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 gcd(int a, int b) {
  while (b) {
    int m = a % b;
    a = b;
    b = m;
  }
  return a;
}
int lcm(int a, int b) { return (a * b) / gcd(a, b); }
int isPrim(int a) {
  if (a == 1) {
    return 0;
  }
  for (int i = 2; i <= (a + 1) / 2; i++) {
    if (a % i == 0) {
      return 0;
    }
  }
  return 1;
}
long long mod_pow(long long x, long long n, long long mod) {
  long long ret = 1;
  while (n > 0) {
    if (n % 2 == 1) {
      ret = (ret * x) % mod;
    }
    x = (x * x) % mod;
    n = n / 2;
  }
  return ret;
}
struct VV {
  int x;
  int y;
  int z;
};
class LessInt {
 public:
  bool operator()(const VV& riLeft, const VV& riRight) const {
    if (riLeft.x == riRight.x) {
      return riLeft.y > riRight.y;
    }
    return riLeft.x > riRight.x;
  }
};
class indInt {
 public:
  bool operator()(const VV& riLeft, const VV& riRight) const {
    return riLeft.x < riRight.x;
  }
};
struct XX {
  long long min = 0;
  long long kake = 0;
};
class xxIntu {
 public:
  bool operator()(const XX& riLeft, const XX& riRight) const {
    if (riLeft.kake != riRight.kake) {
      return riLeft.kake > riRight.kake;
    }
    return riLeft.min > riRight.min;
  }
};
bool operator<(const VV& riLeft, const VV& riRight) {
  return riLeft.z < riRight.z;
};
int main(int argc, const char* argv[]) {
  long long N;
  long long x;
  long long a[2000];
  XX xxx[2000];
  cin >> N >> x;
  for (int i = 0; i < N; i++) {
    cin >> a[i];
    xxx[i].min = a[i];
    xxx[i].kake = 0;
  }
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < N; j++) {
      long long tmp;
      if (i < j) {
        tmp = a[j] + x * (N - j + i);
      } else if (i > j) {
        tmp = a[j] + x * (abs(i - j));
      } else {
        tmp = a[j];
      }
      if (xxx[i].min > tmp) {
        xxx[i].min = a[j];
        if (i > j) {
          xxx[i].kake = (abs(i - j));
        } else if (i < j) {
          xxx[i].kake = (N - j + i);
        } else {
          xxx[i].kake = 0;
        }
      }
    }
  }
  long long ans = 0;
  sort(xxx, xxx + N, xxIntu());
  long long cnt = 0;
  for (int i = 0; i < N; i++) {
    if (cnt == 0) {
      ans = ans + xxx[i].min + xxx[i].kake * x;
      if (xxx[i].kake > 1) {
        cnt = xxx[i].kake - 1;
      }
    } else {
      ans = ans + xxx[i].min;
      cnt--;
    }
  }
  cout << ans << endl;
  return 0;
}
