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;
const long long MOD = 1e9 + 7;
inline void in() {}
template <class T, class... Ts>
inline void in(T& x, Ts&... xs) {
  int c, s = 0;
  x = 0;
  while (c = getchar(), c != '-' && (c < '0' || c > '9'))
    ;
  if (c == '-') s = 1, c = getchar();
  do x = x * 10 + (c - '0');
  while (c = getchar(), c >= '0' && c <= '9');
  if (s) x = -x;
  in(xs...);
}
inline void ins(char* s) {
  char c;
  while (c = getchar(), c < 33)
    ;
  do *s++ = c;
  while (c = getchar(), c > 32);
  *s = 0;
}
int a[4000];
int main() {
  int n, x;
  in(n, x);
  for (long long i = 0; i < n; i++) in(a[i]), a[i + n] = a[i];
  long long ans = LLONG_MAX;
  for (long long i = 0; i < n; i++) {
    long long t = 0;
    for (long long j = i; j < i + n; j++) {
      t += min(a[i] + x, a[j]);
    }
    ans = min(ans, t);
  }
  printf("%lld\n", ans);
}
