## Problem Statement

Joisino has a lot of red and blue bricks and a large box. She will build a tower of these bricks in the following manner.

First, she will pick a total of $N$ bricks and put them into the box. Here, there may be any number of bricks of each color in the box, as long as there are $N$ bricks in total. Particularly, there may be zero red bricks or zero blue bricks. Then, she will repeat an operation $M$ times, which consists of the following three steps:

Take out an arbitrary brick from the box.
Put one red brick and one blue brick into the box.
Take out another arbitrary brick from the box.
After the M operations, Joisino will build a tower by stacking the $2×M$ bricks removed from the box, in the order they are taken out. She is interested in the following question: how many different sequences of colors of these $2×M$ bricks are possible? Write a program to find the answer. Since it can be extremely large, print the count modulo $10^9+7$.

### Constraints

$1≤N≤3000$
$1≤M≤3000$

### Input

Input is given from Standard Input in the following format:

$N M$
Output
Print the count of the different possible sequences of colors of $2×M$ bricks that will be stacked, modulo $10^9+7$.

2 3

#### Sample Output 1

56
A total of six bricks will be removed from the box. The only impossible sequences of colors of these bricks are the ones where the colors of the second, third, fourth and fifth bricks are all the same. Therefore, there are $26−2×2×2=56$ possible sequences of colors.

1000 10

1048576

1000 3000

693347555

## 题解

1.抓箱子里一个球堆在塔顶。
2.往箱子里放入一个黑球和一个白球。
3.再抓箱子里的一个球堆在塔顶。

Flowey 是一朵能够通过友谊颗粒传播 LOVE 的小花.它的友谊颗粒分为两种,

1) $i$ 为偶数, $j$ 为奇数
2)第 $i$ 颗友谊颗粒和第 $j$ 颗友谊颗粒同为圆粒或同为皱粒
3)第 $i$ 颗友谊颗粒和第j 颗友谊颗粒都还没有被使用过