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You are given the number of rows n_rows and number of columns n_cols of a 2D binary matrix where all values are initially 0. Write a function flip which chooses a 0 value uniformly at random, changes it to 1, and then returns the position [row.id, col.id] of that value. Also, write a function reset which sets all values back to 0. Try to minimize the number of calls to system's Math.random() and optimize the time and space complexity.

Note:

  1. 1 <= n_rows, n_cols <= 10000
  2. 0 <= row.id < n_rows and 0 <= col.id < n_cols
  3. flip will not be called when the matrix has no 0 values left.
  4. the total number of calls to flip and reset will not exceed 1000.

Example 1:

Input: 
["Solution","flip","flip","flip","flip"]
[[2,3],[],[],[],[]]
Output: [null,[0,1],[1,2],[1,0],[1,1]]

Example 2:

Input: 
["Solution","flip","flip","reset","flip"]
[[1,2],[],[],[],[]]
Output: [null,[0,0],[0,1],null,[0,0]]

Explanation of Input Syntax:

The input is two lists: the subroutines called and their arguments. Solution's constructor has two arguments, n_rows and n_colsflip and reset have no arguments. Arguments are always wrapped with a list, even if there aren't any.

class Solution { public Solution(int n_rows, int n_cols) { } public int[] flip() { } public void reset() { } } /** * Your Solution object will be instantiated and called as such: * Solution obj = new Solution(n_rows, n_cols); * int[] param_1 = obj.flip(); * obj.reset(); */