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>
inline void Min(int &x, int y) {
  if (x > y) x = y;
}
const int INF = 0x3f3f3f3f;
const int N = 2003;
int n, x;
int mn[N], a[N << 1];
long long ans = INF, sum;
int main() {
  scanf("%d %d", &n, &x);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    a[i + n] = a[i];
    mn[i] = INF;
  }
  for (int k = 0; k < n; k++) {
    sum = 1ll * k * x;
    for (int i = 1; i <= n; i++) {
      Min(mn[i], a[i + k]);
      sum += mn[i];
    }
    if (sum < ans) ans = sum;
  }
  printf("%lld\n", ans);
  return 0;
}
