Problem: You are given two integers n and k. Find k-th smallest divisor of n, or report that it doesn't exist.

Divisor of n is any such natural number, that n can be divided by it without remainder.

Input

The first line contains two integers n and k (1 ≤ n ≤ 1015, 1 ≤ k ≤ 109).

Output

If n has less than k divisors, output -1.

Otherwise, output the k-th smallest divisor of n.

Examples

Input

4 2


Output

2


Input

5 3


Output

-1


Input

12 5


Output

6

Note

In the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.

In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1.

Solution (in PYTHON3):

Solution:
from random import randint


def MillerRabin(n):
    d = minus_one = n - 1
    for s in range(100000):
        if d & 1:
            for a in 2, 3, 5, 7, 11, 13, 17:
                a = pow(a, d, n)
                if a != 1:
                    for _ in range(s):
                        if a == minus_one:
                            return True
                        a = a * a % n
                    else:
                        return False
            return True
        d //= 2


def pollard_brent(n):
    y, c, m = randint(1, n - 1), randint(1, n - 1), randint(1, n - 1)
    g = r = q = 1
    while g == 1:
        x = y
        for _ in range(r):
            y = (y * y + c) % n
        k = 0
        while k < r and g == 1:
            ys = y
            for _ in range(min(m, r - k)):
                y = (y * y + c) % n
                q *= abs(x - y)
                q %= n
            g, b = n, q
            while b:
                g, b = b, g % b
            k += m
        r *= 2
    if g == n:
        while True:
            ys = (ys * ys + c) % n
            g, b = n, abs(x - ys)
            while b:
                g, b = b, g % b
            if g > 1:
                break
    return g


P = (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)


def factor(x):
    result, cnt = [], 0
    for p in P:
        while not x % p:
            x //= p
            cnt += 1
        if cnt:
            result.append((p, cnt))
            if x == 1:
                return result
            cnt = 0
    if x < 3972049:  # 1993 ** 2
        result.append((x, 1))
        return result

    buf, dbuf = [], {}
    while True:
        if MillerRabin(x):
            dbuf[x] = dbuf.get(x, 0) + 1
            if buf:
                x = buf.pop()
            else:
                break
        else:
            p = pollard_brent(x)
            buf.append(p)
            x //= p
    result.extend(sorted(dbuf.items()))
    return result


def main():
    n, k = map(int, input().split())
    if k == 1:
        print(1)
        return
    if MillerRabin(n):
        print(n if k == 2 else -1)
        return
    divisors = [1]
    if n > 1 and k < 26881:
        for p, v in factor(n):
            divisors += [p * q for p in [p ** i for i in range(1, v + 1)] for q in divisors]
    print(-1 if len(divisors) < k else sorted(divisors)[k - 1])


if __name__ == '__main__':
    main()