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>
const int maxn = 1e5 + 10;
using namespace std;
long long gcd(long long p, long long q) { return q == 0 ? p : gcd(q, p % q); }
long long qpow(long long p, long long q) {
  long long f = 1;
  while (q) {
    if (q & 1) f = f * p;
    p = p * p;
    q >>= 1;
  }
  return f;
}
int n, m, k, t, pos;
long long a[maxn];
long long p[maxn];
long long ans, mi;
void gao(long long a[]) {
  for (int i = 0; i < n; i++) {
    if (i == 0)
      p[0] = a[0];
    else
      p[i] = min(a[0] + m + p[i - 1], p[i - 1] + a[i]);
  }
  printf("%lld\n", ans = p[n - 1]);
}
int main() {
  int i, j;
  mi = 1e19;
  scanf("%d%d", &n, &m);
  for (i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
    a[n + i] = a[i];
    if (mi > a[i]) mi = a[i], pos = i;
  }
  if (n == 1)
    return 0 * printf("%lld\n", a[i]);
  else
    gao(a + pos);
  return 0;
}
