RSA Factorization

Time Limit: 1000MS

Memory Limit: 65536K

Description

The positive integer n is given. It is known that n = p * q, where p and q are primes, q <= p and |q - kp| <= 105 for some given positive integer k. You must find p and q.

Input

Each line contains integers n (1 < n < 10120) and k (0 < k < 108).

Output

For each pair of numbers n and k print in separate line the product p * q such that q <= p.

Sample Input

35 1 
121 1 
1000730021 9

Sample Output

5 * 7 
11 * 11 
10007 * 100003

Hint

Source

Southeastern European Regional Programming Co

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