#include "encoder.h"
#include "encoderlib.h"
#include <bits/stdc++.h>
using namespace std;
namespace encoder {
struct bignum {
vector<int> digits;
int len = 0;
bignum() {}
bignum(int X) {
while (X) {
digits.push_back(X & 1);
X >>= 1;
}
len = digits.size();
}
void norm() {
while (len > 0 && digits.back() == 0) {
digits.pop_back();
len--;
}
}
int& operator[](int pos) {
if (pos >= len) {
digits.resize(pos + 1);
len = pos + 1;
}
return digits[pos];
}
};
ostream& operator<<(ostream &out, bignum B) {
int X = 0;
for (int i = B.len - 1; i >= 0; i--) {
X = X << 1 | B[i];
}
out << X;
return out;
}
bignum operator+(bignum B1, bignum B2) {
bignum res;
int len = max(B1.len, B2.len);
int rem = 0;
for (int i = 0; i < len; i++) {
int sum = B1[i] + B2[i] + rem;
res[i] = sum & 1;
rem = sum >> 1;
}
if (rem) {
res[len] = 1;
}
return res;
}
bignum operator-(bignum B1, bignum B2) {
bignum res;
int rem = 0;
for (int i = 0; i < B1.len; i++) {
int diff = B1[i] - B2[i] + rem;
res[i] = diff & 1;
rem = diff >> 1;
}
res.norm();
return res;
}
bool operator>(bignum B1, bignum B2) {
B1.norm();
B2.norm();
if (B1.len != B2.len) {
return B1.len > B2.len;
}
for (int i = B1.len - 1; i >= 0; i--) {
if (B1[i] != B2[i]) {
return B1[i] > B2[i];
}
}
return false;
}
const int maxL = 350;
bignum dp[maxL][256];
vector<int> solve(int N, int M[]) {
for (int i = 0; i < 256; i++) {
dp[0][i] = bignum(1);
}
for (int i = 1; i < maxL; i++) {
dp[i][0] = bignum(1);
for (int j = 1; j < 256; j++) {
dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
}
}
bignum msg;
for (int i = 0; i < N; i++) {
for (int j = 0; j < 8; j++) {
msg[i << 3 | j] = (M[i] >> j) & 1;
}
}
msg.norm();
msg = msg + bignum(1);
int len = 0;
while (msg > dp[len][255]) {
msg = msg - dp[len][255];
len++;
}
vector<int> res;
for (int i = len; i >= 1; i--) {
for (int j = 0; j < 256; j++) {
if (!(msg > dp[i][j])) {
res.push_back(j);
if (j > 0) {
msg = msg - dp[i][j - 1];
}
break;
}
}
}
return res;
}
}
void encode(int N, int M[]) {
vector<int> res = encoder::solve(N, M);
for (auto val: res) {
send(val);
}
}
#include "decoder.h"
#include "decoderlib.h"
#include <bits/stdc++.h>
using namespace std;
namespace decoder {
struct bignum {
vector<int> digits;
int len = 0;
bignum() {}
bignum(int X) {
while (X) {
digits.push_back(X & 1);
X >>= 1;
}
len = digits.size();
}
void norm() {
while (len > 0 && digits.back() == 0) {
digits.pop_back();
len--;
}
}
int& operator[](int pos) {
if (pos >= len) {
digits.resize(pos + 1);
len = pos + 1;
}
return digits[pos];
}
};
ostream& operator<<(ostream &out, bignum B) {
int X = 0;
for (int i = B.len - 1; i >= 0; i--) {
X = X << 1 | B[i];
}
out << X;
return out;
}
bignum operator+(bignum B1, bignum B2) {
bignum res;
int len = max(B1.len, B2.len);
int rem = 0;
for (int i = 0; i < len; i++) {
int sum = B1[i] + B2[i] + rem;
res[i] = sum & 1;
rem = sum >> 1;
}
if (rem) {
res[len] = 1;
}
return res;
}
bignum operator-(bignum B1, bignum B2) {
bignum res;
int rem = 0;
for (int i = 0; i < B1.len; i++) {
int diff = B1[i] - B2[i] + rem;
res[i] = diff & 1;
rem = diff >> 1;
}
res.norm();
return res;
}
bool operator>(bignum B1, bignum B2) {
B1.norm();
B2.norm();
if (B1.len != B2.len) {
return B1.len > B2.len;
}
for (int i = B1.len - 1; i >= 0; i--) {
if (B1[i] != B2[i]) {
return B1[i] > B2[i];
}
}
return false;
}
const int maxL = 350;
bignum dp[maxL][256];
vector<int> solve(int N, int L, int X[]) {
for (int i = 0; i < 256; i++) {
dp[0][i] = bignum(1);
}
for (int i = 1; i < maxL; i++) {
dp[i][0] = bignum(1);
for (int j = 1; j < 256; j++) {
dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
}
}
sort(X, X + L);
bignum msg(0);
for (int i = 0; i < L; i++) {
msg = msg + dp[i][255];
}
for (int i = L - 1; i >= 0; i--) {
if (X[i] > 0) {
msg = msg + dp[i + 1][X[i] - 1];
}
}
vector<int> res(N);
for (int i = 0; i < N; i++) {
for (int j = 0; j < 8; j++) {
res[i] |= (msg[i << 3 | j] << j);
}
}
return res;
}
}
void decode(int N, int L, int X[]) {
vector<int> res = decoder::solve(N, L, X);
for (auto val: res) {
output(val);
}
}
