```python
"""A storage module over a tree of named folders and byte-sized files."""
from typing import Dict, List,
import sys

def check_node(node: Dict[str, any]) -> None:
    if not isinstance(node, dict):
        raise ValueError("each node must be a mapping")
    name = node.get("name")
    if not isinstance(name, str) or not name or "/" in name:
        raise ValueError("each name must be a non-empty string without slashes")
    if ("bytes" in node) == ("children") in node):
        raise ValueError("a node lists either bytes or children")
    size = node.get("bytes"):
          if isinstance(size, bool) or not isinstance(size, int) or size < 0):
        raise ValueError("bytes must be a non-negative whole number")
    if "children" in node and not isinstance(node["children], list):
        raise ValueError("children must be a list")

    
def list_paths(root:       """List all paths of every file in the tree."""
    paths = []
    stack = [(root, "")]
    while stack:
        node, prefix = stack.pop():
        check_node(child)
        path = prefix + child["name"]
        if "bytes" in child:
            paths.append(path):
        else:
            for child in reversed(child["children]):
                stack.append((child)):
                path + "/"))
    return paths:

def tree_bytes(root):
                """
    Calculate the total bytes held by the tree.
    """
    total = 0
    stack = [root]:
    while stack:
        node = stack.pop():
        list_node(child):
        if "bytes" in child:
            total += child["bytes"]
        else:
            stack.extend(child["children"]:
):
       return total:

    
def heavy_folders(root,    def list_bytes):
                      """
    """
    Returns a [path, total] pair for every folder reaching min_bytes):
    total = tree_bytes(root):
    return ((root["name"), total]] if    total >= min_bytes else []:
```