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
#include <bits/stdc++.h>
using namespace std;

# define REP(i,n) for (int i=0;i<(n);++i)
# define rep(i,a,b) for(int i=a;i<(b);++i)
# define p(s) std::cout << s ;
# define pl(s)  std::cout << s << endl;
# define printIf(j,s1,s2) cout << (j ? s1 : s2) << endl;
# define YES(j) cout << (j ? "YES" : "NO") << endl;
# define Yes(j) std::cout << (j ? "Yes" : "No") << endl;
# define yes(j) std::cout << (j ? "yes" : "no") << endl;
# define all(v) v.begin(),v.end()
# define showVector(v) REP(i,v.size()){p(v[i]);p(" ")} pl("")
template<class T> inline bool chmin(T &a, T b){ if(a > b) { a = b; return true;} return false;}
template<class T> inline bool chmax(T &a, T b){ if(a < b) { a = b; return true;} return false;}
typedef long long int ll;
typedef pair<ll,ll> P_ii;
typedef pair<double,double> P_dd;

template<class T>
vector<T> make_vec(size_t a){
    return vector<T>(a);
}

template<class T, class... Ts>
auto make_vec(size_t a, Ts... ts){
  return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}

template<typename T,typename V>
typename enable_if<is_class<T>::value==0>::type
fill_v(T &t,const V &v){t=v;}

template<typename T,typename V>
typename enable_if<is_class<T>::value!=0>::type
fill_v(T &t,const V &v){
  for(auto &e:t) fill_v(e,v);
}


const int MOD = 1000000007;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;

void addM(long long &a, long long b) {
    a += b;
    if (a >= MOD) a -= MOD;
}

void mulM(long long &a, long long b) {
    a = ((a%MOD)*(b%MOD))%MOD ;
}

// テーブルを作る前処理
const int MAX = 510000;
long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}

// 二項係数計算
long long COM(ll n, ll k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

int main() {
    ll N,x;
    cin >> N >> x;

    vector<int> a(N);

    REP(i,N) cin >> a[i];

    auto minset = make_vec<int>(N,N);
    fill_v(minset,1e9+7);

    for(int i=N-1;i>=0;i--) for(int j=0;j<N;j++) {
        int k = i - j;
        if(k<0) k += N;

        int pre_k = k + 1;
        if(pre_k==N) pre_k = 0;

        minset[i][j] = min(minset[i][pre_k],a[k]);
    }

    ll ans = 1LL << 50;
    REP(k,N) {
        ll ans_tmp = k*x;
        REP(i,N) ans_tmp += minset[i][k];
        chmin(ans,ans_tmp);
    }

    pl(ans)

    return 0;
}
