Given two numbers n and k, find the k^{th} prime factor of n. 
Example 1:
Input: n = 225, k = 2
Output: 3
Explaination: The prime factors 3, 3, 5 
and 5. So 3 is the 2nd one.
Example 2:
Input: n = 81, k = 5
Output: -1
Explaination: The 4 prime factors are 
3, 3, 3, 3. So there is no 5th one.
Your Task:
You do not need to read input or print anything. Your task is to complete the function kthPrime() which takes the value n and k as input parameters and return the kth prime number. If k is greater than total number of primes then return -1.
Expected Time Complexity: O(n*log(log n))
Expected Auxiliary Space: O(n)
Constraints:
1 ≤ n ≤ 10^{4}
1 ≤ k ≤ 50

Source: geeksforgeeks | Difficulty: EASY
Tags: Number theory

Mathematics

Starter code: #User function Template for python3



class Solution:

    def kthPrime(self, n, k):

        # code here

Solutions:
class Solution:

	def prime(self, n):
		for i in range(2, int(n ** 0.5) + 1):
			if n % i == 0:
				return False
		return True

	def kthPrime(self, n, k):
		l = []
		c = 0
		for i in range(2, n + 1):
			if self.prime(i):
				while n % i == 0:
					l.append(i)
					n = n // i
		if len(l) >= k:
			return l[k - 1]
		else:
			return -1


class Solution:

	def isprime(self, n):
		if n == 1:
			return False
		for i in range(2, int(n ** 0.5) + 1):
			if n % i == 0:
				return False
		return True

	def kthPrime(self, n, k):
		l = []
		for i in range(2, n + 1, 1):
			if n % i == 0 and self.isprime(i):
				while n % i == 0:
					l.append(i)
					n = n // i
		if len(l) < k:
			return -1
		return l[k - 1]


class Solution:

	def kthPrime(self, n, k):
		div = 2
		while n > 1 and k > 0:
			if n % div == 0:
				n //= div
				k -= 1
			else:
				div += 1
		if k != 0:
			return -1
		return div


class Solution:

	def kthPrime(self, n, k):
		result = -1
		cnt = 0
		if n == 0:
			return -1
		while n % 2 == 0:
			cnt += 1
			if cnt == k:
				return 2
			n = n // 2
		for i in range(3, int(n ** 0.5) + 1, 2):
			while n % i == 0:
				cnt += 1
				if k == cnt:
					return i
				n = n // i
		if n > 2 and cnt + 1 == k:
			return n
		return result


class Solution:

	def kthPrime(self, n, k):
		if n == 0:
			return -1
		else:
			l1 = []
			sieve = [0] * (n + 1)
			for i in range(n + 1):
				sieve[i] = i
			for i in range(2, int(n ** 0.5)):
				if sieve[i] == i:
					for j in range(i * i, n + 1, i):
						if sieve[j] == j:
							sieve[j] = i
			while n != 1:
				factor = sieve[n]
				if k > 1:
					k -= 1
				else:
					return factor
				n = n // sieve[n]
			return -1


import math

class Solution:

	def kthPrime(self, n, k):

		def isprime(x):
			if x <= 1:
				return False
			for i in range(2, int(math.sqrt(x)) + 1):
				if x % i == 0:
					return False
			return True
		a = []
		for i in range(2, n + 1):
			if isprime(i):
				while n % i == 0:
					a.append(i)
					n //= i
		a.sort()
		if len(a) >= k:
			return a[k - 1]
		else:
			return -1


class Solution:

	def foo(self, n):
		for i in range(2, n + 1):
			if n % i == 0:
				return i

	def factor(self, n):
		l = []
		while n > 1:
			p = self.foo(n)
			l.append(p)
			n = n // p
		return l

	def check_prime(self, n):
		for i in range(2, int(n ** 0.5 + 1)):
			if n % i == 0:
				return False
		return True

	def kthPrime(self, n, k):
		res = self.factor(n)
		if len(res) < k:
			return -1
		c = 0
		for i in res:
			if self.check_prime(i):
				c += 1
			if c == k:
				return i
		return -1


class Solution:

	def kthPrime(self, n, k):
		m = n
		for i in range(2, m + 1):
			while n % i == 0:
				k -= 1
				n = n // i
				if k == 0:
					return i
			i = i * i
		if n > 1:
			k -= 1
			if k == 0:
				return n
		return -1


class Solution:

