Problem:
Score : 200 points

Problem Statement

There are K pieces of cakes.
Mr. Takahashi would like to eat one cake per day, taking K days to eat them all.

There are T types of cake, and the number of the cakes of type i (1 ≤ i ≤ T) is a_i.

Eating the same type of cake two days in a row would be no fun,
so Mr. Takahashi would like to decide the order for eating cakes that minimizes the number of days on which he has to eat the same type of cake as the day before.

Compute the minimum number of days on which the same type of cake as the previous day will be eaten.

Constraints

1 ≤ K ≤ 10000

1 ≤ T ≤ 100

1 ≤ a_i ≤ 100

a_1 + a_2 + ... + a_T = K

Input

The input is given from Standard Input in the following format:

K T
a_1 a_2 ... a_T

Output

Print the minimum number of days on which the same type of cake as the previous day will be eaten.

Sample Input 1

7 3
3 2 2

Sample Output 1

0

For example, if Mr. Takahashi eats cakes in the order of 2, 1, 2, 3, 1, 3, 1, he can avoid eating the same type of cake as the previous day.

Sample Input 2

6 3
1 4 1

Sample Output 2

1

There are 6 cakes.
For example, if Mr. Takahashi eats cakes in the order of 2, 3, 2, 2, 1, 2, he has to eat the same type of cake (i.e., type 2) as the previous day only on the fourth day.
Since this is the minimum number, the answer is 1.

Sample Input 3

100 1
100

Sample Output 3

99

Since Mr. Takahashi has only one type of cake, he has no choice but to eat the same type of cake as the previous day from the second day and after.

Solution in Go (1.6) (judge verdict: Wrong Answer)

// ProblemURL : https://atcoder.jp/contests/code-festival-2016-qualc/tasks/codefestival_2016_qualC_b
// ---------------------------------------------
package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
	"strings"
)

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}
func diff(a, b int) int {
	if a > b {
		return a - b
	}
	return b - a
}
func larger(a, b int) int {
	if a > b {
		return a
	}
	return b
}
func smaller(a, b int) int {
	if a < b {
		return a
	}
	return b
}
func largest(a, b, c int) (lgst int) {
	if a > b {
		lgst = a
	} else {
		lgst = b
	}
	if c > lgst {
		lgst = c
	}
	return
}
func smallest(a, b, c int) (slst int) {
	if a < b {
		slst = a
	} else {
		slst = b
	}
	if c < slst {
		slst = c
	}
	return
}
func intsMax(a []int) (val int) {
	if len(a) == 0 {
		panic("func intsMax: argument slice length must not be zero")
	}
	val = a[0]
	for _, aa := range a {
		if aa > val {
			val = aa
		}
	}
	return
}
func intsMaxIdx(a []int) (idx, val int) {
	if len(a) == 0 {
		panic("func intsMaxIdx: argument slice length must not be zero")
	}
	val = a[0]
	for i, aa := range a {
		if aa > val {
			idx, val = i, aa
		}
	}
	return
}
func intsMin(a []int) (val int) {
	if len(a) == 0 {
		panic("func intsMin: argument slice length must not be zero")
	}
	val = a[0]
	for _, aa := range a {
		if aa < val {
			val = aa
		}
	}
	return
}
func intsMinIdx(a []int) (idx, val int) {
	if len(a) == 0 {
		panic("func intsMinIdx: argument slice length must not be zero")
	}
	val = a[0]
	for i, aa := range a {
		if aa < val {
			idx, val = i, aa
		}
	}
	return
}
func intsSum(a []int) int {
	res := 0
	for _, v := range a {
		res += v
	}
	return res
}
func intsAve(s []int) float64 {
	return float64(intsSum(s)) / float64(len(s))
}
func intsAdd(a *[]int, x int)    { *a = append(*a, x) }
func intsDelete(a *[]int, i int) { *a = append((*a)[:i], (*a)[i+1:]...) }
func intsJoin(a, b []int) []int  { return append(a, b...) }
func intsClear(a []int) []int    { return a[:0] }
func intsCopy(a []int) []int     { return append([]int(nil), a...) }
func intsCopySortAsc(a []int) []int {
	s := intsCopy(a)
	sort.Ints(s)
	return s
}
func intsCopySortDesc(a []int) []int {
	s := intsCopy(a)
	sort.Sort(sort.Reverse(sort.IntSlice(s)))
	return s
}
func intsReverse(a []int) {
	for i, j := 0, len(a)-1; i < j; i, j = i+1, j-1 {
		a[i], a[j] = a[j], a[i]
	}
}
func intsFill(a []int, val int) {
	for i := 0; i < len(a); i++ {
		a[i] = val
	}
}
func intsPeekBack(a []int) int {
	if len(a) == 0 {
		panic("func peekBack: zero length slice")
	}
	return a[len(a)-1]
}
func intsPeekFront(a []int) int {
	if len(a) == 0 {
		panic("func peekFront: zero length slice")
	}
	return a[0]
}
func intsPopBack(a *[]int) int {
	if len(*a) == 0 {
		panic("func popBack: zero length slice")
	}
	t := (*a)[len(*a)-1]
	*a = (*a)[:len(*a)-1]
	return t
}
func intsPopFront(a *[]int) int {
	if len(*a) == 0 {
		panic("func popFront: zero length slice")
	}
	h := (*a)[0]
	*a = (*a)[1:]
	return h
}
func intsPushBack(a *[]int, x int) { *a = append(*a, x) }
func intsPushFront(a *[]int, x int) {
	*a = append(*a, 0)
	copy((*a)[1:], (*a)[0:])
	(*a)[0] = x
}
func intsAppendSentinelHead(a *[]int, sentinel int) { intsPushFront(a, sentinel) }
func intsAppendSentinelTail(a *[]int, sentinel int) { intsPushBack(a, sentinel) }
func intsAppendSentinel(a *[]int, sentinel int) {
	intsPushFront(a, sentinel)
	intsPushBack(a, sentinel)
}
func isEven(n int) bool    { return n&1 == 0 }
func isOdd(n int) bool     { return n&1 == 1 }
func floor(x float64) int  { return int(x) }
func ceil(x float64) int   { return int(math.Ceil(x)) }
func ceilDiv(x, y int) int { return (x + y - 1) / y }
func pow(x, y int) int {
	if y < 0 {
		panic("Exponent must be a natural number")
	}
	z := 1
	for i := y; i != 0; i >>= 1 {
		if i&1 == 1 {
			z *= x
		}
		x *= x
	}
	return z
}
func fact(x int) int {
	fact := 1
	for i := 1; i <= x; i++ {
		fact *= i
	}
	return fact
}
func sigmaK(n int) int  { return n * (n + 1) / 2 }
func sigmaKK(n int) int { return (n * (n + 1) / 2) * (2*n + 1) / 3 }
func euclideanDistance(a, b point) float64 {
	s := diff(a.x, b.x)
	s *= s
	t := diff(a.y, b.y)
	t *= t
	return math.Sqrt(float64(s) + float64(t))
}
func manhattanDistance(a, b point) int {
	s := diff(a.x, b.x)
	t := diff(a.y, b.y)
	return s + t
}
func swap(a, b *int) { *a, *b = *b, *a }
func chmax(a *int, b int) {
	if *a < b {
		*a = b
	}
}
func chmin(a *int, b int) {
	if *a > b {
		*a = b
	}
}
func cumSum(a []int) []int {
	b := append([]int{0}, a...)
	for i := 1; i < len(b); i++ {
		b[i] += b[i-1]
	}
	return b
}
func runesReverse(a []rune) {
	for i, j := 0, len(a)-1; i < j; i, j = i+1, j-1 {
		a[i], a[j] = a[j], a[i]
	}
	return
}
func bytesReverse(a []byte) {
	for i, j := 0, len(a)-1; i < j; i, j = i+1, j-1 {
		a[i], a[j] = a[j], a[i]
	}
	return
}
func strUpperCase(s string) string { return strings.ToUpper(s) }
func strLowerCase(s string) string { return strings.ToLower(s) }
func strToInt(s string) int {
	i, err := strconv.Atoi(s)
	if err != nil {
		panic(err)
	}
	return i
}
func intToStr(i int) string     { return strconv.Itoa(i) }
func CalcMod(a, mod int) int    { return (a%mod + mod) % mod }
func ModSum(a *int, b, mod int) { *a = (((*a) % mod) + mod + (b % mod)) % mod }
func ModMul(a *int, b, mod int) { *a = (((*a) % mod) * (b % mod)) % mod }
func ModPow(x, y, mod int) int {
	if y < 0 {
		panic("Exponent must be a natural number")
	}
	z := 1
	for i := y; i != 0; i >>= 1 {
		if i&1 == 1 {
			z = (z * x) % mod
		}
		x = (x * x) % mod
	}
	return z
}
func ModFact(x, mod int) int {
	fact := 1
	for i := 1; i <= x; i++ {
		fact = fact * i % mod
	}
	return fact
}
func ModInv(x, mod int) int { return ModPow(x, mod-2, mod) }
func initMatrixBool(parentSize, childSize int, initialValue bool) *[][]bool {
	res := make([][]bool, parentSize)
	for i := range res {
		res[i] = make([]bool, childSize)
		for j := range res[i] {
			res[i][j] = initialValue
		}
	}
	return &res
}
func initMatrixInt(parentSize, childSize int, initialValue int) *[][]int {
	res := make([][]int, parentSize)
	for i := range res {
		res[i] = make([]int, childSize)
		for j := range res[i] {
			res[i][j] = initialValue
		}
	}
	return &res
}

