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 DecToBin(num):
    if num==0:
        return '0'
    if num==1:
        return '1'
    if num%2==0:
        return DecToBin(num//2)+'0'
    else:
        return DecToBin(num//2)+'1'



n,m,k=list(map(int,input().split()))
B = []
for i in range(0,m+1):
    temp = int(input())
    stemp = DecToBin(temp)
    if len(stemp) != n:
        size = len(stemp)
        for j in range(0,n-size):
            stemp = "0" + stemp
    B.append(stemp)

counter = 0
for i in range(m):
    tcounter = 0
    for j in range(n):
        if (B[m][j] != B[i][j]):
            tcounter += 1
    if (tcounter <= k):
        counter += 1

print(counter)