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:
def dif(a, b):
    b,a,ans=max(a,b),min(a,b),0
    c,d=[],[]
    i=0
    while a>0:
        if a%2==1:
            c.append(1)
        else:
            c.append(0)
        a//=2
        i+=1
    i=0
    while b>0:
        if b%2==1:
            d.append(1)
        else:
            d.append(0)
        b//=2
    for i in range(len(c)):
        if c[i]!=d[i]:
            ans+=1
    for i in range(len(c),len(d)):
        if d[i]==1:
            ans+=1
    return ans
n,m,k = map(int,input().split())
ans=0
x=[]
for i in range(m+1):
    x.append(int(input()))
for i in range(m):
    if dif(x[i], x[m])<=k:
        ans+=1
print(ans)