Background Swarm rewards nodes for storing chunks. It does this by enabling nodes to prove on-chain that they are storing a certain amount of chunks (Swarm's native data type).The Swarm Storage incentives smart-contract suite makes use of Binary Merkle Tree's such that nodes can efficiently prove the storage of chunks. Task Imagine that you are working for Swarm, and the research team has requested that you make the smart-contracts for Swarm's storage incentives. You read up about their plans and decide to first focus on the Binary Merkle Tree as this primitive is critical in the research' team plan. It should be possible for nodes to instantiate a BMT as a compressed representation of all chunks that they are storing and subsequently to prove posession of one of the chunks contained under this representation. Assume that a chunk is 128 bytes. BONUS: Create an automated test of your contract(s) Auxiliary instructions

Contract // SPDX-License-Identifier: MIT pragma solidity ^0.8.0; contract Vault { bool public locked; bytes32 private password; constructor(bytes32 _password) { locked = true;