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 <string>
#include <queue>
#include <stack>
#include <algorithm>
#include <list>
#include <vector>
#include <complex>
#include <utility>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <bitset>
#include <ctime>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <cassert>
#include <cstddef>
#include <iomanip>
#include <numeric>
#include <tuple>
#include <sstream>
#include <fstream>

#define REP(i, n) for (int (i) = 0; (i) < (n); (i)++)
#define FOR(i, a, b) for (int (i) = (a); (i) < (b); (i)++)
#define RREP(i, a) for(int (i) = (a)-1; (i) >= 0; (i)--)
#define FORR(i, a, b) for(int (i) = (a)-1; (i) >= (b); (i)--)
#define PI acos(-1.0)
#define DEBUG(C) cout<< C <<endl;
#define VI vector <int>
#define VII vector <VI>
#define VL vector <LL>
#define VLL vector <VL>
#define VD vector <double>
#define VDD vector <VD>
#define PII pair <int, int>
#define PDD pair <double, double>
#define PLL pair <LL, LL>
#define VPII vector <PII>
#define ALL(a) (a).begin(), (a).end()
#define SORT(a) sort(ALL(a))
#define REVERSE(a) reverse(ALL(a))
#define MP make_pair
#define FORE(a,b) for(auto &&a:b)

using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
const int INF = 1e9;
const int MOD = INF+7;
const LL LLINF = 1e18;

int main(void) {
    int N, x;
    cin >> N >> x;
    VL a(N);
    REP (i, N) cin >> a[i];
    copy_n(ALL(a), back_inserter(a));
    LL ans = LLINF;
    VL b(N, LLINF);
    REP (k, N) {
        LL sum = k*x;
        REP (i, N) {
            int id = (i-k+N);
            b[i] = min<LL>(b[i], a[id]);
            sum += b[i];
        }
        ans = min(ans, sum);
    }
    cout << ans << endl;
}
