In the Cartesian coordinate system, a point $(x, y)$ is called a lattice point if and only if $x \in \mathbb{Z}, y \in \mathbb{Z}$, where $\mathbb{Z}$ denotes the set of integers. If the four vertices of a square in the plane are all lattice points, we call this square a lattice square.

Xiao Yu loves lattice squares. He places an $n \times m$ canvas on the Cartesian coordinate system, where the region covered by the canvas can be represented as $\{(x, y) \mid 0 \le x \le n, 0 \le y \le m\}$.

Now, Xiao Yu wants to pick a lattice point $(a, b)$ on the canvas, where $0 \le a \le n, 0 \le b \le m$, and asks you: how many distinct lattice squares can be drawn within the canvas such that $(a, b)$ is one of their vertices?

Since Xiao Yu has too many queries, you decide to directly provide the answers for all $(a, b)$ where $0 \le a \le n, 0 \le b \le m$. Please output an $(n + 1) \times (m + 1)$ matrix as your answer.

Note: The squares within the canvas must have all their vertices located within the canvas region. Two lattice squares are considered the same if and only if their sets of vertices are identical.

Input

The input contains one line with two integers $n, m$ ($1 \le n, m \le 10^5, n \times m \le 3 \times 10^5$), representing the size of the canvas.

Output

Output $n + 1$ lines, each containing $m + 1$ integers, with the integers in each line separated by spaces. The integer at the $j$-th position of the $i$-th line ($0 \le i \le n, 0 \le j \le m$) represents the number of distinct lattice squares that can be drawn within the canvas having $(i, j)$ as one of their vertices.

Examples

Input 1

1 1

Output 1

1 1
1 1

Input 2

2 2

Output 2

2 3 2
3 4 3
2 3 2

Input 3

4 5

Output 3

4 8 10 10 8 4
7 11 13 13 11 7
8 12 14 14 12 8
7 11 13 13 11 7
4 8 10 10 8 4

Note

Note that according to the problem statement, the sides of the lattice squares are not necessarily parallel to the coordinate axes.