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 = 500000;
const long long INF = 1ll << 60;
int N, X;
int A[MAXN + 5];
int main() {
  scanf("%d%d", &N, &X);
  for (int i = 1; i <= N; i++) scanf("%d", &A[i]);
  long long Ans = 0, T = 0;
  for (int i = 1; i <= N; i++) {
    long long Min = INF;
    int pos = 0;
    for (int j = 0; j < N; j++) {
      long long cur = (long long)j * X + A[(i + j - 1) % N + 1];
      if (cur < Min) Min = cur, pos = j;
    }
    T = std::max(T, (long long)pos);
    Ans += A[(i + pos - 1) % N + 1];
  }
  printf("%lld", Ans + T * X);
  return 0;
}
