Generate tree from tab-indented file

Input:

dir1
	subdir1
		file1.txt
		file2.txt
	file3.txt
dir2
	file4.txt

Output:

.
├── dir1
│   ├── file3.txt
│   └── subdir1
│       ├── file1.txt
│       └── file2.txt
└── dir2
    └── file4.txt

4 directories, 4 files

A rough script for what's desired:

# tab2tree
#!/bin/sh

awk '\
	BEGIN { FS = "\t"; delete stack }

	{
		depth = 0
		while (substr($0, depth+1, 1) == "\t") {
			depth++
		}

		path = ""
		for (i = 0; i < depth; i++) {
			path = path stack[i] "/"
		}
		print path $NF
		stack[depth] = $NF
	}
' | tree --fromfile .

Usage: cat input.txt | tab2tree