C - To Infinity

Score: $300$ points

Problem Statement

Mr. Infinity has a string $S$ consisting of digits from 1 to 9. Each time the date changes, this string changes as follows:

• Each occurrence of 2 in $S$ is replaced with 22. Similarly, each 3 becomes 333, 4 becomes 4444, 5 becomes 55555, 6 becomes 666666, 7 becomes 7777777, 8 becomes 88888888 and 9 becomes 999999999. 1 remains as 1.

For example, if $S$ is 1324, it becomes 1333224444 the next day, and it becomes 133333333322224444444444444444 the day after next. You are interested in what the string looks like after $5 \times 10^{15}$ days. What is the $K$-th character from the left in the string after $5 \times 10^{15}$ days?

Constraints

• $S$ is a string of length between $1$ and $100$ (inclusive).
• $K$ is an integer between $1$ and $10^{18}$ (inclusive).
• The length of the string after $5 \times 10^{15}$ days is at least $K$.

Input

Input is given from Standard Input in the following format:

$S$

$K$

Output

Print the $K$-th character from the left in Mr. Infinity's string after $5 \times 10^{15}$ days.

1214
4

2

The string $S$ changes as follows:

• Now: 1214
• After one day: 12214444
• After two days: 1222214444444444444444
• After three days: 12222222214444444444444444444444444444444444444444444444444444444444444444

The first five characters in the string after $5 \times 10^{15}$ days is 12222. As $K=4$, we should print the fourth character, 2.

3
157

3

The initial string is 3. The string after $5 \times 10^{15}$ days consists only of 3.

299792458
9460730472580800

2