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
import math
#import numpy as np
import queue
from collections import deque,defaultdict
import heapq as hpq
from sys import stdin,setrecursionlimit
#from scipy.sparse.csgraph import dijkstra
#from scipy.sparse import csr_matrix
ipt = stdin.readline
setrecursionlimit(10**7)

def main():
    n,x = map(int,ipt().split())
    ca = [int(i) for i in ipt().split()]
    a = [(ca[i],i) for i in range(n)]
    for i in range(n):
        an = a[n-1]
        for j in range(n-1):
            pa = a[n-j-2]
            if a[n-1-j][0] > pa[0]+x:
                a[n-1-j] = (pa[0]+x,pa[1])
        if a[0][0] > an[0]+x:
            a[0] = (an[0]+x,an[1])
    ma = 0
    for i,ai in enumerate(a):
        if ma < (i-ai[1])%n:
            ma = (i-ai[1])%n
    ans = x*ma
    for i in range(n):
        mi = 10**10
        for j in range(ma+1):
            if mi > ca[i-j]:
                mi = ca[i-j]
        ans += mi
    print(ans)

    return

if __name__ == '__main__':
    main()
