from math import floor, ceil
from sys import stdin, setrecursionlimit
setrecursionlimit(int(2e5))
def solve():
n, k = map(int, input().split(" "))
col = list(map(int, input().split(" ")))
adj = [[] for _ in range(n)]
for i in range(1, n):
x = int(input())
adj[x].append(i)
def dfs1(v: int, level: int, vertices: list[int]): # Calculate the number of vertices in a given level of a subtree
vertices[level] += 1
for to in adj[v]: dfs1(to, level+1, vertices)
def dfs2(v: int, level: int, colorCnt: list[list[int]]): # Calculate the number of vertices of color c at level i
colorCnt[level][col[v]] += 1
for to in adj[v]: dfs2(to, level+1, colorCnt)
res = [0, 0]
def dfs(v: int, level: int, colorCnt: list[list[int]]):
nonlocal res
c = col[v]
vertices = [0] * n
dfs1(v, level, vertices)
colorCntSubtree = [[0] * k for _ in range(n)]
dfs2(v, level, colorCntSubtree)
coders = swaps = 0
for l in range(level+1, n):
swaps += min(vertices[l] - colorCntSubtree[l][c], colorCnt[l][c] - colorCntSubtree[l][c])
# if v == 0 and swaps:
# print(l, vertices[l] - colorCntSubtree[l][c])
# return
coders += min(vertices[l], colorCnt[l][c])
if coders > res[0] or (coders == res[0] and swaps < res[1]):
res = [coders, swaps]
for to in adj[v]:
dfs(to, level+1, colorCnt)
colorCnt = [[0] * k for _ in range(n)] # colorCnt[l][k] denotes number of vertices of color k at level l
dfs2(0, 0, colorCnt)
dfs(0, 0, colorCnt)
print(res[0]+1, res[1])
solve()
