class Solution {
  private TreeNode getLowestCommonAncestor(TreeNode node, int key1, int key2) {
    if (node == null) {
      return null;
    }

    if (node.val == key1 || node.val == key2) {
      return node;
    }

    var left = getLowestCommonAncestor(node.left, key1, key2);
    var right = getLowestCommonAncestor(node.right, key1, key2);

    if (left == null) {
      return right;
    }

    if (right == null) {
      return left;
    }

    return node;
  }

  private record Path(boolean found, StringBuilder path) {}

  private Path getPath(TreeNode node, int key, StringBuilder path) {
    if (node == null) {
      return new Path(false, path);
    }

    if (node.val == key) {
      return new Path(true, path);
    }

    // go left
    path.append('L');
    var leftPath = getPath(node.left, key, path);
    if (leftPath.found) {
      return leftPath;
    }
    path.deleteCharAt(path.length() - 1);

    // go right
    path.append('R');
    var rightPath = getPath(node.right, key, path);
    if (rightPath.found) {
      return rightPath;
    }
    path.deleteCharAt(path.length() - 1);

    return new Path(false, path);
  }

  public String getDirections(TreeNode root, int startValue, int destValue) {
    var commonAncestor = getLowestCommonAncestor(root, startValue, destValue);
    var pathToStart = getPath(commonAncestor, startValue, new StringBuilder());
    var pathToDest = getPath(commonAncestor, destValue, new StringBuilder());

    var directions = new StringBuilder();

    // gotta go up from the start
    directions.repeat('U', pathToStart.path.length());

    // and then follow the directions down
    directions.append(pathToDest.path);

    return directions.toString();
  }
}