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;
const int N = 2000;
int a[2 * N + 5], n, x;
int le[2 * N + 5], ri[N + 5];
long long s[2 * N + 5];
int main() {
  scanf("%d%d", &n, &x);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]), a[n + i] = a[i];
  a[0] = a[2 * n + 1] = 0;
  for (int i = 1; i <= 2 * n; i++) {
    le[i] = i - 1;
    while (a[le[i]] >= a[i]) le[i] = le[le[i]];
  }
  for (int i = 2 * n; i >= 1; i--) {
    ri[i] = i + 1;
    while (a[ri[i]] > a[i]) ri[i] = ri[ri[i]];
  }
  for (int i = 1; i <= n; i++) {
    int p = (n + i) - le[n + i], q = ri[i] - i;
    s[0] += a[i], s[min(p, q)] -= a[i];
    s[max(p, q)] -= a[i], s[min(p, q) + max(p, q)] += a[i];
  }
  for (int i = 1; i <= n; i++) s[i] += s[i - 1];
  for (int i = 1; i <= n; i++) s[i] += s[i - 1];
  long long ans = (1ll << 60);
  for (int i = 0; i <= n; i++) ans = min(ans, s[i] + 1ll * i * x);
  printf("%lld\n", ans);
}
