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≤k≤n≤20;1≤m≤1000).

The i-th of the next (m+1) lines contains a single integer x_i (1≤x_i≤2ⁿ-1), that describes the i-th player's army. We remind you that Fedor is the (m+1)-th player.

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