Dima and Figure

Dima loves making pictures on a piece of squared paper. And yet more than that Dima loves the pictures that depict one of his favorite figures.

A piece of squared paper of size n × m is represented by a table, consisting of n rows and m columns. All squares are white on blank squared paper. Dima defines a picture as an image on a blank piece of paper, obtained by painting some squares black.

The picture portrays one of Dima's favorite figures, if the following conditions hold:

• The picture contains at least one painted cell;
• All painted cells form a connected set, that is, you can get from any painted cell to any other one (you can move from one cell to a side-adjacent one);
• The minimum number of moves needed to go from the painted cell at coordinates (x₁, y₁) to the painted cell at coordinates (x₂, y₂), moving only through the colored cells, equals |x₁ - x₂| + |y₁ - y₂|.

Now Dima is wondering: how many paintings are on an n × m piece of paper, that depict one of his favorite figures? Count this number modulo 1000000007 (10⁹ + 7).