1103. Integer Factorization (30)
The K-P factorization of a positive integer N is to write N as the sum of the P-th power of K positive integers. You are supposed to write a program to find the K-P factorization of N for any positive integers N, K and P.
Input Specification:
Each input file contains one test case which gives in a line the three positive integers N (<=400), K (<=N) and P (1<P<=7). The numbers in a line are separated by a space.
Output Specification:
For each case, if the solution exists, output in the format:
N = n1^P + ... nK^P
where ni (i=1, ... K) is the i-th factor. All the factors must be printed in non-increasing order.
Note: the solution may not be unique. For example, the 5-2 factorization of 169 has 9 solutions, such as 122
If there is no solution, simple output "Impossible".
Sample Input 1:169 5 2Sample Output 1:
169 = 6^2 + 6^2 + 6^2 + 6^2 + 5^2Sample Input 2:
169 167 3Sample Output 2:
Impossible