Fibonacci String

The Fibonacci strings are defined as follows:

• The first Fibonacci string is "a"

• The second Fibonacci string is "bc"

• The (n + 2)nd Fibonacci string is the concatenation of the two previous Fibonacci strings.

For example, the first few Fibonacci strings are

abcabcbcabcabcbcabc

The goal is, given a row and an offset, to determine what character is at that offset.

Input

Two integers separated by a space - K and P(0 < K ≤ 10^8), (0 < P ≤ 10^8), where K is the line number of the Fibonacci string and P is the position number in a row.

Output

The desired character for the relevant test: "a", "b" or "c". If P is greater than the Kth row (K ≤ 10^8), it is necessary to derive "No solution".

Examples