**Difficulty**: Medium**Tags**: LeetCode, Medium, Array, Matrix, Simulation, leetcode-1706, O(m * n), O(1)

# Problem

You have a 2-D `grid`

of size `m x n`

representing a box, and you have `n`

balls. The box is open on the top and bottom sides.

Each cell in the box has a diagonal board spanning two corners of the cell that can redirect a ball to the right or to the left.

- A board that redirects the ball to the right spans the top-left corner to the bottom-right corner and is represented in the grid as
`1`

. - A board that redirects the ball to the left spans the top-right corner to the bottom-left corner and is represented in the grid as
`-1`

.

We drop one ball at the top of each column of the box. Each ball can get stuck in the box or fall out of the bottom. A ball gets stuck if it hits a "V" shaped pattern between two boards or if a board redirects the ball into either wall of the box.

Return *an array *`answer`

* of size *`n`

* where *`answer[i]`

* is the column that the ball falls out of at the bottom after dropping the ball from the *`i`

^{th}* column at the top, or -1 if the ball gets stuck in the box.*

**Example 1:**

Input:grid = [[1,1,1,-1,-1],[1,1,1,-1,-1],[-1,-1,-1,1,1],[1,1,1,1,-1],[-1,-1,-1,-1,-1]]Output:[1,-1,-1,-1,-1]Explanation:This example is shown in the photo. Ball b0 is dropped at column 0 and falls out of the box at column 1. Ball b1 is dropped at column 1 and will get stuck in the box between column 2 and 3 and row 1. Ball b2 is dropped at column 2 and will get stuck on the box between column 2 and 3 and row 0. Ball b3 is dropped at column 3 and will get stuck on the box between column 2 and 3 and row 0. Ball b4 is dropped at column 4 and will get stuck on the box between column 2 and 3 and row 1.

**Example 2:**

Input:grid = [[-1]]Output:[-1]Explanation:The ball gets stuck against the left wall.

**Example 3:**

Input:grid = [[1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1]]Output:[0,1,2,3,4,-1]

**Constraints:**

`m == grid.length`

`n == grid[i].length`

`1 <= m, n <= 100`

`grid[i][j]`

is`1`

or`-1`

.