AoCG2021 Day 21: Blinking through the forestAoCG2021 Day 21: Blinking through the forest
Part of Advent of Code Golf 2021 event. See the linked meta post for details.
Related to AoC2020 Day 3.
In the way to vacation, you're traveling through a forest on an airplane. For some biological and geological reasons, the trees in this forest grow only at the exact integer coordinates on a grid, and the entire forest repeats itself infinitely to the right. For example, if the map (input) looks like this (# for trees and . for empty spaces):
..##.......
#...#...#..
.#....#..#.
..#.#...#.#
.#...##..#.
..#.##.....
.#.#.#....#
.#........#
#.##...#...
#...##....#
.#..#...#.#
the forest actually looks like this:
..##.........##.........##.........##.........##.........##....... --->
#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..
.#....#..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#.
..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#
.#...##..#..#...##..#..#...##..#..#...##..#..#...##..#..#...##..#.
..#.##.......#.##.......#.##.......#.##.......#.##.......#.##..... --->
.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#
.#........#.#........#.#........#.#........#.#........#.#........#
#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...
#...##....##...##....##...##....##...##....##...##....##...##....#
.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.# --->
Starting at the top-left corner of this forest and moving at a rational slope (e.g. 3/2 represents two units to the right and 3 units down), how many trees will you encounter until you escape the forest through the bottom row?
Input: A rectangular grid representing the map, and a rational number (non-zero, non-infinity) representing the slope of your movement. You can use any two distinct values (numbers/chars) to represent trees and empty spaces respectively. You can take two positive integers for the slope instead of a rational number, and the two numbers are guaranteed to be coprime.
Output: The number of trees you will encounter during the flight.
Standard code-golf rules apply. The shortest code in bytes wins.
Test cases
Grid:
.##
#.#
##.
down/right -> trees
1/1 -> 0
99/1 -> 0
2/1 -> 1
2/3 -> 1
1/2 -> 2
1/3 -> 2
1/99 -> 2
Grid: (the one shown at the top)
down/right -> trees
1/1 -> 2
1/3 -> 7
1/5 -> 3
1/7 -> 4
2/1 -> 2