Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

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 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/20/2018 16:09:53 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|