Dima and Figure

题意翻译

你需要从N*M的方格中选出一个连通的格子集，满足任意两个同行/列的集合内的格子之间的仍然是集合内的。求这样的集合个数

题目描述

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 $ (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) $ .

输入输出格式

输入格式

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

输出格式

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

输入输出样例

输入样例 #1

2 2

输出样例 #1

13

输入样例 #2

3 4

输出样例 #2

571