toinfinity
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 × 1015 days. What is the K-th character from the left in the string after 5 × 1015 days?
Constraints
- S is a string of length between 1 and 100 (inclusive).
- K is an integer between 1 and 1018 (inclusive).
- The length of the string after 5 × 1015 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 × 1015 days.
Sample Input 1
1214
4
Sample Output 1
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 × 1015 days is 12222. As K=4, we should print the fourth character, 2.
Sample Input 2
3
157
Sample Output 2
3
The initial string is 3. The string after 5 × 1015 days consists only of 3.
Sample Input 3
299792458
9460730472580800
Sample Output 3
2