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:
list=[int(x) for x in raw_input().split()]
n=list[0]
m=list[1]
k=list[2]
def differenceinbits(n1,n2):
    a=bin(n1)
    b=bin(n2)
    a=a[2:]
    b=b[2:]
    count=0
    if(len(a)>len(b)):
        i=len(b)
        j=len(a)-1
        while(i<len(a)):
            i+=1
            b='0'+b
    else:
        i=len(a)
        j=len(b)-1
        while(i<len(b)):
            i+=1
            a='0'+a
    while(j>=0):
        if(a[j]!=b[j]):
            count+=1
        j-=1
    return count
collection=[]
for i in range(m+1):
    collection.append(input())
finalcount=0
j=0
# print collection[m]
while(j<m):
    if(differenceinbits(collection[j],collection[m]) <= k):
        finalcount+=1
        # print bin(collection[j]),bin(collection[m]),differenceinbits(collection[j],collection[m])
    j+=1
print finalcount