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,k1=map(int,input().split())
#print(n,m,k1)
l=[]
for i in range(m+1):
    a=int(input())
    x=bin(a)
    l.append(x[2:])
#print(l)
count1=0
x=l[m]
k=len(x)-1
for i in range(m):
    #print(count1)
    #print("!!")
    z=l[i]
    #print(z)
    j=len(l[i])-1
    #print(j)
    k=len(x)-1
    #print(k)
    diff=0
    while(j>=0 and k>=0):
     #   print(j,k)
     #  print(z[j],x[k])
        if(z[j]!=x[k]):
            diff=diff+1
        j=j-1
        k=k-1
    while(j>=0):
      #  print(j,z[j])
        if(z[j]=='1'):
            diff=diff+1
        j=j-1
    while(k>=0):
       # print(k,x[k])
        if(x[k]=='1'):
            diff=diff+1
        k=k-1
    if(diff<=k1):
        count1=count1+1
print(count1)