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Codeforces Round 167 (Div. 1) |
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Finished |

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D. Dima and Figure

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputDima 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 (
*x*_{1},*y*_{1}) to the painted cell at coordinates (*x*_{2},*y*_{2}), moving only through the colored cells, equals |*x*_{1}-*x*_{2}| + |*y*_{1}-*y*_{2}|.

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 (10^{9} + 7).

Input

The first line contains two integers *n* and *m* — the sizes of the piece of paper (1 ≤ *n*, *m* ≤ 150).

Output

In a single line print the remainder after dividing the answer to the problem by number 1000000007 (10^{9} + 7).

Examples

Input

2 2

Output

13

Input

3 4

Output

571

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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