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>
int comp(const void *a, const void *b) { return *(int *)a - *(int *)b; }
int compw(const void *a, const void *b) {
  return (*(int *)a > *(int *)b) - (*(int *)a < *(int *)b);
}
uint32_t nextpint(void) {
  char c = getchar();
  while (c < '0' || '9' < c) c = getchar();
  uint_fast32_t x = 0;
  while ('0' <= c && c <= '9') {
    x = x * 10 + c - '0';
    c = getchar();
  }
  return x;
}
inline int min2(const int a, const int b) { return a > b ? b : a; }
inline int dif2(const int a, const int b) { return a > b ? a - b : b - a; }
int a[2000];
int d[2000][2000];
int main(void) {
  int n = nextpint();
  int x = nextpint();
  long ans = 0;
  for (int i = 0; i < n; i++) {
    ans += d[0][i] = a[i] = nextpint();
  }
  for (int j = 1; j < n; j++) {
    long now = x * j;
    for (int i = 0; i < n; i++) {
      now += d[j][i] = min2(d[j - 1][(i + n - 1) % n], a[i]);
    }
    if (now < ans) ans = now;
  }
  printf("%ld\n", ans);
}
