Distribute Coins in Binary Tree

You’re given the root of a binary tree with n nodes and a total of n coins. Each node node.val is the number of coins at that node. In one move, you may move one coin between two adjacent nodes (parent ↔ child).
Return the minimum number of moves to make every node have exactly one coin.

Key idea (postorder flow):
Let balance(node) = coins that must flow out of this node to its parent (positive = surplus to send up, negative = deficit to receive) after balancing its children.
For each node:

• Get L = balance(left), R = balance(right).

• Moves added here = |L| + |R| (each coin unit flowing across an edge costs 1 move).

• Node’s balance to parent = node.val + L + R - 1.
  Sum moves across all nodes.