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;
inline int in() {
  int32_t x;
  scanf("%d", &x);
  return x;
}
inline long long lin() {
  long long x;
  scanf("%lld", &x);
  return x;
}
inline string get() {
  char ch[2000010];
  scanf("%s", ch);
  return ch;
}
const int MAX_LG = 21;
const long long maxn = 1e5 + 10;
const long long base = 29;
const long long mod = 1e9 + 7;
const long long INF = 1e10 + 100;
long long a[maxn];
long long id = -1;
int32_t main() {
  long long n = in(), x = in();
  for (long long i = 0; i < n; i++) {
    a[i] = in();
    if (id == -1 || a[id] > a[i]) id = i;
  }
  long long res = a[id];
  long long j = (id + 1) % n;
  while (j != id) {
    res += min(a[j], a[id] + x);
    j = (j + 1) % n;
  }
  cout << res << "\n";
}
