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= [int(i) for i in input().split()]

players1 = []
for i in range(m+1):
    s = int(input())
    players1.append(s)

#print(players1)


def binary(t,n):
    result = ''
    while True:
        a = t%2
        b = t//2
        if b == 0:
            result = '1' + result
            break
        if b != 1:
            result = str(a)+result
            t = b
        else:
            result = str(b) + str(a) + result
            break
    if len(result)<n:
        result = (n-len(result))*'0'+result
    return result

players2 = []
for j in range(m+1):
    l = binary(players1[j],n)
    players2.append(l)

#print(players2)

Fedor = players2[m]
#print(Fedor)

def friend(s1,s2,k):
    if len(s1) != len(s2):
        return ValueError('lengths not equal')
    else:
        total = 0
        for j in range(len(s1)):
            if s1[j]!=s2[j]:
                total += 1
        if total>k:
            return(0)
        else:
            return(1)

friends = 0
for i in range(m):
    friends += friend(Fedor,players2[i],k)

print(friends)