Do both part and please don't use chat gpt and provide a detailed answer.

2 NP Completeness [30 marks] Scan your cleanly written answer in pdf document. Consider the decision problem called FairSplit-D: Instance: There is a list of n integers, a1,a2,,an, indexed by S=1,,n. Problem: Is there a partition S=AB with AB= such that iAai=iBai. 1. Prove that FairSplit-D NPC. Use reduction from Subset Sum, i.e. show how to transform Subset Sum problem to an instance of FairSplit-D, in such a way that the conversion can be used to solve the Subset Sum question. 1 2. Consider the following modification in the FairSplit-D problem. FairSplit1000 Input: a list of n integers, a1,a2,,an, indexed by S=1,,n. Problem: Is there a partition S=AB with AB= such that iAaiiBai1000. Prove that FairSplit1000 NPC. Use your proof from Part 1 and reduce FairSplit-D to FairSplit1000. 2 NP Completeness [30 marks] Scan your cleanly written answer in pdf document. Consider the decision problem called FairSplit-D: Instance: There is a list of n integers, a1,a2,,an, indexed by S=1,,n. Problem: Is there a partition S=AB with AB= such that iAai=iBai. 1. Prove that FairSplit-D NPC. Use reduction from Subset Sum, i.e. show how to transform Subset Sum problem to an instance of FairSplit-D, in such a way that the conversion can be used to solve the Subset Sum question. 1 2. Consider the following modification in the FairSplit-D problem. FairSplit1000 Input: a list of n integers, a1,a2,,an, indexed by S=1,,n. Problem: Is there a partition S=AB with AB= such that iAaiiBai1000. Prove that FairSplit1000 NPC. Use your proof from Part 1 and reduce FairSplit-D to FairSplit1000