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 int modexp(int a, int b);
using namespace std;
const int MOD(1e9 + 7);
int n, x, a[2016];
long long d[2016][2016];
int main() {
  scanf("%d%d", &n, &x);
  long long ans = 0;
  for (int i = 0; i < n; i++) scanf("%d", a + i), ans += a[i];
  for (int i = 0; i < n; i++) d[0][i] = a[i];
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < n; j++)
      d[i][j] = min(d[i - 1][j], (long long)a[(j + n - i) % n]);
    long long t = 0;
    for (int j = 0; j < n; j++) t += d[i][j];
    ans = min(ans, t + x * i);
  }
  printf("%lld\n", ans);
  return 0;
}
inline int modexp(int a, int b) {
  int e = a, r = 1;
  while (b > 0) {
    if (b & 1) r = r * 1LL * e % MOD;
    e = e * 1LL * e % MOD;
    b >>= 1;
  }
  return r;
}
