Enumerate grid points on 2D plane with descending order of (x * y)

Question

Given N > 0 and M > 0, I want to enumerate all (x, y) pairs such that 1 <= x <= N and 1 <= y <= M in descending order of (x * y). An

Answer 1

A dummy approach that loops from NxM to 1 searching for pairs that when multiplied produce the current number:

#!/usr/bin/perl

my $n = 5;
my $m = 4;

for (my $p = $n * $m; $p > 0; $p--) {
    my $min_x = int(($p + $m - 1) / $m);
    for my $x ($min_x..$n) {
        if ($p % $x == 0) {
            my $y = $p / $x;
            print("x: $x, y: $y, p: $p\n");
        }
    }
}

For N=M, complexity is O(N³) but memory usage is O(1).

Update: Note that the complexity is not as bad as it seems because the number of elements to generate is already N². For comparison, the generate-all-the-pairs-and-sort approach is O(N²logN) with O(N²) memory usage.