101925: [AtCoder]ABC192 F - Potion

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 $X$.

Sample Input 1

3 9999999999
3 6 8

Sample Output 1

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 $4999999994$, 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 $9999999999$.

Sample Input 2

1 1000000000000000000
1

Sample Output 2

999999999999999999