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 dump(a) cout << (a) << '\n';
typedef int64_t Int;
Int mod = 1e9+7;
// Int MOD = 998244353;

int main() {
    ios::sync_with_stdio(false);
    Int n, x;
    cin >> n >> x;
    vector<Int> a(n);
    for (Int i = 0; i < n; i++) cin >> a[i];
    vector<Int> cost = a;
    vector<Int> cnt(n, 1);
    Int rotate = 0;
    for (Int i = 0; i < n; i++) {
        for (Int j = 1; j < n; j++) {
            if (cost[(i + j) % n] > a[i] + x * j) {
                cost[(i + j) % n] = a[i] + x * j;
                rotate = max(rotate, j);
                cnt[i]++;
                cnt[(i + j) % n] = max(0LL, cnt[(i + j) % n] - 1);
            }
        }
    }
    Int res = rotate * x;
    for (Int i = 0; i < n; i++) {
        res += cnt[i] * a[i];
    }
    dump(res);
    return 0;  
} 