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;
int main(void) {
  int N, x;
  scanf("%d", &N);
  scanf("%d", &x);
  vector<unsigned long long> table;
  table.resize(N);
  vector<bool> have;
  have.resize(N);
  for (int i = 0; i < N; i++) {
    scanf("%llu", &table[i]);
    have[i] = false;
  }
  int index = 0;
  unsigned long long cost = 0;
  while (true) {
    bool flag = true;
    for (int i = 0; i < N; i++)
      if (have[i] == false) {
        flag = false;
        break;
      }
    if (flag) break;
    int minPos = -1;
    unsigned long long minValue = 10000000000ULL;
    for (int i = 0; i < N; i++) {
      if (have[(i - index + N) % N] == false && minValue > table[i] &&
          table[i] < x) {
        minPos = i, minValue = table[i];
      }
    }
    if (minPos == -1) {
      cost += x;
      index++;
    } else {
      have[(minPos - index + N) % N] = true;
      cost += table[minPos];
    }
  }
  printf("%llu", cost);
  return 0;
}
