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=list(map(int,input().split()))
a=[]
for i in range(m+1):
    y=int(input())
    a.append(y)
t=bin(a[-1])[2:]
maini=0
for i in range(len(a)-1):
    y=bin(a[i])[2:]
    if len(y)>len(t):
        pepsi='0'*(len(y)-len(t))+t
        pepso=y
    elif len(t)>len(y):
        pepsi='0'*(len(t)-len(y))+y
        pepso=t
    else:
        pepsi=t
        pepso=y
    count=0
    
    for j in range(len(pepsi)):
        if pepsi[j]!=pepso[j]:
            count+=1
            if count>k:
                break
    if count<=k:
        #print(pepso,pepsi,count)
        maini+=1
print(maini)