CF295D.Greg and Caves

Greg has a pad. The pad's screen is an n × m rectangle, each cell can be either black or white. We'll consider the pad rows to be numbered with integers from 1 to n from top to bottom. Similarly, the pad's columns are numbered with integers from 1 to m from left to right.

Greg thinks that the pad's screen displays a cave if the following conditions hold:

• There is a segment [l, r] (1 ≤ l ≤ r ≤ n), such that each of the rows l, l + 1, ..., r has exactly two black cells and all other rows have only white cells.
• There is a row number t (l ≤ t ≤ r), such that for all pairs of rows with numbers i and j (l ≤ i ≤ j ≤ t) the set of columns between the black cells in row i (with the columns where is these black cells) is the subset of the set of columns between the black cells in row j (with the columns where is these black cells). Similarly, for all pairs of rows with numbers i and j (t ≤ i ≤ j ≤ r) the set of columns between the black cells in row j (with the columns where is these black cells) is the subset of the set of columns between the black cells in row i (with the columns where is these black cells).

Greg wondered, how many ways there are to paint a cave on his pad. Two ways can be considered distinct if there is a cell that has distinct colors on the two pictures.

Help Greg.

格雷格有一块电子手写板。该手写板的屏幕是一个 $n \times m$ 的矩形，每个单元格可以是黑色或白色。我们从上到下将手写板的行编号为 $1$ 到 $n$ 的整数；类似地，从左到右将列编号为 $1$ 到 $m$ 的整数。

格雷格认为，当屏幕显示一个“洞穴”（cave）时，需满足以下条件：

• 存在一个区间 $[l,\,r]$（其中 $1 \le l \le r \le n$），使得第 $l,\,l+1,\,\dots,\,r$ 行中每行恰好有两个黑色单元格，而其余所有行全为白色单元格；
• 存在某一行号 $t$（满足 $l \le t \le r$），使得：
  • 对任意满足 $l \le i \le j \le t$ 的行号对 $(i,j)$，第 $i$ 行两个黑格所在列之间（含端点）的所有列构成的集合，是第 $j$ 行两个黑格所在列之间（含端点）的所有列构成的集合的子集；
  • 对任意满足 $t \le i \le j \le r$ 的行号对 $(i,j)$，第 $j$ 行两个黑格所在列之间（含端点）的所有列构成的集合，是第 $i$ 行两个黑格所在列之间（含端点）的所有列构成的集合的子集。

格雷格想知道：有多少种方式可以在他的手写板上绘制一个“洞穴”？若两张图中存在某个单元格颜色不同，则认为这两种方式是不同的。

请帮助格雷格。

The first line contains two integers n, m — the pad's screen size (1 ≤ n, m ≤ 2000).

第一行包含两个整数 $n$、$m$ —— 平板屏幕的尺寸（$1 \leq n, m \leq 2000$）。

In the single line print the remainder after dividing the answer to the problem by 1000000007 (109 + 7).

在单行中输出该问题答案对 1000000007（$10^9 + 7$）取模后的余数。