import java.io.BufferedReader
import java.io.InputStreamReader
import java.io.PrintWriter
import java.util.*

fun main(args: Array<String>) = test2()

fun test2() = FastIO().exec {
    val (k, n) = readLine()!!.split(' ').map { it.toInt() }
    val aList = readLine()!!.split(' ').map { it.toLong() }

    val diff = LongArray(n)
    diff[0] = k - aList.last() + aList.first()

    for (i in 0 until n - 1) {
        diff[i + 1] = aList[i + 1] - aList[i]
    }

    val answer = diff.sum() - diff.max()!!

    println(answer)
}

// region

@Suppress("unused")
class FastIO {
    private val br = BufferedReader(InputStreamReader(System.`in`))
    private var st = StringTokenizer("")
    val pw = PrintWriter(System.out)

    fun string(): String {
        if (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())
        return st.nextToken()
    }

    fun int() = Integer.parseInt(string())
    fun long() = java.lang.Long.parseLong(string())
    fun double() = java.lang.Double.parseDouble(string())
    fun nextLine() = br.readLine()!!
    fun println() = pw.println()
    fun <T> print(o: T) = pw.print(o)
    fun <T> println(o: T) = pw.println(o)

    inline fun exec(code: FastIO.() -> Unit) {
        code()
        pw.flush()
    }
}
// endregion
