While Mike was walking in the subway, all the stuff in his back-bag dropped on the ground. There were several fax messages among them. He concatenated these strings in some order and now he has string $*s*$.

He is not sure if this is his own back-bag or someone else's. He remembered that there were exactly $*k*$ messages in his own bag, each was a palindrome string and all those strings had the same length.

He asked you to help him and tell him if he has worn his own back-bag. Check if the given string $*s*$ is a concatenation of $*k*$ palindromes of the same length.

Input

The first line of input contains string $*s*$ containing lowercase English letters ($1 ≤ |*s*| ≤ 1000$).

The second line contains integer $*k*$ ($1 ≤ *k* ≤ 1000$).

Output

Print "YES"(without quotes) if he has worn his own back-bag or "NO"(without quotes) otherwise.

Note

Palindrome is a string reading the same forward and backward.

In the second sample, the faxes in his back-bag can be "saddas" and "tavvat".