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 = 1000000007;
const long long INF = 1000000009;
const long long INFL = 1000000000000000018ll;
long long N, X, a[10000], c[10000], cnt[10000];
signed main() {
  cin >> N >> X;
  for (long long i = 0; i < N; i++) {
    cin >> a[i];
    a[i + N] = a[i];
  }
  long long ans = 0;
  for (long long i = N * 2 - 1; i >= N; i--) {
    long long mn = INFL;
    long long cur = i;
    for (long long j = i; j >= i - N + 1; j--) {
      long long res = (i - j) * X + a[j];
      if (mn > res) {
        mn = res;
        cur = j;
      }
    }
    c[i % N] = cur % N;
  }
  for (long long i = 0; i < N; i++) {
    cnt[c[i]]++;
  }
  long long mx = 0;
  for (long long i = 0; i < N; i++) {
    if (cnt[i] > 0) ans += a[i] * cnt[i];
    mx = max(mx, cnt[i]);
  }
  cout << ans + (max(mx - 1, 0ll) * X) << endl;
  return 0;
}
