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()))
p=[]
sa=[]
sol=0
ki=0
for x in range(m+1):
    if x!=m:
        p.append((bin(int(input())))[2:])
    else:
     sa.append((bin(int(input())))[2:])
pin=list(str(sa[0]))
for item in p:
    td=list(str(item))
    if abs(len(td)-len(pin))>0:
        if len(td)>len(pin):
            for z in range(abs(len(td)-len(pin))):
                pin.insert(0,"0")
        else:
            for z in range(abs(len(td)-len(pin))):
                td.insert(0,"0")
    for x in range(len(td)):
        if td[x]==pin[x]:
            pass
        else:
            sol+=1
    if sol<=k:
        ki+=1
    else:
        pass
    sol=0
    pin=list(str(sa[0]))
print(ki)