[PAT]:1103 Integer Factorization——DFS

PAT:1103 Integer Factorization （30 分）
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 = n[1]^P + … n[K]^P

where n[i] (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+4²+2²+2²+1², or 11²​ +6^​2+​2²+2^​2+2²,or more. You must output the one with the maximum sum of the factors. If there is a tie, the largest factor sequence must be chosen – sequence { a​1​​ ,a​2,⋯,a​K} is said to be larger than { b1,b​2,⋯,bK } if there exists 1≤L≤K such that a​i=b​ifor ib​L.
If there is no solution, simple output Impossible.

Sample Input 1:

169 5 2

Sample Output 1:

169 = 6² + 6² + 6² + 6² + 5²

Sample Input 2:

169 167 3

Sample Output 2:

Impossible