Buggy python submission (verdict: Runtime Error):
#d  tree
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
def dfs(u, d):
    change = 0
    if d>k:
        d = 1
        change += 1
    for v in edges[u]:
        if u!=v:
            change += dfs(v, d+1)
    return change


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

edges = [[] for _ in range(n)]
for i in range(0,n):
    pa = a[i]
    edges[a[i]].append(i)   

cnt += dfs(0,0)    
print(cnt)

Fixed submission:
#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)

Buggy python submission (verdict: Runtime Error):
#d  tree
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
def dfs(u, d):
    change = 0
    if d>k:
        d = 1
        change += 1
    for v in edges[u]:
        if u==v:
            continue
        change += dfs(v, d+1)
    return change


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

edges = [[] for _ in range(n)]
for i in range(0,n):
    pa = a[i]
    edges[a[i]].append(i)   

cnt += dfs(0,0)    
print(cnt)

Fixed submission:
#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)

Buggy python submission (verdict: Runtime Error):
#d  tree
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
def dfs(u, d):
    change = 0
    if d>k:
        d = 1
        change += 1
    for v in edges[u]:
        change += dfs(v, d+1)
    return change


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)   

cnt += dfs(0,0)    
print(cnt)

Fixed submission:
#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)