A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level.

Now, consider a perfect binary tree T with n$=2047$ nodes. The nodes of T are labeled as follows. We label the root with value $1.$ Then we label the rest of the nodes in the way we count natural numbers in a level order. For example, the nodes in the second level have values $2$ and $3$ from left to right, and the third level has values $4,5,6,$ and $7...$ If we run depth$-$first search on T starting from the root of the tree and always visit the left child first, what is the label v of the node visted by the algorithm after running for k$=10$ steps?Now, consider a perfect binary tree T with n$=2047$ nodes. The nodes of T are labeled as follows. We label the root with value $1.$ Then we label the rest of the nodes in the way we count natural numbers in a level order. For example, the nodes in the second level have values $2$ and $3$ from left to right, and the third level has values $4,5,6,$ and $7...$ If we run depth$-$first search on T starting from the root of the tree and always visit the left child first, what is the label v of the node visted by the algorithm after running for k$=10$ steps?