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.

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