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:
l1=[int(x) for x in input().split()]
n=l1[0]
m=l1[1]
k1=l1[2]
l2=[]
out=0
for i in range(0,m+1):
    inp=int(input())
    l2.append(inp)
b2=str(bin(l2[len(l2)-1]))
l3=[]
for i in range(2,len(b2)):
    l3.append(b2[i])
for i in range(0,len(l2)-1):
    b1=str(bin(l2[i]))
    l4=[]
    for j in range(2,len(b1)):
        l4.append(b1[j])
    k=len(l4)-1
    m1=len(l3)-1
    enemy=0
    while k>=0 or m1>=0:
        if(k>=0 and m1>=0):
            if(l3[m1]!=l4[k]):
                enemy+=1
        elif(k>=0 and m1<0):
            if(l4[k]=='1'):
                enemy+=1
        elif(m1>=0 and k<0):
            if(l3[m1]=='1'):
                enemy+=1
        m1-=1
        k-=1
    if(enemy<=k1):
        out+=1
print(out)