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;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vb = vector<bool>;
using vs = vector<string>;
using msi = map<string, int>;
using mii = map<int, int>;
using psi = pair<string, int>;
using pii = pair<int, int>;
using tii = tuple<int, int>;
using vlai = valarray<int>;
#define rep(i,n) for(int i=0;i<n;i++)
#define range(i,s,n) for(int i=s;i<n;i++)
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define fs first
#define sc second
#define INF 1E9
#define LINF 1E18*5
#define EPS 1E-9
#define MOD 1000000007
#define PI 3.1415926535897932384

template<class S, class T>ostream& operator<<(ostream&os, pair<S, T>p) { os << "[" << p.first << ", " << p.second << "]"; return os; };
template<class S>auto&operator<<(ostream&os, vector<S>t) { bool a = 1; for (auto s : t) { os << (a ? "" : " ") << s; a = 0; } return os; }

//int dx[]={1,1,1,0,-1,-1,-1,0},dy[8]={1,0,-1,-1,-1,0,1,1,1};
//
constexpr ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; }

class compare {
public:
	bool operator()(tuple<int, int> a, tuple<int, int> b) {
		return (get<1>(a) < get<1>(b));
	}
};
class rcompare {
public:
	bool operator()(tuple<int, int> a, tuple<int, int> b) {
		return (get<0>(a) < get<0>(b));
	}
};
int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int n, x;
	ll ans = LINF;
	cin >> n >> x;
	vl v(n);
	vvl vv(n, vl(n, LINF));
	rep(i, n) {
		cin >> v[i];
	}
	rep(i, n) {
		rep(j, n) {
			vv[i][j] = min(vv[i][j - (j == 0 ? 0 : 1)], v[(i-j+n)%n]);
		}
	}
	rep(i, n) {
		ll tmp = i*x;
		rep(j, n) {
			tmp += vv[j][i];
		}
		ans = min(ans, tmp);
	}
	cout << ans << endl;
}