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 sys
input = sys.stdin.buffer.readline

def main():
    n, x = map(int, input().split())
    A = list(map(int, input().split()))

    def segfunc(x, y):
        if x <= y:
          return x
        else:
          return y

    def init(init_val):
        # set_val
        for i in range(n):
            seg[i+num-1] = init_val[i]
        # built
        for i in range(num-2, -1, -1):
            seg[i] = segfunc(seg[2*i+1], seg[2*i+2])

    def update(k, x):
        k += num - 1
        seg[k] = x
        while k:
            k = (k-1)//2
            seg[k] = segfunc(seg[2*k+1], seg[2*k+2])

    def query(p, q):
        if q <= p:
            return ide_ele
        p += num - 1
        q += num - 2
        res = ide_ele
        while q-p>1:
            if p&1 == 0:
                res = segfunc(res, seg[p])
            if q&1 == 1:
                res = segfunc(res, seg[q])
                q -= 1
            p = p//2
            q = (q-1)//2
        if p == q:
            res = segfunc(res, seg[p])
        else:
            res = segfunc(segfunc(res, seg[p]), seg[q])
        return res

    # identity element
    ide_ele = 10**9+1

    # num: n以上の最小の2のべき乗
    num = 2**(n-1).bit_length()
    seg = [ide_ele]*2*num

    init(A)

    ans = float('inf')
    for k in range(n):
        t = k*x
        for i in range(n):
            if k <= i:
                t += query(i-k, i+1)
            else:
                t += min(query(0, i+1), query(n-(k-i), n))
        ans = min(t, ans)
    print(ans)

if __name__ == '__main__':
    main()