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:
def solve(a,k):
    ans=0
    for i in range(len(a)-1):
        if get(a[i],a[-1])<=k:
            ans+=1
    
    return ans
    


def get(A,B):
    count=0
    for i in range(0,32): 
        # right shift both the numbers by 'i' and 
        # check if the bit at the 0th position is different 
        if ((( A >>  i) & 1) != (( B >>  i) & 1)):  
             count=count+1
    
    return count


# s='GGGB'
# print(solve(list(s),1))

    
# t=int(input(''))
# ans=[]
# while t>0:
#     # n=int(input(''))
#     a=list(map(int,input('').split(' ')))
#     s=input('')
#     ans.append(solve(list(s),a[1]))
#     t-=1

# for i in ans:
#     for j in i:
#         print(j,end='')
#     print()


# n=int(input(''))
a=list(map(int,input('').split(' ')))
x=[]
for i in range(a[1]+1):
    x.append(int(input('')))
print(solve(x,a[2]))