T x, T y) if (isIntegral!T || is(T == BigInt)) {
  // `(x+y-1)/y` will only work for positive numbers ...
  T t = x / y;
  if (y > 0 && t * y < x) t++;
  if (y < 0 && t * y > x) t++;
  return t;
}

T floor(T)(T x, T y) if (isIntegral!T || is(T == BigInt)) {
  T t = x / y;
  if (y > 0 && t * y > x) t--;
  if (y < 0 && t * y < x) t--;
  return t;
}

ref T ch(alias fun, T, S...)(ref T lhs, S rhs) {
  return lhs = fun(lhs, rhs);
}
unittest {
  long x = 1000;
  x.ch!min(2000);
  assert(x == 1000);
  x.ch!min(3, 2, 1);
  assert(x == 1);
  x.ch!max(100).ch!min(1000); // clamp
  assert(x == 100);
  x.ch!max(0).ch!min(10); // clamp
  assert(x == 10);
}

mixin template Constructor() {
  import std.traits : FieldNameTuple;
  this(Args...)(Args args) {
    // static foreach(i, v; args) {
    foreach(i, v; args) {
      mixin("this." ~ FieldNameTuple!(typeof(this))[i]) = v;
    }
  }
}

void scanln(Args...)(auto ref Args args) {
  enum sep = " ";
  enum n = Args.length;
  enum fmt = n.rep!(()=>"%s").join(sep);

  string line = readln.chomp;
  static if (__VERSION__ >= 2074) {
    line.formattedRead!fmt(args);
  } else {
    enum argsTemp = n.iota.map!(
      i => "&args[%d]".format(i)
    ).join(", ");
    mixin(
      "line.formattedRead(fmt, " ~ argsTemp ~ ");"
    );
  }
}

// fold was added in D 2.071.0
static if (__VERSION__ < 2071) {
  template fold(fun...) if (fun.length >= 1) {
    auto fold(R, S...)(R r, S seed) {
      static if (S.length < 2) {
        return reduce!fun(seed, r);
      } else {
        return reduce!fun(tuple(seed), r);
      }
    }
  }
}

// popcnt with ulongs was added in D 2.071.0
static if (__VERSION__ < 2071) {
  ulong popcnt(ulong x) {
    x = (x & 0x5555555555555555L) + (x>> 1 & 0x5555555555555555L);
    x = (x & 0x3333333333333333L) + (x>> 2 & 0x3333333333333333L);
    x = (x & 0x0f0f0f0f0f0f0f0fL) + (x>> 4 & 0x0f0f0f0f0f0f0f0fL);
    x = (x & 0x00ff00ff00ff00ffL) + (x>> 8 & 0x00ff00ff00ff00ffL);
    x = (x & 0x0000ffff0000ffffL) + (x>>16 & 0x0000ffff0000ffffL);
    x = (x & 0x00000000ffffffffL) + (x>>32 & 0x00000000ffffffffL);
    return x;
  }
}


Measured memory_bytes: 11732