Problem: In Walrusland public transport tickets are characterized by two integers: by the number of the series and by the number of the ticket in the series. Let the series number be represented by a and the ticket number — by b, then a ticket is described by the ordered pair of numbers (a, b). 

The walruses believe that a ticket is lucky if a * b = rev(a) * rev(b). The function rev(x) reverses a number written in the decimal system, at that the leading zeroes disappear. For example, rev(12343) = 34321, rev(1200) = 21.

The Public Transport Management Committee wants to release x series, each containing y tickets, so that at least w lucky tickets were released and the total number of released tickets (x * y) were minimum. The series are numbered from 1 to x inclusive. The tickets in each series are numbered from 1 to y inclusive. The Transport Committee cannot release more than maxx series and more than maxy tickets in one series.

Input

The first line contains three integers maxx, maxy, w (1 ≤ maxx, maxy ≤ 105, 1 ≤ w ≤ 107).

Output

Print on a single line two space-separated numbers, the x and the y. If there are several possible variants, print any of them. If such x and y do not exist, print a single number  - 1.

Examples

Input

2 2 1


Output

1 1

Input

132 10 35


Output

7 5

Input

5 18 1000


Output

-1


Input

48 132 235


Output

22 111

Solution (in PYTHON):

Solution:
from collections import defaultdict
from fractions import gcd

(max_x, max_y, w) = map( int, raw_input().split() )

def Pair(x):
    inv_x = 0
    val = x
    while val:
        inv_x = inv_x * 10 + val % 10
        val /= 10
    uc = gcd( x, inv_x )
    return ( x/uc, inv_x/uc )

def Reverse(P):
    return ( P[1], P[0] )

MapX = defaultdict(int)
MapY = defaultdict(int)
for y in xrange(1, max_y+1):
    MapY[ Pair(y) ] += 1
    
y = max_y
lucky_tickets = 0
res = ( 100007, 100007 )
for x in xrange(1, max_x+1):
    lucky_tickets += MapY[ Reverse( Pair(x) ) ]
    MapX[ Pair(x) ] += 1
    while (y > 0)and( lucky_tickets - MapX[ Reverse( Pair(y) ) ] >= w ):
        lucky_tickets -= MapX[ Reverse( Pair(y) ) ]
        MapY[ Pair(y) ] -= 1
        y -= 1
        
    if (lucky_tickets >= w) and ( x * y < res[0] * res[1] ):
        res = (x, y)
        
if res[0] == 100007:
    print -1
else:
    print "%d %d" % res