Contest Duration: - (local time) (100 minutes) Back to Home
F - Potion /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

N 種類の素材があり、素材 i には A_i の魔力があります。

k 種類の素材を合成して出来たポーションの魔力は、合成した直後には素材の魔力の合計であり、時間が 1 経過するごとに k 増加します。 魔力の増加は連続的ではなく離散的であることに注意してください。

なお、制約下で魔力がちょうど X のポーションを作れることが証明されます。

制約

• 1 \leq N \leq 100
• 1 \leq A_i \leq 10^7
• 10^9 \leq X \leq 10^{18}
• 入力は全て整数

入力

N X
A_1 \ldots A_N


入力例 1

3 9999999999
3 6 8


出力例 1

4999999994


入力例 2

1 1000000000000000000
1


出力例 2

999999999999999999


Score : 600 points

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