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:
frenz = 0
store = []
main = []
n,m,k = raw_input().split()
n = int(n)
m = int(m)
k = int(k)

for o in range(0,n):
    main.append(0)

for i in range(0,m):
    x = bin(input())
    temp = []
    for o in range(0,n):
        temp.append(0)
    for ii in range(0,len(x)-2):
        temp[n-(len(x)-2)+ii] = int(x[ii+2])
    store.append(temp)

x = bin(input())
for i in range(0,len(x)-2):
    main[n-(len(x)-2)+i] = int(x[i+2])

for z in store:
    q = 0
    w = k
    na = True
    for zz in z:
        if zz != main[q]:
            w -= 1
        q += 1
    if w >= 0:
        frenz += 1

print frenz