p00788 Rational Irrationals
Rational numbers are numbers represented by ratios of two integers. For a prime number p, one of the elementary theorems in the number theory is that there is no rational number equal to √p. Such numbers are called irrational numbers. It is also known that there are rational numbers arbitrarily close to √p

Now, given a positive integer n, we define a set Qn of all rational numbers whose elements are represented by ratios of two positive integers both of which are less than or equal to n. For example, Q4 is a set of 11 rational numbers {1/1, 1/2, 1/3, 1/4, 2/1, 2/3, 3/1, 3/2, 3/4, 4/1, 4/3}. 2/2, 2/4, 3/3, 4/2 and 4/4 are not included here because they are equal to 1/1, 1/2, 1/1, 2/1 and 1/1, respectively.

Your job is to write a program that reads two integers p and n and reports two rational numbers x / y and u / v, where u / v < √p < x / y and there are no other elements of Qn between u/v and x/y. When n is greater than √p, such a pair of rational numbers always exists.



Input

The input consists of lines each of which contains two positive integers, a prime number p and an integer n in the following format.


p n


They are separated by a space character. You can assume that p and n are less than 10000, and that n is greater than √p. The end of the input is indicated by a line consisting of two zeros.

Output

For each input line, your program should output a line consisting of the two rational numbers x / y and u / v (x / y > u / v) separated by a space character in the following format.


x/y u/v


They should be irreducible. For example, 6/14 and 15/3 are not accepted. They should be reduced to 3/7 and 5/1, respectively.

Example

Input

2 5
3 10
5 100
0 0


Output

3/2 4/3
7/4 5/3
85/38 38/17
```python
import sys
readline = sys.stdin.readline
write = sys.stdout.write

def stern_brocot(p, n):
    la = 0; lb = 1
    ra = 1; rb = 0
    lu = ru = 1
    lx = 0; ly = 1
    rx = 1; ry = 0
    while lu or ru:
        ma = la + ra; mb = lb + rb
        if p * mb**2 < ma**2:
            ra = ma; rb = mb
            if ma <= n and mb <= n:
                rx = ma; ry = mb
            else:
                lu = 0
        else:
            la = ma; lb = mb
            if ma <= n and mb <= n:
                lx = ma; ly = mb
            else:
                ru = 0
    return lx, ly, rx, ry

while 1:
    p, n = map(int, readline().split())
    if p == 0:
        break
    lx, ly, rx, ry = stern_brocot(p, n)
    write("%d/%d %d/%d\n" % (rx, ry, lx, ly))

```