CF467B Fedor and New Game

After you had helped George and Alex to move in the dorm, they went to help their friend Fedor play a new computer game «Call of Soldiers 3». The game has $ (m+1) $ players and $ n $ types of soldiers in total. Players «Call of Soldiers 3» are numbered form $ 1 $ to $ (m+1) $ . Types of soldiers are numbered from $ 0 $ to $ n-1 $ . Each player has an army. Army of the $ i $ -th player can be described by non-negative integer $ x_{i} $ . Consider binary representation of $ x_{i} $ : if the $ j $ -th bit of number $ x_{i} $ equal to one, then the army of the $ i $ -th player has soldiers of the $ j $ -th type. Fedor is the $ (m+1) $ -th player of the game. He assume that two players can become friends if their armies differ in at most $ k $ types of soldiers (in other words, binary representations of the corresponding numbers differ in at most $ k $ bits). Help Fedor and count how many players can become his friends.

The first line contains three integers $ n $ , $ m $ , $ k $ $ (1

Print a single integer — the number of Fedor's potential friends.