using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
static string InputPattern = "InputX";
static List<string> GetInputList()
{
var WillReturn = new List<string>();
if (InputPattern == "Input1") {
WillReturn.Add("2 10");
WillReturn.Add("1 100");
//12
}
else if (InputPattern == "Input2") {
WillReturn.Add("3 10");
WillReturn.Add("100 1 100");
//23
}
else if (InputPattern == "Input3") {
WillReturn.Add("4 10");
WillReturn.Add("1 2 3 4");
//10
}
else {
string wkStr;
while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
}
return WillReturn;
}
static void Main()
{
List<string> InputList = GetInputList();
long[] wkArr = InputList[0].Split(' ').Select(pX => long.Parse(pX)).ToArray();
long X = wkArr[1];
long[] AArr = InputList[1].Split(' ').Select(pX => long.Parse(pX)).ToArray();
long UB = AArr.GetUpperBound(0);
var InsSegmentTree = new SegmentTree(AArr.Length * 2, long.MaxValue);
for (long I = 0; I <= AArr.GetUpperBound(0); I++) {
InsSegmentTree[I] = AArr[I];
InsSegmentTree[I + UB + 1] = AArr[I];
}
long Answer = long.MaxValue;
// 魔法の使用回数を全探索
for (long I = 0; I <= AArr.Length - 1; I++) {
long CatchCost = 0;
// 開始添字のループ
for (long J = 0; J <= UB; J++) {
long EndInd = J + UB + 1;
long StaInd = EndInd - I;
long RangeMin = InsSegmentTree.Internal_Query(StaInd, EndInd);
CatchCost += RangeMin;
}
long MagicCost = X * I;
long AnswerKouho = CatchCost + MagicCost;
Answer = Math.Min(Answer, AnswerKouho);
}
Console.WriteLine(Answer);
}
}
#region SegmentTree
// SegmentTreeクラス (RMinQ and 1点更新)
internal class SegmentTree
{
private long[] mTreeNodeArr;
private long UB; // 木のノードの配列のUB
private long mLeafCnt; // 葉ノードの数
private long mExternalArrUB;
// ノードの添字を引数とし、範囲の開始添字と終了添字を持つ配列
private struct RangeInfoDef
{
internal long StaInd;
internal long EndInd;
}
private RangeInfoDef[] mRangeInfo;
// ノードのIndexの列挙を返す
internal IEnumerable<long> GetNodeIndEnum()
{
for (long I = 0; I <= mExternalArrUB; I++) {
yield return I;
}
}
// 木のノードのUBを返す
internal long GetUB()
{
return mExternalArrUB;
}
// コンストラクタその1
// 引数1 外部IndのUB
// 引数2 単位元
internal SegmentTree(long pExternalArrUB, long pInitVal)
{
mExternalArrUB = pExternalArrUB;
ConstructorTreeInit();
// すべての値をpInitValに
for (long I = 0; I <= UB; I++) {
mTreeNodeArr[I] = pInitVal;
}
}
// コンストラクタその2
// 引数1 初期化用の配列
// 引数2 単位元
internal SegmentTree(long[] pInitArr, long pInitVal)
{
mExternalArrUB = pInitArr.GetUpperBound(0);
ConstructorTreeInit();
// すべての値をpInitValに
for (long I = 0; I <= UB; I++) {
mTreeNodeArr[I] = pInitVal;
}
for (long I = 0; I <= pInitArr.GetUpperBound(0); I++) {
long TreeNode = DeriveTreeNode(I);
mTreeNodeArr[TreeNode] = pInitArr[I];
}
// 木DPの要領で、葉から根に伝播
ExecTreeDP();
}
// コンストラクタその3
// 引数1 初期化用のList
// 引数2 単位元
internal SegmentTree(List<long> pInitList, long pInitVal)
{
mExternalArrUB = pInitList.Count - 1;
ConstructorTreeInit();
// すべての値をpInitValに
for (long I = 0; I <= UB; I++) {
mTreeNodeArr[I] = pInitVal;
}
for (long I = 0; I <= pInitList.Count - 1; I++) {
long TreeNode = DeriveTreeNode(I);
mTreeNodeArr[TreeNode] = pInitList[(int)I];
}
