C. Calendar of an Enthusiastic Worker
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

You are an enthusiastic worker. You want to know how many days you can work during the next specified number of days.

Saturdays and Sundays are non-working days. In addition, a number of national holidays and some company-specific days are non-working days. You cannot work on non-working days. Such non-working days may overlap: The founding anniversary of the company may coincide with a national holiday. Even when such non-working days coincide, there is no system to grant additional non-working days.

Today is Monday. Your task is to count the number of days you can work within a specified period starting from today.

Input

The input consists of at most $$$100$$$ test cases. Each test case is given in the following format.

$$$n$$$ $$$m$$$
$$$a_1$$$ $$$\cdots$$$ $$$a_n$$$

The first line contains the number of additional non-working days $$$n,$$$ and the number of days of the specified period $$$m$$$ ($$$1 \le n \le 300$$$, $$$1 \le m \le 10^{18}$$$). The second line contains $$$n$$$ integers, $$$a_1, \ldots, a_n$$$ ($$$1 \le a_i \le 10^{18}$$$). With today being the first day, the $$$a_i$$$-th day for $$$i=1,\ldots,n$$$ is a non-working day. The list $$$a_1, \ldots, a_n$$$ may contain duplicates.

The end of the input is indicated by a line consisting of two zeros.

Output

For each test case, output in a line the number of days you can work during $$$m$$$ days starting from today.

Example
Input
4 8
1 2 3 4
2 10
15 3
3 14
6 7 13
5 1000000000000000000
8 15 1 8 999999999999999994
2 3
1 4
0 0
Output
2
7
10
714285714285714282
2