K. Get the numbers
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Slava has a set of $$$N$$$ numbers: $$$x_1, x_2, x_3, \dots, x_n$$$. At one turn, he can get a non-empty set $$$y_1, y_2, y_3, \dots, y_m$$$, in which for any $$$i$$$ from $$$1$$$ to $$$m$$$ $$$y_i$$$ is included in the set $$$x_1, x_2, \dots, x_n$$$, and then he can add in the set $$$X$$$ sum of all products of numbers of all the possible subsets $$$y_1, y_2, \dots, y_m$$$. Slava is wondering: how many numbers not superior to $$$L$$$ exist that can be calculated by the above-described method for the finite number of actions? (For better understanding, see the note).

Input

The first line of the input data consists of numbers $$$N$$$ and $$$L$$$ $$$(2 \le N \le 20, 1 \le L \le 10^{12})$$$.

The second line consists of $$$N$$$ numbers $$$x_i$$$ $$$(2 \le x_i \le 15)$$$.

Output

In one line, output the number – the amount of numbers not superior to $$$L$$$ that can be calculated by the above-described method for a finite number of actions.

Examples
Input
3 7
2 2 3
Output
2
Input
2 100
14 15
Output
2
Note

Consider set of numbers $$$X = [14, 15], L = 100$$$.

We can get set $$$Y$$$ like that:

$$$[14], [15], [14, 14], [14, 15], [15, 15], [14, 14, 14], \dots$$$

Then we get numbers:

$$$14 + 14 + 14 * 14 = 224$$$

$$$15 + 15 + 15 * 15 = 255$$$

$$$14 = 14$$$

$$$15 = 15$$$

$$$14 + 15 + 14 * 15 = 239$$$

$$$14 + 14 + 14 + 14 * 14 + 14 * 14 + 14 * 14 + 14 * 14 * 14 = 3374$$$

$$$\dots$$$

Among these numbers, only two are not superior to $$$100:~14,~15$$$.