Problem 300: Dream

Task

Old Man Ivan, a hard working farmer, tired after a long day of beating the fields, he decided to go to bed.

Being a religious man, he was visited at night by Apostle in a dream. He promised Ivan that his next harvest will be rich, if the farmer is able to help him out with a problem that had been bothering the poor Apostle for a long time.

"Given $K$ and $X$ , natural numbers, and $X$ is even, find out the sum of the first $K$ palindromes with $X$ digits".

Because Apostle knows that Old Man Ivan is a mere mortal, he only wants the remainder of this sum when divided by $666 \ 013$ .

Help Ivan solve the problem.

Input

The only line of the input consists of two integers, $K$ and $X$ .

Output

The output will contain the answer requested by the Apostle.

Restrictions

$1 \leq K, X \leq 10^5$
For tests worth $15$ points, $X \le 8$ .
For tests worth $20$ more points, $X \le 18$ .
For tests worth $35$ more points, $X \cdot K \leq 10^5$ .

Example

stdin

3 4

stdout

Explanation

The first $3$ palindromes with $4$ digits are $1001, 1111, 1221$ . The sum will be $1001 + 1111 + 1221 = 3333$ .

Dream