Exercise 4.7. Let A[1..m] be a sequence of integers. Recalling that a subsequence is (strictly) increasing if each successive integer is strictly greater than the previous. Here we consider two variants of the longest increasing subsequence problem. In the first problem, we want to find the longest increasing subsequence where the sum of integers in the subsequence is even. In the second problem, we want to find the longest increasing subsequence where the sum of integers in the subsequence is odd. For both of these problems, either (a) design and analyze an efficient algo- rithm for the problem, or (b) show that a polynomial time algorithm implies a polynomial time algorithm for SAT