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.

输入描述:

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 xi(1 ≤ xi ≤ 2n - 1), that describes the i-th player's army. We remind you that Fedor is the (m + 1)-th player.

输出描述:

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