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 PYTHON):

Solution:
#!/usr/bin/python

def ir():
    return int(raw_input())

def ia():
    line = raw_input()
    line = line.split()
    return map(int, line)

def n2d(d):
    ans = []
    for i in range(n):
        ans.append(d % 2)
        d = d / 2
    return ans

n, m, k = ia()

L = list()
for i in range(m):
    a = ir()
    L.append(n2d(a))

def diff(A, B):
    ans = 0
    for a, b in zip(A, B):
        if a is not b:
            ans = ans + 1
    return ans
    
M = n2d(ir())
ans = 0
for l in L:
    if diff(l, M)<=k: ans=ans+1

print ans