Jumps in a cycle

A cycle $[a_1,\dots ,a_n][a\_1,\; \backslash dots,\; a\_n]$ can be written in a extended form with a jump rate equal to 1 as $a_1\to a_2\to \mathrm{.}\mathrm{.}\mathrm{.}\to a_n\to a_1\to \mathrm{.}\mathrm{.}\mathrm{.}\to a_n\mathrm{.}\mathrm{.}\mathrm{.}a\_1\; \backslash rightarrow\; a\_2\backslash rightarrow\; ...\; \backslash rightarrow\; a\_n\backslash rightarrow\; a\_1\; \backslash rightarrow\; ...\; \backslash rightarrow\; a\_n\; ...$

Given a jump rate k and starting in the first element, you must find the number of jumps you have to take in order to reach the same element.

ASSUMPTION: The elements in the cycle are distinguishable.

Examples

[1, 5, 7, 8, 9] and jump rate 1, then $1\to 5\to 7\to 8\to 9\to 11\; \backslash rightarrow\; 5\backslash rightarrow\; 7\backslash rightarrow\; 8\backslash rightarrow\; 9\; \backslash rightarrow\; 1$. That is, 5 jumps.

[1, 5, 7, 8, 9] and jump rate 2, then $1\to 7\to 9\to 5\to 8\to 11\; \backslash rightarrow\; 7\backslash rightarrow\; 9\backslash rightarrow\; 5\; \backslash rightarrow\; 8\; \backslash rightarrow\; 1$. That is, 5 jumps.

[1, 5, 1] and jump rate 2, then $1\to 1\to 5\to 11\; \backslash rightarrow\; 1\backslash rightarrow\; 5\backslash rightarrow\; 1$. That is, 3 jumps.

Input

• cl: (list) the list with the cycle. $2\le cl\le 2^{30}2\backslash leq\; cl\backslash leq2^\{30\}$
• k: (int) the jump rate. $1\le k\le 2^{40}1\backslash leq\; k\backslash leq2^\{40\}$

Output

(int) The number of jumps in order to reach the same first element in the cycle.