H. New Password
time limit per test
3 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

One day, Sachin's password $$$p$$$ was found in a leaked passwords database. Since Sachin refuses to remember more than 1 password, this means he now has to change his password on every single account he has. Instead of coming up with a new password, he decides to make his new password derivable from his old one with the following transformation:

  • Add every substring of $$$p$$$ to a list. If string $$$s$$$ is a substring of $$$p$$$ multiple times, then it will appear in the list multiple times.
  • Sort the list lexicographically.
  • Concatenate the list into a new string $$$p'$$$.
  • Use the $$$L$$$-th to $$$R$$$-th characters of $$$p'$$$ as the new password.

Determine what Sachin's new password should be.

Input

The first line of input consists of a single integer $$$n$$$ $$$(1 \le n \le 10^6)$$$ — the length of Sachin's password $$$p$$$.

The second line of input consists of two integers $$$L$$$ and $$$R$$$ $$$(1 \le L \le R \le {n+2 \choose 3})$$$ — the substring of $$$p'$$$ to use as the new password.

The third line of input consists of a single string of $$$n$$$ lowercase English letters — Sachin's old password $$$p$$$.

It is guaranteed that $$$R-L+1\le 10^6$$$.

Output

Output a single string of $$$R-L+1$$$ characters — Sachin's new password.

Examples
Input
3
1 10
aba
Output
aaabababba
Input
3
2 6
aba
Output
aabab
Input
7
5 17
bbbcaaa
Output
aaaaaabbbbbbb