// 木DPの要領で、葉から根に伝播
ExecTreeDP();
}
// コンストラクタのヘルパメソッド(木の初期化)
private void ConstructorTreeInit()
{
// 簡単のため、葉ノード数を2のべき乗に
long ArrLength = 0;
for (long I = 1; I < long.MaxValue; I *= 2) {
ArrLength += I;
mLeafCnt = I;
if (mExternalArrUB + 1 < mLeafCnt) break;
}
UB = ArrLength - 1;
mTreeNodeArr = new long[UB + 1];
// ノードの添字を引数とし、範囲の開始添字と終了添字を持つ配列の作成
mRangeInfo = new RangeInfoDef[UB + 1];
for (long I = 0; I <= UB; I++) {
if (I == 0) {
RangeInfoDef WillSet1;
WillSet1.StaInd = 0;
WillSet1.EndInd = mLeafCnt - 1;
mRangeInfo[I] = WillSet1;
continue;
}
long ParentNode = DeriveParentNode(I);
RangeInfoDef ParentRangeInfo = mRangeInfo[ParentNode];
RangeInfoDef WillSet2;
long Mid = (ParentRangeInfo.StaInd + ParentRangeInfo.EndInd) / 2;
if (I % 2 == 1) { // 奇数ノードの場合
WillSet2.StaInd = ParentRangeInfo.StaInd;
WillSet2.EndInd = Mid;
}
else { // 偶数ノードの場合
WillSet2.StaInd = Mid + 1;
WillSet2.EndInd = ParentRangeInfo.EndInd;
}
mRangeInfo[I] = WillSet2;
}
}
// 木DPの要領で、葉から根に伝播
private void ExecTreeDP()
{
for (long I = UB; 0 < I; I--) {
long SendNode = DeriveParentNode(I);
mTreeNodeArr[SendNode] = Math.Min(mTreeNodeArr[SendNode], mTreeNodeArr[I]);
}
}
// インデクサ
internal long this[long pInd]
{
get
{
long CurrNode = DeriveTreeNode(pInd);
return mTreeNodeArr[CurrNode];
}
set { Update(pInd, value); }
}
// 親ノードの添字を取得
private long DeriveParentNode(long pTarget)
{
return (pTarget - 1) / 2;
}
// 子ノードの添字(小さいほう)を取得
private long DeriveChildNode(long pTarget)
{
return pTarget * 2 + 1;
}
// 葉ノードの配列の添字を木の添字に変換して返す
private long DeriveTreeNode(long pLeafArrInd)
{
long BaseInd = UB - mLeafCnt + 1;
return BaseInd + pLeafArrInd;
}
// 葉ノードの配列のK番目の値をNewValに変更
internal void Update(long pK, long pNewVal)
{
long CurrNode = DeriveTreeNode(pK);
mTreeNodeArr[CurrNode] = pNewVal;
// 登りながら更新
while (CurrNode > 0) {
CurrNode = DeriveParentNode(CurrNode);
long ChildNode1 = DeriveChildNode(CurrNode);
long ChildNode2 = ChildNode1 + 1;
mTreeNodeArr[CurrNode] =
Math.Min(mTreeNodeArr[ChildNode1], mTreeNodeArr[ChildNode2]);
}
}
// 開始添字と終了添字とカレントノードを引数として、最小値を返す
internal long Internal_Query(long pSearchStaInd, long pSearchEndInd)
{
return Private_Query(pSearchStaInd, pSearchEndInd, 0);
}
private long Private_Query(long pSearchStaInd, long pSearchEndInd, long pCurrNode)
{
long CurrNodeStaInd = mRangeInfo[pCurrNode].StaInd;
long CurrNodeEndInd = mRangeInfo[pCurrNode].EndInd;
// OverLapしてなければ、long.MaxValue
if (CurrNodeEndInd < pSearchStaInd || pSearchEndInd < CurrNodeStaInd)
return long.MaxValue;
// 完全に含んでいれば、このノードの値
if (pSearchStaInd <= CurrNodeStaInd && CurrNodeEndInd <= pSearchEndInd)
return mTreeNodeArr[pCurrNode];
// そうでなければ、2つの子の最小値
long ChildNode1 = DeriveChildNode(pCurrNode);
long ChildNode2 = ChildNode1 + 1;
long ChildVal1 = Private_Query(pSearchStaInd, pSearchEndInd, ChildNode1);
long ChildVal2 = Private_Query(pSearchStaInd, pSearchEndInd, ChildNode2);
return Math.Min(ChildVal1, ChildVal2);
}
internal void DebugPrint()
{
for (long I = 0; I <= UB; I++) {
Console.WriteLine("mTreeNodeArr[{0}] = {1}", I, mTreeNodeArr[I]);
}
}
}
#endregion