	def kthPrime(self, n, k):
		if n < 1:
			return -1
		cnt = 0
		while n % 2 == 0:
			n //= 2
			cnt += 1
			if cnt == k:
				return 2
		i = 3
		while i * i <= n:
			while n % i == 0:
				n //= i
				cnt += 1
				if cnt == k:
					return i
			i += 2
		if n > 2:
			cnt += 1
			if cnt == k:
				return n
		return -1


class Solution:

	def kthPrime(self, n, k):
		a = []
		for i in range(2, n + 1):
			while n % i == 0:
				a.append(i)
				n = n // i
		if k > len(a):
			return -1
		else:
			return a[k - 1]


class Solution:

	def kthPrime(self, n: int, k: int) -> int:
		import math
		if n < 2:
			return -1
		count = 0
		while n % 2 == 0:
			count += 1
			if count == k:
				return 2
			n //= 2
		for i in range(3, int(math.sqrt(n)) + 1):
			while n % i == 0:
				count += 1
				if count == k:
					return i
				n //= i
		if n > 1:
			count += 1
			if count == k:
				return n
		return -1


def isprime(n):
	if n <= 1:
		return 0
	for i in range(2, n // 2):
		if n % i == 0:
			return 0
	return 1

class Solution:

	def kthPrime(self, n, k):
		c = 0
		i = 2
		while i <= n and n != 0:
			if n % i == 0:
				n //= i
				c += 1
				if c == k:
					return i
				i -= 1
			i += 1
		return -1


def prime(a):
	if a <= 1:
		return 0
	if a == 2:
		return 1
	for i in range(2, int(a ** 0.5) + 1):
		if a % i == 0:
			return 0
	else:
		return 1

class Solution:

	def kthPrime(self, n, k):
		s = []
		l = []
		for i in range(2, 10000):
			if prime(i):
				s.append(i)
		while n > 0:
			for i in s:
				if n % i == 0:
					l.append(i)
					n //= i
					break
			else:
				n = 0
		if k > len(l):
			return -1
		else:
			return l[k - 1]


from math import sqrt

class Solution:

	def kthPrime(self, n, k):
		ans = []
		for i in range(2, n + 1):
			while n % i == 0:
				ans.append(i)
				n = n // i
		if len(ans) < k:
			return -1
		return ans[k - 1]


class Solution:

	def kthPrime(self, n, k):

		def prime_factors(N):
			i = 2
			lst = []
			if N == 2:
				lst.append(2)
				return lst
			else:
				while i * i <= N + 1:
					if N % i == 0:
						while N % i == 0:
							lst.append(i)
							N = N // i
					i += 1
				if N != 1:
					lst.append(N)
			return lst
		res = prime_factors(n)
		if k > len(res):
			return -1
		return res[k - 1]


class Solution:

	def kthPrime(self, num, k):
		i = 2
		ans = []
		while num > 1:
			if num % i == 0:
				ans.append(i)
				num //= i
			else:
				i += 1
		if len(ans) < k:
			return -1
		else:
			return ans[k - 1]


class Solution:

	def kthPrime(self, n, k):
		count = 0
		i = 2
		while i <= n and n > 0:
			if n % i == 0:
				n = n // i
				count = count + 1
				if count == k:
					return i
				i = i - 1
			i = i + 1
		return -1


class Solution:

	def kthPrime(self, n, k):
		m = int(n ** 0.5)
		l = []
		for i in range(2, m + 1):
			while n % i == 0:
				l.append(i)
				n = n // i
		if n != 1:
			l.append(n)
		try:
			return l[k - 1]
		except:
			return -1


class Solution:

	def kthPrime(self, n, k):
		i = 2
		while i * i <= n:
			while n % i == 0:
				k -= 1
				n = n // i
				if k == 0:
					return i
			else:
				i += 1
		if n > 1:
			k -= 1
			if k == 0:
				return n
		return -1


class Solution:

	def kthPrime(self, n, k):
		spf = []
		for i in range(n + 1):
			spf.append(i)
		for i in range(2, int(n ** 0.5) + 1):
			if spf[i] == i:
				for j in range(i * i, n + 1, i):
					if spf[j] == j:
						spf[j] = i
		cnt = 0
		while n > 1:
			x = spf[n]
			while n % x == 0:
				cnt += 1
				if cnt == k:
					return x
				n = n // x
		return -1


class Solution:

