Hth Number

Problem

There is a string $S$ of length $N$. All characters in $S$ are numbers between 0 and 9. When you make a sequence of $\ frac {N \ times (N + 1)} {2}$, which is the number of terms created by enumerating all the numbers created from all the substrings of $S$, Find the smallest value in $H$.

Constraints

The input satisfies the following conditions.

• $1 \ leq N \ leq 10 ^ 5$
• $1 \ leq H \ leq \ frac {N \ times (N + 1)} {2}$
• $| S | = N$
• All characters in $S$ are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Input

The input is given in the following format.

$N$ $H$ $S$

All inputs are given as integers. $N$ and $H$ are given on the first line, separated by blanks. The second line is given the string $S$ of length $N$.

Output

Output the $H$ th value on one line. (Do not include extra 0s at the beginning of the output.)

Examples

Input

2 3 00

Output

0

Input

4 9 0012

Output

12

Input

5 13 10031

Output

100

inputFormat

input satisfies the following conditions.

• $1 \ leq N \ leq 10 ^ 5$
• $1 \ leq H \ leq \ frac {N \ times (N + 1)} {2}$
• $| S | = N$
• All characters in $S$ are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Input

The input is given in the following format.

$N$ $H$ $S$

All inputs are given as integers. $N$ and $H$ are given on the first line, separated by blanks. The second line is given the string $S$ of length $N$.

outputFormat

Output

Output the $H$ th value on one line. (Do not include extra 0s at the beginning of the output.)

Examples

Input

2 3 00

Output

0

Input

4 9 0012

Output

12

Input

5 13 10031

Output

100

样例

5 13
10031

100