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 $y$.

Input is given from Standard Input in the following format:

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

Print the number of possible values for $y$.

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

3

y can be 9, 10, or 14.
For example, when y=14, Lunlun gives one 10-yen coin and four 1-yen coins, and the clerk returns one 5-yen coin.
Here, the clerk is not returning any kind of coins that Lunlun gives him, satisfying the requirement.

5

y can be 198, 200, 203, 208, or 248.

4

y can be 44, 60, 100, or 104.