CF558D Guess Your Way Out! II

Amr bought a new video game "Guess Your Way Out! II". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height $ h $ . The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the nodes of the tree such that - The root is number $ 1 $ - Each internal node $ i $ ( $ i

The first line contains two integers $ h,q $ ( $ 1

If the information provided by the game is contradictory output "Game cheated!" without the quotes. Else if you can uniquely identify the exit to the maze output its index. Otherwise output "Data not sufficient!" without the quotes.

Node $ u $ is an ancestor of node $ v $ if and only if - $ u $ is the same node as $ v $ , - $ u $ is the parent of node $ v $ , - or $ u $ is an ancestor of the parent of node $ v $ . In the first sample test there are $ 4 $ leaf nodes $ 4,5,6,7 $ . The first question says that the node isn't in the range $ [4,6] $ so the exit is node number $ 7 $ . In the second sample test there are $ 8 $ leaf nodes. After the first question the exit is in the range $ [10,14] $ . After the second and the third questions only node number $ 14 $ is correct. Check the picture below to fully understand.