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 = map(int,input().split())
mylist = [None]*(m+1)
for i  in range(0,m+1):
    mylist[i] = int(input())
    str2 = str(n)
    strr = ('{0:0'+str2+'b}')
    mylist[i] = strr.format(mylist[i])
NoOfOnes = 0
res = 0
for i in range(m):
    y = int(mylist[m],2) ^ int(mylist[i],2)
    ybinary = strr.format(y)
    for j in range(len(ybinary)):
        if ybinary[j] == '1':
            NoOfOnes = NoOfOnes + 1
            if NoOfOnes > k:
                break
    if NoOfOnes <= k:
        res = res + 1
    NoOfOnes = 0
print(res)