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Language/Type: PHP recursion

Write a recursive function named count_to_by that accepts integer parameters $n and $m and that produces output indicating how to count to $n in increments of $m separated by commas. For example, to count to 10 by 1 you'd say count_to_by(10, 1); The following table shows several other calls and their expected output:

Call Meaning Output
count_to_by(10,1); count to 10 by 1s 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
count_to_by(25,4); count to 25 by 4s 1, 5, 9, 13, 17, 21, 25
count_to_by(30,4); count to 30 by 4s 2, 6, 10, 14, 18, 22, 26, 30
count_to_by(34,5); count to 34 by 5s 4, 9, 14, 19, 24, 29, 34
count_to_by(3,6); count to 3 by 6s 3
count_to_by(17,3); count to 17 by 3s 2, 5, 8, 11, 14, 17

Notice that the increment does not have to be 1, such as when counting to 25 by 4s. The count must always end at $n, but notice that at will not always be possible to start counting at 1, as shown in the output when $n is 30 and $m is 4. But the first number should always be in the range of 1 to $m inclusive. It is possible that only one number will be printed, as shown in the output when $n is 3 and $m is 6.

Your function should throw an Exception if either $m or $n is less than 1. Note that the output does not advance to the next line.

Type your PHP solution code here:

This is a function exercise. Write a PHP function as described. Do not write a complete program; just the function(s) above.

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