Sereja and BOX

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Sereja has a box A with size N*N*N, where N=2^{Q} for some integer Q. Each cell A(i, j, k) contains some binary value (zero or one). Sereja now has C++ function F(A) (where the box A is parameter of the function F):
int F(box A, int dx = 0, int dy = 0, int dz = 0, int size = N) {
vector B = {};
for (int i = dx; i < dx + size; i++) {
for (int j = dy; j < dy + size; j++) {
for (int k = dz; k < dz + size; k++) {
B.push_back(A[i][j][k]);
}
}
}
sort(B.begin(), B.end());
if (B[0] == B[size * size * size  1]) {
return 1;
}
int result = 0;
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
for (int k = 0; k < 2; k++) {
result += f(A,
dx + i * size / 2,
dy + j * size / 2,
dz + k * size / 2,
size / 2);
}
}
}
return result;
}
This function computes compression level of the box. Sereja now wants to know minimal and maximal value of F(D) among all boxes D which has same dimensions as A and differ in no more than K cells with A.
Input
First line contains integers N and K.
Each of N next blocks contains N lines, each line contains N numbers, kth number in jth line of ith block means value of A(i,j,k).
Output
Output two numbers in a single line  minimal and maximal value of F(D).
Constraints
 1 ≤ N ≤ 32
 1 ≤ K ≤ N^{3}
Subtasks
 Subtask #1: 1 ≤ N ≤ 2 (5 points)
 Subtask #2: 1 ≤ N ≤ 4 (15 points)
 Subtask #3: 1 ≤ N ≤ 8 (20 points)
 Subtask #4: 1 ≤ N ≤ 16 (25 points)
 Subtask #5: original constraints (35 points)
Example 1
Input: 2 0 0 0 0 0 0 0 0 0 Output: 1 1
Example 2
Input: 2 1 0 0 0 0 0 0 0 0 Output: 1 8
Author:  sereja 
Editorial  https://discuss.codechef.com/problems/SEABOX 
Tags  adhoc, dynamicprogramming, jan17, knapsack, mediumhard, sereja 
Date Added:  7102016 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, PYP3, CLOJ, FS 
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