Apptica gathered $N$ integers in an array $A$ and another integer $X$. He loves Qt Sequences.

Let $S$ contains $M$ elements $S_1, S_2, S_3 ... S_M$ and $S$ is a Qt sequence, then it satisfies following property:

$\sum (d(S_i)*S_i^2) \lt X, \text{ where } d(n) \text{ is the number of divisors of } n.$

He is determined to find out number of Qt subsequences in $A$. Unfortunately, he is very tired after staying awake for almost 24 hours continuosly, and asks you for your help.

Input:

First line contains two space separated integers $N$ and $X$. Next line contains $N$ space separated integers.

Output:

Print a single integer denoting number of Qt subsequences in array $A$.

Constraints:

$1 \leq N \leq 45$

$1 \le X \le 10^{18}$

$1 \le A_i \le 10^7$