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:

9b0bd546db9f28b4093d417b8f274124.png

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.

Examples

Input

1 6

Output

2

Input

12345 678901

Output

175897

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