	def kthPrime(self, n, k):
		import math
		if n == 0 or n == 1:
			return -1
		lista = []
		for i in range(2, int(math.sqrt(n)) + 1):
			while n % i == 0:
				lista.append(i)
				n = n // i
		if n > 1:
			lista.append(n)
		if len(lista) < k:
			return -1
		return lista[k - 1]


import math

class Solution:

	def kthPrime(self, n, k):
		l = 10001
		siv = [0] * l
		for i in range(2, int(math.sqrt(l)) + 1):
			if siv[i] == 0:
				for j in range(2 * i, l, i):
					siv[j] = 1
		lis = []
		for i in range(2, n + 1):
			if siv[i] == 0 and n % i == 0:
				m = n
				while m % i == 0:
					lis.append(i)
					m //= i
		if len(lis) < k:
			return -1
		return lis[k - 1]
if __name__ == '__main__':
	t = int(input())
	for _ in range(t):
		(n, k) = [int(x) for x in input().split()]
		ob = Solution()
		print(ob.kthPrime(n, k))


class Solution:

	def kthPrime(self, n, k):
		if n < 2:
			return -1
		for i in range(2, n + 1):
			if n % i == 0:
				while n % i == 0:
					k -= 1
					n //= i
					if k == 0:
						return i
		return -1
if __name__ == '__main__':
	t = int(input())
	for _ in range(t):
		(n, k) = [int(x) for x in input().split()]
		ob = Solution()
		print(ob.kthPrime(n, k))


class Solution:

	def kthPrime(self, N, k):
		a = N
		ans = []
		if N == 0:
			return -1
		while N % 2 == 0:
			N = N // 2
			ans.append(2)
		for i in range(3, a + 1, 2):
			while N % i == 0:
				ans.append(i)
				N = N // i
		if k > len(ans):
			return -1
		return ans[k - 1]


import math

class Solution:

	def kthPrime(self, N, k):
		if N == 0:
			return -1
		ans = []
		while N % 2 == 0:
			ans.append(2)
			N = N // 2
		while N % 3 == 0:
			ans.append(3)
			N = N // 3
		for i in range(5, int(math.sqrt(N)) + 1, 6):
			while N % i == 0:
				ans.append(i)
				N = N // i
			while N % (i + 2) == 0:
				ans.append(i + 2)
				N = N // (i + 2)
		if N > 4:
			ans.append(N)
		if k > len(ans):
			return -1
		return ans[k - 1]


import math

class Solution:

	def kthPrime(self, n, k):
		l = 10001
		siv = [0] * l
		for i in range(2, int(math.sqrt(l)) + 1):
			if siv[i] == 0:
				for j in range(2 * i, l, i):
					siv[j] = 1
		lis = []
		for i in range(2, n + 1):
			if siv[i] == 0 and n % i == 0:
				m = n
				while m % i == 0:
					lis.append(i)
					m //= i
		if len(lis) < k:
			return -1
		return lis[k - 1]


class Solution:

	def kthPrime(self, n, k):
		if n == 0 or n == 1:
			return -1
		l = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973]
		i = 0
		j = 0
		while n != 1 and j != k:
			if n % l[i] == 0:
				n = n // l[i]
				j += 1
			else:
				i += 1
		if j == k:
			return l[i]
		else:
			return -1


class Solution:

	def kthPrime(self, n, k):
		l = []
		x = 2
		while n > 1:
			if n % x == 0:
				l.append(x)
				n = n / x
			else:
				x = x + 1
		if len(l) < k:
			return -1
		else:
			return l[k - 1]


class Solution:

	def kthPrime(self, n, k):
		if n == 0:
			return -1
		a = []
		N = n + 1
		primes = [0] * N

		def Seive(self, N):
			for i in range(N):
				primes[i] = i
			primes[0] = primes[1] = 0
			i = 2
			while i * i <= N:
				if primes[i] == i:
					j = i * i
					while j < N:
						primes[j] = i
						j += i
				i += 1
			return primes
		Seive(self, N)
		i = n
		while n != 1:
			a.append(primes[i])
			n = n // primes[i]
			i = n
		if len(a) < k:
			return -1
		a.sort()
		return a[k - 1]


class Solution:

	def kthPrime(self, n, k1):
		l = []
		sieve = []
		if n == 0:
			return -1
		for i in range(n + 1):
			sieve.append(i)
		for i in range(2, n + 1):
			if sieve[i] == i:
				for j in range(i * i, n + 1, i):
					sieve[j] = i
		while n != 1:
			k = sieve[n]
			l.append(k)
			n = n // k
		l.sort()
		if len(l) < k1:
			return -1
		return l[k1 - 1]


