Problem Statement

In Republic of AtCoder, $N$ kinds of coins are used: $A_1$-yen, $A_2$-yen, $A_3$-yen, $\dots$, $A_N$-yen coins. Here, $A_1 = 1$ holds, and for each $i$ such that $1 \le i \lt N$, $A_i \lt A_{i + 1}$ holds and $A_{i + 1}$ is a multiple of $A_i$.

At some shop in this country, Lunlun the dog bought an $X$-yen product by giving $y\ (\ge X)$ yen to the clerk and receiving the change of $y - X$ yen from the clerk. (The change may have been $0$ yen.) Here, both Lunlun and the clerk used the minimum number of coins needed to represent those amounts of money. Additionally, the clerk did not return any kind of coins that Lunlun gave him.

Given $X$, find the number of possible values for $y$.

Constraints

• $1 \le N \le 50$
• $1 = A_1 \lt A_2 \lt A_3 \lt \dots \lt A_N \le 10^{15}$
• $A_{i + 1}$ is a multiple of $A_i$. $(1 \le i \lt N)$
• $1 \le X \le 10^{15}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N X
A_1 \hspace{7pt} A_2 \hspace{7pt} A_3 \hspace{5pt} \dots\ \hspace{5pt} A_N

Output

Print the number of possible values for $y$.