2017 Fall Waterloo Local ACM Contest, Problem D

Vera has a grid with $H$ rows and $N$ columns. Rows are numbered $1$ to $H$ and columns are numbered $1$ to $N$. Let the cell in the $r$-th row and $c$-th column be $(r,c)$. Cells are coloured white or black. A colouring is a pyramid if:

• Exactly $N$ cells are black.
• $(1,1)$ is black.
• If $(r,a)$ and $(r,b)$ are black, then $(r,k)$ is black for $a<k<b$.
• If $(r,c)$ is black, then $(r-1,c)$, if it exists, is black.
• If $(r,c)$ is black and there is no $k<c$ such that $(r,k)$ is black, then $(r+1,c)$, if it exists, is white.

Two pyramids are different if there is a cell that is white in one pyramid and black in the other. Compute the number of different pyramids modulo ${10}^9+7$.

Input

Line $1$ contains integers $H$ and $N$ $(1\le H,N\le {10}^5)$.

Output

Print one line with one integer, the number of different pyramids modulo ${10}^9+7$.

Sample Input 1

2 6

Sample Output 1

7

Sample Input 2

3 20

Sample Output 2

487

Note

For the first example, the seven pyramids are:

######
......
####..
.##...
####..
..##..
#####.
.#....
#####.
..#...
#####.
...#..
#####.
....#.