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:
a=input().split()
c=[]
for i in range(0,int(a[1])+1):
    b=int(input())
    c.append(int(b))
m=max(c)
friends=0
def binary(aa):
    bb=""
    while(aa>1):
        bb=bb+str(aa%2)
        aa=aa//2
    bb=bb+str(aa%2)
    bb=(bb[::-1])
    return list(bb)
poo=binary(m)
poo=len(poo)
def bits(fg,kg):
    global friends
    binn=binary(fg)
    binnn=binary(kg)
    if(len(binn)<poo):
        pd=poo-len(binn)
        binn=['0']*pd+binn
    if(len(binnn)<poo):
        pd=poo-len(binnn)
        binnn=['0']*pd+binnn
    #print(binn)
    #print(binnn)
    count=0
    for i in range(0,poo):
        #print(binn[i],binnn[i])
        if(binn[i]!=binnn[i]):
            count=count+1
            #print(count)
    if(count<=int(a[2])):
        friends=friends+1
for i in range(0,int(a[1])):
    bits(c[-1],c[i])
print(friends)