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
#!/usr/bin/env python3
import sys
import copy

def solve(N: int, x: int, a: "List[int]"):
    least = copy.deepcopy(a)
    for _ in range(N):
        for i in range(N):
            if least[i] > least[i-1] + x:
                least[i] = least[i-1] + x
    current = [0] * N
    count = 0
    spent = 0
    while count < N:
        for i, ai in enumerate(a):
            if ai < x and current[i] == 0:
                spent += ai
                count += 1
                current[i] = 1
        if count < N:
            current = [current[j-1] for j in range(N)]
            spent += x
    print(spent)
    return


# Generated by 1.1.4 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    x = int(next(tokens))  # type: int
    a = [ int(next(tokens)) for _ in range(N) ]  # type: "List[int]"
    solve(N, x, a)

if __name__ == '__main__':
    main()
