There are $N$ kinds of materials. Material $i$ has a magic power of $A_i$.

Takahashi, the magician, wants to make a potion by choosing one or more kinds from these materials and mixing them.

At the moment when he makes a potion by mixing $k$ kinds of materials, the magic power of the potion is the sum of the materials used. Then, every second, its magic power increases by $k$. Note that the increase of the magic power is a discrete - not continuous - process.

Takahashi will mix materials just once, at time $0$. What is the earliest time he can get a potion with a magic power of exactly $X$?

Under the constraints, it can be proved that it is possible to make a potion with a magic power of exactly $X$.

Input is given from Standard Input in the following format:

```
$N$ $X$
$A_1$ $\ldots$ $A_N$
```

Print the earliest time he can get a potion with a magic power of exactly $X$.

-   $1 \leq N \leq 100$
-   $1 \leq A_i \leq 10^7$
-   $10^9 \leq X \leq 10^{18}$
-   All values in input are integers.

4999999994

The potion made by mixing Material 1 and Material 3 has a magic power of 3+8=11 at time 0, and it increases by 2 every second, so it will be 9999999999 at time 999999994, which is the earliest possible time.

The potion made by mixing all the materials 1,2,3 will have a magic power of 9999999998 at time 3333333327 and 10000000001 at time 3333333328, so it will never be exactly 9999999999.