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:
arr1 = str(input())
arr2 = arr1.split()
#print(arr2)
n = int(arr2[0])
m = int(arr2[1])
k = int(arr2[2])

arr = []
for i in range(m + 1):
    v = int(input())
    arr.append(v)

me = arr[-1]

xor = []

for i in range(m):
    diff = me ^ arr[i]
    xor.append(diff)

count = 0 

for i in xor:
    bits = "{0:b}".format(i)
    countbit = 0
    for j in bits:
        if j == "1":
            countbit += 1 
        
        if countbit > k:
            count += 1 
            break

diff = m - count 

print(diff)