Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.

Snuke can perform the following two actions:

* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.

* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.




Find the minimum time that Snuke needs to have slimes in all N colors.

Constraints

* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9

Input

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


N x
a_1 a_2 ... a_N


Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
#define debug_interval ','
#define dump_interval ' '
#define debug_toggle 1
//{
#include<bits/stdc++.h>
using namespace std;
#define hi cerr<<"hi"<<endl;
#define int long long
#define INT_MAX LLONG_MAX
#define rep(i,n) for(int i=0;i<(n);i++)
#define rep1(i,n) for(int i=1;i<=(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define fi first
#define se second
#define mp make_pair
#define rev reverse
#define dans dump(ans)
#define MOD 1000000007
#define amp(v,n) (v).count(n)?v[n]++:v[n]=1
#define sysp system("pause")
#define PI acos(-1)
#define pf push_front
#define ins insert

//{
inline int toInt(string s){int v;istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x){ostringstream sout;sout<<x;return sout.str();}
template<class...A> inline void dump(){cout<<endl;}
template<class...A> inline void dump_rest() {cout<<endl;}
template<class T, class...A> inline void dump_rest(const T& first, const A&... rest){cout<<dump_interval<<first;dump_rest(rest...);}
template<class T,class...A> inline void dump(const T&first,const A&...rest){cout<<first;dump_rest(rest...);}
template<class...A> inline void debug(){cerr<<endl;}
template<class...A> inline void debug_rest() {cerr<<endl;}
template<class T, class...A> inline void debug_rest(const T& first, const A&... rest){cerr<<debug_interval<<first;debug_rest(rest...);}
template<class T,class...A> inline void debug(const T&first,const A&...rest){if(debug_toggle)cerr<<first,debug_rest(rest...);}
unsigned XorShift(void){static unsigned x = 123456789;static unsigned y = 362436069;static unsigned z = 521288629;static unsigned w = 88675123;unsigned t;t = x ^ (x << 11);x = y; y = z; z = w;return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));}
//}

typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;

template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}
template<int m>class mint{private:int i;public:mint() : i(0){}mint(int i): i((i%m+m)%m){}mint operator+(const mint& o){return o.i+i;}mint operator*(const mint& o){return o.i*i;}mint operator-(){return -i;}operator int() {return i;}};

//}

main(){
	int n,m;cin>>n>>m;int a[n];rep(i,n)cin>>a[i];
	sort(a,a+n);
	int cc=m+a[0],ans=0;
	rep(i,n)ans+=min(cc,a[i]);
	dans;
}


