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 bi(l,n):
    b = ''
    for i in range(0,l):
        b = str(n%2) + b
        n//=2
    return b

def exe():
    players = []
    n,m,k = list(map(int,input().split()))
    for i in range(m+1):
        players.append(int(input()))
    def bil(num):
        return bi(n,num)
    print(result(list(map(bil,players)),n,k))

def result(bip,n,k):
    fed = bip.pop(-1)
    ans=0
    for i in range(len(bip)):
        temp = 0
        for j in range(n):
            temp += 1 if (str(fed)[j] != str(bip[i])[j]) else 0
        if temp<=k:
            ans += 1
    return ans

exe()