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:
x=[int(item) for item in input().split()]
n=x[0]
m=x[1]
k=x[2]
list2=[]
for item in range(m+1):
    list2.append(int("{0:b}".format(int(input()))))
list1=[str(i) for i in list2]
x1=list1.pop()
ansall=0
for item in list1:
    ans=0
    for char in range(1,len(str(min([int(item),int(x1)])))+1):
        if item[-char]==x1[-char]:
            ans+=0
        else:
            ans+=1
    if len(item)>len(x1):
        for num in range(len(item)-len(x1)):
            if item[num]=='1':
                ans+=1
            else:
                pass
    elif len(item)==len(x1):
        pass
    else:
        for num in range(len(x1)-len(item)):
            if x1[num]=='1':
                ans+=1 
    if ans<=k:
        ansall+=1
    else:
        ansall+=0
print(ansall)