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>
static FILE *szpFpI;
static int si1Time[2000 + 5];
static int siSCnt;
static int siMagic;
static int si1Catch[2000 + 5];
static int siMCnt;
int fMain(int piTNo) {
  int i, j;
  char lc1Buf[1024], lc1Out[1024];
  siMCnt = 0;
  szpFpI = stdin;
  fgets(lc1Buf, sizeof(lc1Buf), szpFpI);
  sscanf(lc1Buf, "%d%d", &siSCnt, &siMagic);
  for (i = 1; i <= siSCnt; i++) {
    fscanf(szpFpI, "%d", &si1Time[i]);
  }
  fgets(lc1Buf, sizeof(lc1Buf), szpFpI);
  for (i = 1; i <= siSCnt; i++) {
    long long llMin = INT_MAX;
    int liSNo, liMCnt;
    for (j = 1; j <= siSCnt; j++) {
      int liCnt = (i - j + siSCnt) % siSCnt;
      long long llTime =
          (long long)si1Time[j] + (long long)siMagic * (long long)liCnt;
      if (llMin > llTime) {
        llMin = llTime;
        liSNo = j;
        liMCnt = liCnt;
      }
    }
    si1Catch[i] = liSNo;
    if (siMCnt < liMCnt) {
      siMCnt = liMCnt;
    }
  }
  long long llSum = (long long)siMagic * (long long)siMCnt;
  for (i = 1; i <= siSCnt; i++) {
    llSum += (long long)si1Time[si1Catch[i]];
  }
  sprintf(lc1Out, "%lld\n", llSum);
  printf("%s", lc1Out);
  return 0;
}
int main() {
  fMain(0);
  return 0;
}
