Buggy python submission (verdict: Runtime Error):
def delete_head_zeros(n):
	n = str(n)
	l = len(n)
	if "." in n:
		l = n.find(".")
	head_zeros = 0
	for i in range(l - 1):
		if n[i] == "0":
			head_zeros += 1
		else:
			break

	return n[head_zeros:]

# compare a, b
# a, b: int or string
def bigint_compare(a, b):
	a = delete_head_zeros(a)
	b = delete_head_zeros(b)
	if len(a) > len(b):
		return 1
	elif len(a) < len(b):
		return -1
	else:
		if a > b:
			return 1
		elif a < b:
			return -1
		else:
			return 0

# calculate a + b
# a, b: int or string
def bigint_plus(a, b):
	a = str(a)
	b = str(b)

	d = max([len(a), len(b)])
	a = '0' * (d - len(a)) + a
	b = '0' * (d - len(b)) + b

	ans = ""
	carry = 0
	for i in range(d):
		s = int(a[-i-1]) + int(b[-i-1]) + carry
		carry = s // 10
		ans = str(s % 10) + ans
	else:
		if carry:
			ans = str(carry) + ans

	return ans

# calculate a - b
# a, b: int or string
def bigint_minus(a, b): 
	a = str(a)
	b = str(b)
	M = []
	m = []
	sign = ""

	if len(a) > len(b) or (len(a) == len(b) and a >= b):
		[M, m] = [a, b]
	else:
		[M, m] = [b, a]
		sign = "-"
	m = '0' * (len(M) - len(m)) + m

	ans = ""
	borrow = 0
	for i in range(len(M)):
		s = int(M[-i-1]) - int(m[-i-1]) - borrow
		if s < 0:
			borrow = 1
			s += 10
		else:
			borrow = 0
		ans = str(s) + ans

	return sign + delete_head_zeros(ans)

# calculate a * b
# a, b: int or string
def bigint_multiply(a, b):
	a = str(a)
	b = str(b)

	md = []
	for j in range(len(b)):
		carry = 0
		mj = ""
		for i in range(len(a)):
			m = int(a[-i-1]) * int(b[-j-1]) + carry
			carry = m // 10
			mj = str(m % 10) + mj
		else:
			if carry:
				mj = str(carry) + mj
		md.append(mj)

	ans = 0
	for k in range(len(md)):
		ans = bigint_plus(md[k] + "0" * k, ans)

	return ans


# calculate a / b to d digits after decimal point
# a, b, d: int or string
def bigint_divide(a, b, d = 0):
	a = str(a)
	b = str(b)
	d = int(d)
	if d < 0:
		d = 0

	ans = ""
	r = ""
	for i in range(len(a) + d):
		q = 0
		if i < len(a):
			r += a[i]
		elif i == len(a):
			ans += "."
			r += "0"
		else:
			r += "0"

		if bigint_compare(r, b) == -1:
			ans += str(q)
		else:
			while bigint_compare(r, b) >= 0:
				r = bigint_minus(r, b)
				q += 1
			ans += str(q)

	return delete_head_zeros(ans)

def main():
	N, K = input().split(" ")
	A = [int(a) - 1 for a in input().split(" ")]
	visited = [0] * int(N)
	towns = []
	now = 0
	while visited[now] == 0:
		towns.append(now)
		visited[now] = 1
		now = A[now]
	else:
		loop_begin_idx = towns.index(now)
		loop_end_idx = len(towns) - 1
		loop_n = loop_end_idx - loop_begin_idx + 1
	if int(K) <= len(towns) + 1:
		print(towns[int(K)] + 1)
		return 0
	K_from_loop = bigint_minus(K, loop_begin_idx)
	q = bigint_divide(K_from_loop, loop_n)
	r = bigint_minus(K_from_loop, bigint_multiply(loop_n, q))
	print(towns[loop_begin_idx + int(r)] + 1)

main()


Fixed submission:
def delete_head_zeros(n):
	n = str(n)
	l = len(n)
	if "." in n:
		l = n.find(".")
	head_zeros = 0
	for i in range(l - 1):
		if n[i] == "0":
			head_zeros += 1
		else:
			break

	return n[head_zeros:]

# compare a, b
# a, b: int or string
def bigint_compare(a, b):
	a = delete_head_zeros(a)
	b = delete_head_zeros(b)
	if len(a) > len(b):
		return 1
	elif len(a) < len(b):
		return -1
	else:
		if a > b:
			return 1
		elif a < b:
			return -1
		else:
			return 0

# calculate a + b
# a, b: int or string
def bigint_plus(a, b):
	a = str(a)
	b = str(b)

	d = max([len(a), len(b)])
	a = '0' * (d - len(a)) + a
	b = '0' * (d - len(b)) + b

	ans = ""
	carry = 0
	for i in range(d):
		s = int(a[-i-1]) + int(b[-i-1]) + carry
		carry = s // 10
		ans = str(s % 10) + ans
	else:
		if carry:
			ans = str(carry) + ans

	return ans

# calculate a - b
# a, b: int or string
def bigint_minus(a, b): 
	a = str(a)
	b = str(b)
	M = []
	m = []
	sign = ""

	if len(a) > len(b) or (len(a) == len(b) and a >= b):
		[M, m] = [a, b]
	else:
		[M, m] = [b, a]
		sign = "-"
	m = '0' * (len(M) - len(m)) + m

	ans = ""
	borrow = 0
	for i in range(len(M)):
		s = int(M[-i-1]) - int(m[-i-1]) - borrow
		if s < 0:
			borrow = 1
			s += 10
		else:
			borrow = 0
		ans = str(s) + ans

	return sign + delete_head_zeros(ans)

# calculate a * b
# a, b: int or string
def bigint_multiply(a, b):
	a = str(a)
	b = str(b)

	md = []
	for j in range(len(b)):
		carry = 0
		mj = ""
		for i in range(len(a)):
			m = int(a[-i-1]) * int(b[-j-1]) + carry
			carry = m // 10
			mj = str(m % 10) + mj
		else:
			if carry:
				mj = str(carry) + mj
		md.append(mj)

	ans = 0
	for k in range(len(md)):
		ans = bigint_plus(md[k] + "0" * k, ans)

	return ans


# calculate a / b to d digits after decimal point
# a, b, d: int or string
def bigint_divide(a, b, d = 0):
	a = str(a)
	b = str(b)
	d = int(d)
	if d < 0:
		d = 0

	ans = ""
	r = ""
	for i in range(len(a) + d):
		q = 0
		if i < len(a):
			r += a[i]
		elif i == len(a):
			ans += "."
			r += "0"
		else:
			r += "0"

		if bigint_compare(r, b) == -1:
			ans += str(q)
		else:
			while bigint_compare(r, b) >= 0:
				r = bigint_minus(r, b)
				q += 1
			ans += str(q)

	return delete_head_zeros(ans)

def main():
	N, K = input().split(" ")
	A = [int(a) - 1 for a in input().split(" ")]
	visited = [0] * int(N)
	towns = []
	now = 0
	while visited[now] == 0:
		towns.append(now)
		visited[now] = 1
		now = A[now]
	else:
		loop_begin_idx = towns.index(now)
		loop_end_idx = len(towns) - 1
		loop_n = loop_end_idx - loop_begin_idx + 1
	if int(K) < len(towns):
		print(towns[int(K)] + 1)
		return 0
	K_from_loop = bigint_minus(K, loop_begin_idx)
	q = bigint_divide(K_from_loop, loop_n)
	r = bigint_minus(K_from_loop, bigint_multiply(loop_n, q))
	print(towns[loop_begin_idx + int(r)] + 1)

main()