p04008 AtCoder Grand Contest 004 - Teleporter
There are N towns in Snuke Kingdom, conveniently numbered 1 through N. Town 1 is the capital.

Each town in the kingdom has a Teleporter, a facility that instantly transports a person to another place. The destination of the Teleporter of town i is town a_i (1≤a_i≤N). It is guaranteed that one can get to the capital from any town by using the Teleporters some number of times.

King Snuke loves the integer K. The selfish king wants to change the destination of the Teleporters so that the following holds:

* Starting from any town, one will be at the capital after using the Teleporters exactly K times in total.



Find the minimum number of the Teleporters whose destinations need to be changed in order to satisfy the king's desire.

Constraints

* 2≤N≤10^5
* 1≤a_i≤N
* One can get to the capital from any town by using the Teleporters some number of times.
* 1≤K≤10^9

Input

The input is given from Standard Input in the following format:


N K
a_1 a_2 ... a_N


Output

Print the minimum number of the Teleporters whose destinations need to be changed in order to satisfy King Snuke's desire.

Examples

Input

3 1
2 3 1


Output

2


Input

4 2
1 1 2 2


Output

0


Input

8 2
4 1 2 3 1 2 3 4


Output

3
```python
#d  tree
#code自体はあっている。ただ、そもそもアルゴリズムが違う。
#下から調べていかないと最適でない。
#Right Answer. 
import sys
sys.setrecursionlimit(2 * 10 ** 5 + 10)

n,k =  [int(i) for i in input().split()]
a   =  [int(i)-1 for i in input().split()]

#this is directed tree so every node is not reached yet
#return the depth from its lowest bottom
def dfs(u):
    global cnt
    depth = 0 #default, this value is used when bottom
    
    for v in edges[u]:
        depth = max(depth, (dfs(v)+1)%k) #apply the maximum depth
        #because the edge was alerady cut, by the following procedure
    
    if depth==k-1 and u!=0 and a[u] != 0:
        cnt += 1
        
    return depth


cnt = 0
if a[0]!=0:
    cnt += 1

edges = [[] for _ in range(n)]
for i in range(1,n):
    pa = a[i]
    edges[a[i]].append(i)   

dfs(0)    
print(cnt)
```