Problem Statement

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 $X$.

Constraints

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

Input

Input is given from Standard Input in the following format:

N X
A_1 \ldots A_N

Output

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