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:
n,m,k=[int(x) for x in input().split()]
arr=[]
for _ in range(m+1):
    arr.append(int(input()))
curr=arr[-1]
bits=set()
i=0
ans=0
for _ in range(n):
    if curr&1:
        bits.add(i)
    curr=curr>>1
    i+=1
#print(bits)
for l in arr[:-1]:
    curr=l
    #b=bits
    #print(b)
    i=0
    count=0
    for _ in range(n):
        if curr&1:
            if i not in bits:
                count+=1
        else:
            if i in bits:
                #b.remove(i)
                count+=1
                
        curr=curr>>1
        i+=1
    if count<=k:
        #print(l)
        ans+=1
print(ans)