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())
    count = N
    N *= 2
    a = list(map(int,input().split()))
    ans = sum(a)
    a += a
    
    def segfunc(x,y):
        return min(x,y)
        
    def init(init_val):
        for i in range(N):
            seg[i+num-1] = init_val[i]
        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
        ret = ide_ele
        while q-p > 1:
            if p&1 == 0:
                ret = segfunc(ret,seg[p])
            if q&1 == 1:
                ret = segfunc(ret,seg[q])
                q -= 1
            p = p//2
            q = (q-1)//2
        ret = segfunc(segfunc(ret,seg[p]),seg[q])
        return ret
        
    ide_ele = 10**15
    num = 2**(N-1).bit_length()
    seg = [ide_ele]*2*num
    init(a)
    
    for i in range(count-1):
        i += 1
        time = i*x
        for now in range(count):
            ret = query(now+count-i,now+count+1)
            time += ret
        ans = min(ans,time)
        
    print(ans)

if __name__ == "__main__":
    main()
    
