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
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))

n, x = getList()
nums = getList()
ans = 0
waits = []

def custmin(tgt):
    tc, ts = 1000000000, 0
    for cost, spell in tgt:
        if cost < tc:
            tc, ts = cost, spell
        elif cost == tc and ts > spell:
            tc, ts = cost, spell

    return tc,ts

for i , c in enumerate(nums):
    target = [(tgt + x * ((j+n-i) % n), j) for j, tgt in enumerate(nums)]
    cost, wait = custmin(target)
    ans += nums[wait]

    waits.append((wait+n-i) % n)

print(ans + max(waits) * x)