class Solution:

	def kthPrime(self, n, k):
		se = [0] * (n + 1)
		l = []
		for i in range(0, n + 1):
			se[i] = i
		i = 2
		while i * i <= n:
			if se[i] == i:
				for j in range(i * i, n + 1, i):
					se[j] = i
			i += 1
		if n == 0 or n == 1:
			return -1
		while n != 1:
			l.append(se[n])
			n = int(n / se[n])
		l.sort()
		if k > len(l):
			return -1
		else:
			return l[k - 1]


class Solution:

	def kthPrime(self, n, k):
		import math
		a = []
		b = []
		for i in range(n + 1):
			a.append(i)
		for i in range(2, int(math.sqrt(n)) + 1):
			for j in range(i + i, n + 1, i):
				if a[j] == j:
					a[j] = i
		while n > 1:
			b.append(a[n])
			n = n // a[n]
		if k > len(b):
			return -1
		else:
			return b[k - 1]


class Solution:

	def kthPrime(self, n, k):
		r = []
		for i in range(n + 1):
			r.append(i)
		for i in range(2, n + 1):
			if i == r[i]:
				for j in range(i * i, n + 1, i):
					if j != r[j]:
						continue
					else:
						r[j] = i
			else:
				continue
		re = []
		if n == 0 or n == 1:
			re = []
		else:
			a = n // r[n]
			re.append(r[n])
			while a > 1:
				b = a
				c = r[a]
				a = a // r[a]
				if a == 1:
					re.append(b)
					break
				else:
					re.append(c)
		if k > len(re):
			return -1
		else:
			return re[k - 1]


class Solution:

	def kthPrime(self, n, k):
		m = 0
		p = 2
		while n:
			if n % p == 0:
				n = n // p
				m = m + 1
			else:
				p = p + 1
			if m == k:
				return p
			if p > n:
				break
		return -1


import math

class Solution:

	def kthPrime(self, n, k):
		d = []
		ni = []
		for i in range(n + 1):
			d.append(i)
		for i in range(2, n + 1):
			if i == d[i]:
				for x in range(i * i, n + 1, i):
					if d[x] > i:
						d[x] = i
		while n > 1:
			c = d[n]
			ni.append(c)
			n = n // c
		a = sorted(ni)
		if len(a) > k - 1:
			return a[k - 1]
		return '-1'


class Solution:

	def kthPrime(self, n, k):
		m = n + 3
		a = [1] * m

		def seive():
			a[0] = a[1] = 0
			i = 2
			while i * i <= n:
				for j in range(i * i, n, i):
					a[j] = 0
				i += 1
			return a
		seive()
		x = []
		for i in range(n + 1):
			if a[i] == 1:
				x.append(i)
		i = 0
		arr = []
		while i <= len(x) - 1:
			if n % x[i] == 0:
				n = n // x[i]
				arr.append(x[i])
			else:
				i += 1
		if k > len(arr):
			return -1
		return arr[k - 1]


import math as m

class Solution:

	def kthPrime(self, n, k):

		def pr(x):
			if x == 0 or x == 1:
				return False
			for i in range(2, int(m.sqrt(x) + 1)):
				if x % i == 0:
					return False
			return True
		l = []
		a = 2
		while a <= n:
			if n % a == 0 and pr(a):
				l.append(a)
				n = n // a
				a = 2
			else:
				a = a + 1
		z = len(l)
		if z < k:
			return -1
		elif z == k:
			return l[-1]
		else:
			return l[k - 1]


class Solution:

	def kthPrime(self, n, k):
		a = 0
		c = 2
		while n > 1:
			if n % c == 0:
				n = n // c
				a = a + 1
			else:
				c = c + 1
			if a >= k:
				return c
		return -1


class Solution:

	def kthPrime(self, n, k):
		if n == 1 or n == 0:
			return -1
		sieve = [True for i in range(n + 1)]
		for i in range(2):
			sieve[i] = False
		i = 2
		while i * i <= n:
			if sieve[i]:
				j = i * i
				while j <= n:
					sieve[j] = False
					j += i
			i += 1
		cnt = 0
		last = n
		for i in range(2, n + 1):
			if sieve[i] and n % i == 0:
				while n % i == 0:
					n //= i
					cnt += 1
					if cnt == k:
						return i
		return -1