Fibonacci String#1311

Fibonacci String

1 second

256 megabytes

Medium

The Fibonacci strings are defined as follows:

The first Fibonacci string is "a".
The second Fibonacci string is "bc".
The ( $n + 2$ n+2)-th Fibonacci string is the concatenation of the two previous Fibonacci strings.

For example, the first five Fibonacci strings are:

a
bc
abc
bcabc
abcbcabc

Given the string number and the position of a character, determine which character is at that position in the string.

Input

Two integers separated by a space are given: $K$ and $P$ ( $0 < K \leq 1 0^{8}$ 0 < K \leq 10^8, $0 < P \leq 1 0^{8}$ 0 < P \leq 10^8), where $K$ is the number of the Fibonacci string and $P$ is the position to check.

Output

Print one of the three possible characters: "a", "b", or "c". If the $K$ -th string does not contain a character at position $P$ , print "No solution".

Examples

Example 1