J. Birthdays
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Misha wants to get a job in the Kolya's department. He doesn't know the number of employees in the firm and assumes that there could be any number of employees with equal probability of cases.

To verify Misha mathematical abilities Kolya asked him to determine the number of employees knowing only the number of employees with the same birthdays.

All employees can be separated in groups, where all employees have the same birthday. The birthdays of two employees of the different group are different.

The all employees can be separated to the following groups. There are $$$m_2$$$ groups of two employees, $$$m_3$$$ groups of 3 employees, ..., $$$m_s$$$ groups of s employees and other groups that contain only one employee.

Assuming that there are $$$d$$$ days in any year and probability to have birthday is equal for any day in the year, help Misha find the most probable number of employees in the firm.

Input

The first line contains two integers $$$s$$$ and $$$d$$$ ( $$$365 \leq d \leq 40\, 000$$$, $$$2 \leq s \leq d$$$). The second line contains $$$s - 1$$$ integers $$$m_2$$$, $$$m_3$$$, ..., $$$m_s$$$ ( $$$0 \leq \sum\limits_{i=2}^s{m_i} \leq d$$$).

Output

Output one positive integer number $$$n$$$ denotes the most probable number of employees. If there are several possible answers output the maximum one.

Examples
Input
2 365
1
Output
28
Input
4 365
3 5 2
Output
113