<p>You are given a <code>m x n</code> matrix <code>grid</code>. Initially, you are located at the top-left corner <code>(0, 0)</code>, and in each step, you can only <strong>move right or down</strong> in the matrix.</p>

<p>Among all possible paths starting from the top-left corner <code>(0, 0)</code> and ending in the bottom-right corner <code>(m - 1, n - 1)</code>, find the path with the <strong>maximum non-negative product</strong>. The product of a path is the product of all integers in the grid cells visited along the path.</p>

<p>Return the <em>maximum non-negative product <strong>modulo</strong> </em><code>10<sup>9</sup> + 7</code>. <em>If the maximum product is <strong>negative</strong>, return </em><code>-1</code>.</p>

<p>Notice that the modulo is performed after getting the maximum product.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product1.jpg" style="width: 244px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [[-1,-2,-3],[-2,-3,-3],[-3,-3,-2]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> It is not possible to get non-negative product in the path from (0, 0) to (2, 2), so return -1.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product2.jpg" style="width: 244px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [[1,-2,1],[1,-2,1],[3,-4,1]]
<strong>Output:</strong> 8
<strong>Explanation:</strong> Maximum non-negative product is shown (1 * 1 * -2 * -4 * 1 = 8).
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product3.jpg" style="width: 164px; height: 165px;" />
<pre>
<strong>Input:</strong> grid = [[1,3],[0,-4]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Maximum non-negative product is shown (1 * 0 * -4 = 0).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 15</code></li>
	<li><code>-4 &lt;= grid[i][j] &lt;= 4</code></li>
</ul>

class Solution {
public:
  int maxProductPath(vector<vector<int>> &grid) {
    const int MOD = 1e9 + 7;

    int m = grid.size();
    int n = grid[0].size();

    vector<vector<long long>> max_product(m, vector<long long>(n));
    vector<vector<long long>> min_product(m, vector<long long>(n));

    max_product[0][0] = grid[0][0];
    min_product[0][0] = grid[0][0];

    // fill row
    for (int i = 1; i < n; ++i) {
      max_product[0][i] = max_product[0][i - 1] * grid[0][i];
      min_product[0][i] = max_product[0][i];
    }

    // fill column
    for (int i = 1; i < m; ++i) {
      max_product[i][0] = max_product[i - 1][0] * grid[i][0];
      min_product[i][0] = max_product[i][0];
    }

    for (int i = 1; i < m; ++i) {
      for (int j = 1; j < n; ++j) {
        if (grid[i][j] >= 0) {
          max_product[i][j] =
              max(max_product[i - 1][j], max_product[i][j - 1]) * grid[i][j];
          min_product[i][j] =
              min(min_product[i - 1][j], min_product[i][j - 1]) * grid[i][j];
        } else {
          max_product[i][j] =
              min(min_product[i - 1][j], min_product[i][j - 1]) * grid[i][j];
          min_product[i][j] =
              max(max_product[i - 1][j], max_product[i][j - 1]) * grid[i][j];
        }
      }
    }

    long long result = max_product[m - 1][n - 1];

    if (result >= 0) {
      return result % MOD;
    } else {
      return -1;
    }
  }
};
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