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:

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