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>
int max(int a, int b) {
  if (a > b) {
    return a;
  }
  return b;
}
int min(int a, int b) {
  if (a < b) {
    return a;
  }
  return b;
}
int zt(int a, int b) { return max(a, b) - min(a, b); }
int round(int a, int b) {
  if ((a % b) * 2 >= b) {
    return (a / b) + 1;
  }
  return a / b;
}
int ceil(int a, int b) {
  if (a % b == 0) {
    return a / b;
  }
  return (a / b) + 1;
}
int gcd(int a, int b) {
  int c;
  while (b != 0) {
    c = a % b;
    a = b;
    b = c;
  }
  return a;
}
int lcm(int a, int b) {
  int c = gcd(a, b);
  a /= c;
  return a * b;
}
int nCr(int a, int b) {
  int i, r = 1;
  for (i = 1; i <= b; i++) {
    r *= (a + 1 - i);
    r /= i;
  }
  return r;
}
int fact(int a) {
  int i, r = 1;
  for (i = 1; i <= a; i++) {
    r *= i;
  }
  return r;
}
int pow(int a, int b) {
  int i, r = 1;
  for (i = 1; i <= b; i++) {
    r *= a;
  }
  return r;
}
long long llmax(long long a, long long b) {
  if (a > b) {
    return a;
  }
  return b;
}
long long llmin(long long a, long long b) {
  if (a < b) {
    return a;
  }
  return b;
}
long long llzt(long long a, long long b) { return llmax(a, b) - llmin(a, b); }
long long llround(long long a, long long b) {
  if ((a % b) * 2 >= b) {
    return (a / b) + 1;
  }
  return a / b;
}
long long llceil(long long a, long long b) {
  if (a % b == 0) {
    return a / b;
  }
  return (a / b) + 1;
}
long long llgcd(long long a, long long b) {
  long long c;
  while (b != 0) {
    c = a % b;
    a = b;
    b = c;
  }
  return a;
}
long long lllcm(long long a, long long b) {
  long long c = llgcd(a, b);
  a /= c;
  return a * b;
}
long long llnCr(long long a, long long b) {
  long long i, r = 1;
  for (i = 1; i <= b; i++) {
    r *= (a + 1 - i);
    r /= i;
  }
  return r;
}
long long llfact(long long a) {
  long long i, r = 1;
  for (i = 1; i <= a; i++) {
    r *= i;
  }
  return r;
}
long long llpow(long long a, long long b) {
  long long i, r = 1;
  for (i = 1; i <= b; i++) {
    r *= a;
  }
  return r;
}
double dbmax(double a, double b) {
  if (a > b) {
    return a;
  }
  return b;
}
double dbmin(double a, double b) {
  if (a < b) {
    return a;
  }
  return b;
}
double dbzt(double a, double b) { return dbmax(a, b) - dbmin(a, b); }
int sortfncsj(const void *a, const void *b) {
  if (*(int *)a > *(int *)b) {
    return 1;
  }
  if (*(int *)a == *(int *)b) {
    return 0;
  }
  return -1;
}
int sortfnckj(const void *a, const void *b) {
  if (*(int *)a < *(int *)b) {
    return 1;
  }
  if (*(int *)a == *(int *)b) {
    return 0;
  }
  return -1;
}
int llsortfncsj(const void *a, const void *b) {
  if (*(long long *)a > *(long long *)b) {
    return 1;
  }
  if (*(long long *)a == *(long long *)b) {
    return 0;
  }
  return -1;
}
int llsortfnckj(const void *a, const void *b) {
  if (*(long long *)a < *(long long *)b) {
    return 1;
  }
  if (*(long long *)a == *(long long *)b) {
    return 0;
  }
  return -1;
}
int dbsortfncsj(const void *a, const void *b) {
  if (*(double *)a > *(double *)b) {
    return 1;
  }
  if (*(double *)a == *(double *)b) {
    return 0;
  }
  return -1;
}
int dbsortfnckj(const void *a, const void *b) {
  if (*(double *)a < *(double *)b) {
    return 1;
  }
  if (*(double *)a == *(double *)b) {
    return 0;
  }
  return -1;
}
int strsortfncsj(const void *a, const void *b) {
  return strcmp((char *)a, (char *)b);
}
int strsortfnckj(const void *a, const void *b) {
  return strcmp((char *)b, (char *)a);
}
int main(void) {
  long long ou = 0, no, p, nc, i, j, n, x, a[2048], r[2048];
  scanf("%lld%lld", &n, &x);
  for (i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
    r[i] = a[i];
    ou += a[i];
  }
  for (i = 1; i <= n; i++) {
    nc = a[i];
    p = i;
    no = a[i];
    for (j = 1; j < n; j++) {
      p++;
      if (p == n + 1) {
        p = 1;
      }
      no += llmin(x + a[i], a[p]);
    }
    ou = llmin(no, ou);
  }
  printf("%lld\n", ou);
  return 0;
}
