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;
inline int read(int f = 1, int x = 0, char ch = ' ') {
  while (!isdigit(ch = getchar()))
    if (ch == '-') f = -1;
  while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
  return f * x;
}
const int N = 4e3 + 5;
int n, x, a[N], p;
long long f[N];
int main() {
  n = read(), x = read();
  memset(f, 0x3f, sizeof(f));
  f[0] = 0;
  a[0] = f[n];
  for (int i = 1; i <= n; ++i) a[i] = read(), p = a[p] > a[i] ? i : p;
  for (int i = 1; i < p; ++i) a[n + i] = a[i];
  for (int i = 1; i <= n; ++i) a[i] = a[i + p - 1];
  for (int i = 1; i <= n; ++i)
    for (int j = 0; j < i; ++j)
      f[i] = min(f[i], f[j] + 1ll * (i - j) * a[j + 1] + 1ll * (i - j - 1) * x);
  printf("%lld\n", f[n]);
  return 0;
}
