Monocarp is wandering through a matrix consisting of $$$2$$$ rows and $$$n$$$ columns. Let's denote the cell in the $$$i$$$-th row and $$$j$$$-th column as $$$(i, j)$$$. Monocarp starts at cell $$$(1, 1)$$$ and wants to reach cell $$$(2, n)$$$.

In one move, Monocarp can move in one of two directions:

right — from cell $$$(i, j)$$$ to cell $$$(i, j + 1)$$$;
down — from cell $$$(i, j)$$$ to cell $$$(i + 1, j)$$$.

Monocarp can't go outside the matrix.

Polycarp wants to prevent Monocarp from freely wandering through the matrix. To do this, he wants to choose exactly $$$k$$$ different cells in the matrix and block them. He cannot choose cells $$$(1, 1)$$$ and $$$(2, n)$$$.

For each $$$i$$$ from $$$0$$$ to $$$n$$$, Polycarp wants to know how many ways he can block exactly $$$k$$$ cells, so that Monocarp has exactly $$$i$$$ different paths from $$$(1, 1)$$$ to $$$(2, n)$$$. Two paths are considered different if there exists a cell that Monocarp visits in one path but not in the other.

As the number of ways can be quite large, output it modulo $$$10^9 + 7$$$.

Input

The only line contains two integers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 2 \cdot 10^5$$$; $$$2 \le k \le 2 \cdot n - 2$$$) — the number of columns in the matrix and the number of cells Polycarp wants to block.

Output

Output $$$n + 1$$$ integers: for each $$$i$$$ from $$$0$$$ to $$$n$$$, the number of ways to block exactly $$$k$$$ cells, so that Monocarp has exactly $$$i$$$ different paths from $$$(1, 1)$$$ to $$$(2, n)$$$. Output all answers modulo $$$10^9 + 7$$$.

Narrow Paths

Examples