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 <iostream>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <algorithm>
#include <cassert>
#include <bitset>
#include <fstream>
#include <cstring>
#include <stack>

using namespace std;

#define fst first
#define snd second
#define pb push_back
#define mp make_pair
#define ll long long
#define ull unsigned long long
#define ld long double

const ld pi = acos(-1);

template<typename T>
T abs(T x) {
    return x > 0 ? x : -x;
}

template<typename T>
T sqr(T x) {
    return x * x;
}

template<typename T>
ostream& operator << (ostream &s, const vector<T> &x) {
    s << "[";
    for (auto it : x) {
        s << it << ", ";
    }
    s << "]";
    return s;
}

template<typename T>
ostream& operator << (ostream &s, const set<T> &x) {
    s << "{";
    for (auto it : x) {
        s << it << ", ";
    }
    s << "}";
    return s;
}


template<typename U, typename V>
ostream& operator << (ostream &s, const pair<U, V> &x) {
    s << "(" << x.fst << ", " << x.snd << ")";
    return s;
}

template<typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

template<typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}

//---------------------------------------------------------------------

const int maxn = 2005;

ll dp[maxn][maxn];

int main() {
    srand(time(NULL));
    retry:
#ifdef LOCAL
    freopen("a.in", "r", stdin);
    //freopen("a.out", "w", stdout);
#else
    //freopen("sum.in", "r", stdin);
	//freopen("sum.out", "w", stdout);
#endif

    int n;
    ll x;
    cin >> n >> x;

    vector<ll> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }

    for (int i = 0; i < maxn; i++) {
        for (int j = 0; j < maxn; j++) {
            dp[i][j] = 1e18;
        }
    }

    for (int i = 0; i < n; i++) {
        dp[i][0] = a[i];
        for (int j = 1; j < n; j++) {
            chmin(dp[i][j], min(dp[i][j - 1], a[(i - j + n) % n]));
        }
    }

    ll ans = 1e18;
    for (int i = 0; i <= n; i++) {
        ll curr = i * x;
        for (int j = 0; j < n; j++) {
            curr += dp[j][i];
        }
        chmin(ans, curr);
    }
    cout << ans << endl;

    return 0;
}
