Bohdan against "tails"

Having seen Sasha's skill in solving "tails", Bohdanchik also decided to settle all his debts in mathematics.

In total, he has $n$ tasks, each of which has a specific topic denoted by the number $a_i$.

Because some topics are repeated, Bohdanchik solves them faster, namely:

• If Bohdanchik solves a task of a certain topic for the first time, he uses $x$ minutes of time.

• If he solves it not for the first time and the last time he solved this topic he spent $q$ minutes, then this time he will spend $\max (\lfloor \frac{q}{2}\rfloor ,1)$ minutes.

Find the total time in minutes that he will spend solving the homework.

In the notation, $\lfloor X\rfloor$ means rounding down (to the nearest integer), for example, $\lfloor 3.14\rfloor =3$, $\lfloor 3.9\rfloor =3$.

Input

The first line contains two integers $n$ and $x$ ($1\le n\le 10^5$, $1\le x\le 10^9$) — the number of math tasks and how long Bohdanchik solves the homework of a certain topic for the first time.

The second line contains $n$ numbers $a_1,a_2,\dots ,a_n$ ($1\le a_i\le 10^9$) — the topic of the $i$-th task.

Output

Output a single number — the number of minutes needed for Bohdanchik to solve all the tasks.

Examples

Note

In the first test, he will complete the task with topic $1$ in $2$ minutes, and the task with topic $2$ in $2$ minutes, spending a total of $4$ minutes.

In the second test, when solving the task with topic $2$ for the first time, he will spend $4$ minutes, when solving it again, he will spend $\max (\lfloor \frac{4}{2}\rfloor ,1)=2$ minutes, and when solving the task with topic $2$ for the third time, he will spend $\max (\lfloor \frac{2}{2}\rfloor ,1)=1$ minute, so in total he will spend $4+2+1=7$ minutes.

Scoring

In this problem, there are conditional blocks. If your solution works correctly for certain constraints, it will receive a certain number of points. Note that each test is graded individually.

1. ($5$ points): $x=1$;

2. ($15$ points): $n\le 1000$;

3. ($15$ points): $a_i\le n$;

4. ($15$ points): $a_1=a_2=\cdots =a_n$;

5. ($50$ points): without additional constraints.