4[bvg 3.6 (modified)] in this exercise, all integers are considered to be nonnegative, for simplicity. a divisor of an integer k is any integer d 6= 0 such that k/d has no remainder. a common divisor for a set of integers is an integer that is a divisor for each integer in the set. euclid’s algorithm for finding the greatest common divisor (gcd) of two nonnegative integers, m and n, can be written as follows: 1: procedure gcd(int m, int n) 2: if n = 0 then 3: nser ← m 4: else if m < n then 5: nser ← gcd(n, m) 6: else 7: r ← m − n · b m n c . r is the remainder of m n 8: nser ← gcd(n, r) 9: end if 10: return nser 11: end procedure the preconditions for gcd(m, n) are that m ≥ 0, n ≥ 0 and m + n > 0. prove the following using induction. a. if the preconditions of gcd(m, n) are satisfied, then the value that the function returns is some common divisor of m and n. data structures and algorithms homework 1 fall 2019 — crn 41417 b. if the preconditions of gcd(m, n) are satisfied, then the value that the function returns is the greatest common divisor of m and n. hints: if d is a divisor of k, how can you rewrite k in terms of d? how do you show that two sets are equal?