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;
template <typename T>
void read(T &x) {
  x = 0;
  char c;
  for (c = getchar(); !isdigit(c); c = getchar())
    ;
  for (; isdigit(c); c = getchar()) x = x * 10 + c - '0';
}
const int N = 2e5 + 50;
long long n, x, a[N], ans = 1e18, q[N], h, t;
long long solve(int k) {
  long long res = 0;
  for (int i = 0; i < (n + n); ++i) {
    while (h != t && i - q[h] > k) ++h;
    while (h != t && a[i] < a[q[t - 1]]) --t;
    q[t++] = i;
    if (i >= n) res += a[q[h]];
  }
  return res;
}
int main(int argc, char *argv[]) {
  read(n), read(x);
  for (int i = 0; i < (n); ++i) read(a[i]);
  for (int i = n; i < (n + n); ++i) a[i] = a[i - n];
  for (int k = 0; k < (n); ++k) ans = min(ans, solve(k) + x * k);
  printf("%lld\n", ans);
  return 0;
}
