Colorful Slimes

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

inputFormat

Input

The input is given from Standard Input in the following format:

N x a_1 a_2 ... a_N

outputFormat

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

样例

4 10
1 2 3 4

10