var (
	sc = bufio.NewScanner(os.Stdin)
	bw = bufio.NewWriterSize(os.Stdout, bwBufSize)
)

func init() {
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 1e7), 1e7)
}
func ru() (n int) {
	sc.Scan()
	if err := sc.Err(); err != nil {
		panic(err)
	}
	for _, v := range sc.Bytes() {
		n = n*10 + int(v-48)
	}
	return
}
func ri() (n int) {
	sc.Scan()
	if err := sc.Err(); err != nil {
		panic(err)
	}
	b := sc.Bytes()
	neg := false
	if b[0] == 45 {
		neg = true
		b = b[1:]
	}
	for _, v := range b {
		n = n*10 + int(v-48)
	}
	if neg {
		n = -n
	}
	return
}
func ri64() (n int64) {
	sc.Scan()
	if err := sc.Err(); err != nil {
		panic(err)
	}
	b := sc.Bytes()
	neg := false
	if b[0] == 45 {
		neg = true
		b = b[1:]
	}
	for _, v := range b {
		n = n*10 + int64(v-48)
	}
	if neg {
		n = -n
	}
	return
}
func rf64() float64 {
	sc.Scan()
	if err := sc.Err(); err != nil {
		panic(err)
	}
	f, err := strconv.ParseFloat(sc.Text(), 64)
	if err != nil {
		panic(err)
	}
	return f
}
func rs() string {
	sc.Scan()
	if err := sc.Err(); err != nil {
		panic(err)
	}
	return sc.Text()
}
func rb() []byte {
	sc.Scan()
	if err := sc.Err(); err != nil {
		panic(err)
	}
	return sc.Bytes()
}
func rr() []rune {
	sc.Scan()
	if err := sc.Err(); err != nil {
		panic(err)
	}
	return []rune(sc.Text())
}
func ris(n int) []int {
	s := make([]int, n)
	for i := range s {
		s[i] = ri()
	}
	return s
}
func risZeroBased(n int) []int {
	s := make([]int, n)
	for i := range s {
		s[i] = ri() - 1
	}
	return s
}
func ri64s(n int) []int64 {
	s := make([]int64, n)
	for i := range s {
		s[i] = ri64()
	}
	return s
}
func rss(n int) []string {
	s := make([]string, n)
	for i := range s {
		s[i] = rs()
	}
	return s
}
func pf(format string, a ...interface{}) {
	if _, err := fmt.Fprintf(bw, format, a...); err != nil {
		panic(err)
	}
}
func pln(a ...interface{}) {
	if _, err := fmt.Fprintln(bw, a...); err != nil {
		panic(err)
	}
}
func pints(a []int) {
	for _, v := range a {
		fmt.Fprintln(bw, v)
	}
}
func pintsol(a []int) {
	s := fmt.Sprint(a)
	if _, err := fmt.Fprintln(bw, s[1:len(s)-1]); err != nil {
		panic(err)
	}
}
func dbg(a ...interface{}) {
	if _, err := fmt.Fprintln(os.Stderr, a...); err != nil {
		panic(err)
	}
}
func dbgMatrix(a [][]int) {
	for i := 0; i < len(a); i++ {
		dbg(a[i])
	}
}
func YESorNO(b bool) string {
	if b {
		return "YES"
	} else {
		return "NO"
	}
}
func YesOrNo(b bool) string {
	if b {
		return "Yes"
	} else {
		return "No"
	}
}
func main() {
	solve()
	bw.Flush()
}

const (
	bwBufSize = 1e6

	alphabetLower = "abcdefghijklmnopqrstuvwxyz"
	alphabetUpper = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"

	// maxInt64  = 9223372036854775807  // 9e18
	// maxInt32  = 2147483647           // 2e9
	// maxUint64 = 18446744073709551615 // 1e19
	inf = 1 << 60
	mod = 1e9 + 7
)

type pair struct{ fi, se int }
type byFiSe []pair

func (p byFiSe) Len() int      { return len(p) }
func (p byFiSe) Swap(i, j int) { p[i], p[j] = p[j], p[i] }
func (p byFiSe) Less(i, j int) bool {
	if p[i].fi == p[j].fi {
		return p[i].se < p[j].se
	}
	return p[i].fi < p[j].fi
}

type point struct{ x, y int }

func solve() {
	k, t := ri(), ri()
	as := ris(t)

	if t == 1 {
		pln(k - 1)
		return
	}

	mn := k / 2
	if isOdd(k) {
		mn++
	}

	ans := 0
	for i := range as {
		if as[i] > mn {
			ans = as[i] - mn
		}
	}
	pln(ans)
}