Problem Statement

Snuke loves puzzles.

Today, he is working on a puzzle using S- and c-shaped pieces. In this puzzle, you can combine two c-shaped pieces into one S-shaped piece, as shown in the figure below:

Snuke decided to create as many Scc groups as possible by putting together one S-shaped piece and two c-shaped pieces.

Find the maximum number of Scc groups that can be created when Snuke has $N$ S-shaped pieces and $M$ c-shaped pieces.

Constraints

• $1 ≤ N,M ≤ 10^{12}$

Input

The input is given from Standard Input in the following format:

N M

Output

Print the answer.