You have a string $s$ and you may modify it by making long swaps of its letters. Two letters can be swapped if their positions differ by at least $k$. That is, you may swap the $i$-th letter with the $j$-th letter in $s$ if $|i - j| \geq k$. Is it possible to sort all the letters in $s$ increasingly, if you are allowed to swap any number of times (possibly zero)?

-----Input-----
The first line has a string $s$ ($2 \leq |s| \leq 100$) and an integer $k$ ($1 \leq k \leq |s| - 1$), separated by a single space. The string $s$ consists of only lowercase letters.

-----Output-----
If it is possible to sort the letters increasingly, output “Yes”. Otherwise output “No”.

-----Examples-----
Sample Input:
prognova 4
Sample Output:
Yes

Source: kattis | Difficulty: MEDIUM


Solutions: