1253 - Reconstruct a 2-Row Binary Matrix.

Medium

Given the following details of a matrix with n columns and 2 rows :

• The matrix is a binary matrix, which means each element in the matrix can be 0 or 1.

• The sum of elements of the 0-th(upper) row is given as upper.

• The sum of elements of the 1-st(lower) row is given as lower.

• The sum of elements in the i-th column(0-indexed) is colsum[i], where colsum is given as an integer array with length n.

Your task is to reconstruct the matrix with upper, lower and colsum.

Return it as a 2-D integer array.

If there are more than one valid solution, any of them will be accepted.

If no valid solution exists, return an empty 2-D array.

Example 1:

Input: upper = 2, lower = 1, colsum = 1,1,1

Output: [1,1,0,0,0,1]

Explanation: [1,0,1,0,1,0], and [0,1,1,1,0,0] are also correct answers.

Example 2:

Input: upper = 2, lower = 3, colsum = 2,2,1,1

Output: []

Example 3:

Input: upper = 5, lower = 5, colsum = 2,1,2,0,1,0,1,2,0,1

Output: [1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0,1,1,0,1]

Constraints:

• 1 <= colsum.length <= 10^5

• 0 <= upper, lower <= colsum.length

• 0 <= colsum[i] <= 2