Given a 0-indexed 2D integer matrix grid of size n * m, we define a 0-indexed 2D matrix p of size n * m as the product matrix of grid if the following condition is met:
p[i][j] is calculated as the product of all elements in grid except for the element grid[i][j]. This product is then taken modulo 12345.Return the product matrix of grid.
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Example 1:
\n\n\nInput: grid = [[1,2],[3,4]]\nOutput: [[24,12],[8,6]]\nExplanation: p[0][0] = grid[0][1] * grid[1][0] * grid[1][1] = 2 * 3 * 4 = 24\np[0][1] = grid[0][0] * grid[1][0] * grid[1][1] = 1 * 3 * 4 = 12\np[1][0] = grid[0][0] * grid[0][1] * grid[1][1] = 1 * 2 * 4 = 8\np[1][1] = grid[0][0] * grid[0][1] * grid[1][0] = 1 * 2 * 3 = 6\nSo the answer is [[24,12],[8,6]].\n\n
Example 2:
\n\n\nInput: grid = [[12345],[2],[1]]\nOutput: [[2],[0],[0]]\nExplanation: p[0][0] = grid[0][1] * grid[0][2] = 2 * 1 = 2.\np[0][1] = grid[0][0] * grid[0][2] = 12345 * 1 = 12345. 12345 % 12345 = 0. So p[0][1] = 0.\np[0][2] = grid[0][0] * grid[0][1] = 12345 * 2 = 24690. 24690 % 12345 = 0. So p[0][2] = 0.\nSo the answer is [[2],[0],[0]].\n\n
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Constraints:
\n\n1 <= n == grid.length <= 1051 <= m == grid[i].length <= 1052 <= n * m <= 1051 <= grid[i][j] <= 109给你一个下标从 0 开始、大小为 n * m 的二维整数矩阵 grid ，定义一个下标从 0 开始、大小为 n * m 的的二维矩阵 p。如果满足以下条件，则称 p 为 grid 的 乘积矩阵 ：
p[i][j] ，它的值等于除了 grid[i][j] 外所有元素的乘积。乘积对 12345 取余数。返回 grid 的乘积矩阵。
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示例 1：
\n\n\n输入：grid = [[1,2],[3,4]]\n输出：[[24,12],[8,6]]\n解释：p[0][0] = grid[0][1] * grid[1][0] * grid[1][1] = 2 * 3 * 4 = 24\np[0][1] = grid[0][0] * grid[1][0] * grid[1][1] = 1 * 3 * 4 = 12\np[1][0] = grid[0][0] * grid[0][1] * grid[1][1] = 1 * 2 * 4 = 8\np[1][1] = grid[0][0] * grid[0][1] * grid[1][0] = 1 * 2 * 3 = 6\n所以答案是 [[24,12],[8,6]] 。\n\n
示例 2：
\n\n\n输入：grid = [[12345],[2],[1]]\n输出：[[2],[0],[0]]\n解释：p[0][0] = grid[0][1] * grid[0][2] = 2 * 1 = 2\np[0][1] = grid[0][0] * grid[0][2] = 12345 * 1 = 12345. 12345 % 12345 = 0 ，所以 p[0][1] = 0\np[0][2] = grid[0][0] * grid[0][1] = 12345 * 2 = 24690. 24690 % 12345 = 0 ，所以 p[0][2] = 0\n所以答案是 [[2],[0],[0]] 。\n\n
\n\n
提示：
\n\n1 <= n == grid.length <= 1051 <= m == grid[i].length <= 1052 <= n * m <= 1051 <= grid[i][j] <= 109'/' (division operation).",
"Create two 2D arrays for suffix and prefix product, and use them to find the product for each position."
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