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;
double pi = 3.141592653589793;
long long mod = 1000000007;
int intmax = 2147483647;
int intmin = -2147483648;
long long llmax = 9223372036854775807;
long long llmin = -9223372036854775808;
long long m[2001][2001];
long long modminus(long long x, long long y) { return (x - y + mod) % mod; }
int main() {
  long long N, x;
  cin >> N >> x;
  mod = N;
  for (int i = 0; i < N; i++) {
    cin >> m[0][i];
  }
  for (int n = 1; n < N; n++) {
    for (int i = 0; i < N; i++) {
      m[n][i] = min(m[n - 1][i], m[n - 1][modminus(i, 1)]);
    }
  }
  long long ans = llmax;
  for (int n = 0; n < N; n++) {
    long long num = accumulate(m[n], m[n] + N, 0) + x * n;
    ans = min(ans, num);
  }
  cout << ans << endl;
}
