404458: GYM101510 D Drama

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 10⁹ + 7.

Line 1 contains integers H and N (1 ≤ H, N ≤ 10⁵).

Print one line with one integer, the number of different pyramids modulo 10⁹ + 7.

2 6

7

3 20

487

For the first example, the seven pyramids are:

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