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>
typedef struct Time {
  long long mlTime;
  int miCNo;
} Time;
static FILE *szpFpI;
static int siSCnt;
static int siMagic;
static Time sz2Time[2000 + 5][2000];
int fMain(int piTNo) {
  int i;
  char lc1Buf[1024], lc1Out[1024];
  szpFpI = stdin;
  fgets(lc1Buf, sizeof(lc1Buf), szpFpI);
  sscanf(lc1Buf, "%d%d", &siSCnt, &siMagic);
  for (i = 1; i <= siSCnt; i++) {
    fscanf(szpFpI, "%lld", &sz2Time[i][0].mlTime);
    sz2Time[i][0].miCNo = i;
  }
  fgets(lc1Buf, sizeof(lc1Buf), szpFpI);
  int liSNo, liMCnt;
  for (liSNo = 1; liSNo <= siSCnt; liSNo++) {
    for (liMCnt = 1; liMCnt < siSCnt; liMCnt++) {
      int liCNo = (liSNo - liMCnt - 1 + siSCnt) % siSCnt + 1;
      long long llTime =
          sz2Time[liCNo][0].mlTime + (long long)siMagic * (long long)liMCnt;
      if (sz2Time[liSNo][liMCnt - 1].mlTime < llTime) {
        sz2Time[liSNo][liMCnt].mlTime = sz2Time[liSNo][liMCnt - 1].mlTime;
        sz2Time[liSNo][liMCnt].miCNo = sz2Time[liSNo][liMCnt - 1].miCNo;
      } else {
        sz2Time[liSNo][liMCnt].mlTime = llTime;
        sz2Time[liSNo][liMCnt].miCNo = liCNo;
      }
    }
  }
  long long llMin = LLONG_MAX;
  for (liMCnt = 0; liMCnt < siSCnt; liMCnt++) {
    long long llSum = (long long)siMagic * (long long)liMCnt;
    for (liSNo = 1; liSNo <= siSCnt; liSNo++) {
      llSum += sz2Time[sz2Time[liSNo][liMCnt].miCNo][0].mlTime;
    }
    if (llMin > llSum) {
      llMin = llSum;
    }
  }
  sprintf(lc1Out, "%lld\n", llMin);
  printf("%s", lc1Out);
  return 0;
}
int main() {
  fMain(0);
  return 0;
}
