Description

Compute

$$\sum_{x=1}^m \sum_{i=1}^n \left( \left\lfloor\frac{a_i}{x}\right\rfloor + a_i \bmod x \right) $$

modulo $2^{32}$.

Format

Input Format

The first line contains two positive integers $n,m\,(1\le n\le 10^7, \max_i\{a_i\}\le m\le 10^{11})$.

The second line contains $n$ positive integers $a_1,a_2,\ldots,a_n\,(1\le a_i\le 10^7)$.

Output Format

Output a single integer representing the result.

Samples

4 5
2 3 4 5

48

10 616
9 1 8 3 2 4 5 10 7 6

33672