Problem: 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 xi. Consider binary representation of xi: if the j-th bit of number xi 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.

Input

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.

Output

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

Examples

Input

7 3 1
8
5
111
17


Output

0


Input

3 3 3
1
2
3
4


Output

3

Solution (in PYTHON3):

Solution:
m=input()
m=m.split(' ')
n=int(m[0])
k=int(m[2])
m=int(m[1])
count=0
arr=list()
for i in range(0,m+1):
    a=int(input())
    arr.append(a)
for i in range(0,m):
    num=arr[i]&arr[m]
    num1=arr[i]|arr[m]
    num1=bin(num1).count('0')-1
    num=bin(num)
    size1=len(bin(arr[i]))
    size2=len(bin(arr[m]))
    if(size1>size2):
        size=size1-2-num1
    else:
        size=size2-2-num1
    num=size-num.count('1')
    if(num<=k):
        count=count+1
print(count)