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())
q=[]
for j in range(m):
    x=int(input())
    bits = [0] * 21
    i=20
    while i>=0:
        if x//2**(i)>=1:
            x=x%(2**(i))
            bits[i]=1
        i-=1
    q.append(bits)
x=int(input())
bits=[0]*21
i=20
while i >= 0:
    if x // 2 ** (i) >= 1:
        x = x % (2 ** (i))
        bits[i] = 1
    i -= 1
c=0
l=[]
s=0
for j in range(m):
   for i in range(21):
     if bits[i]!=q[j][i]:
         c+=1
   if c<=k:
       s+=1
   c=0
print(s)