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:
n,m,k=map(int,input().split())
t=[]
mx=0
c1=0
for i in range(m+1):
    zahl=input()
    bit=bin(int(zahl))
    if len(bit)>mx:
        mx=len(bit)
    t.append(bit[2::])
pepe=t[-1][::-1]
pepe+=str(0)*(mx-len(pepe))
lol=pepe[::-1]
for i in range(m):
    pepe=t[i][::-1]
    pepe+=str(0)*(mx-len(pepe))
    pepe=pepe[::-1]
    j=0
    ch=0
    while ch<=k and j<mx:
        if pepe[j]!=lol[j]:
            ch+=1
        j+=1
    if ch<=k:
        c1+=1
print(c1)