#include <bits/stdc++.h>
#include "encoder.h"
#include "encoderlib.h"
using namespace std;
int base = 1e9;
struct bigint {
vector<int> d;
bigint() {}
bigint(long long res) {
if (res == 0) d.emplace_back(0);
while (res > 0) {
d.emplace_back(res % 1000000000);
res /= 1000000000;
}
}
void add(const bigint& res) {
int carry = 0;
for (int i = 0; i < max(res.d.size(), d.size()) || carry; i++) {
if (i == d.size()) d.emplace_back(0);
long long cur = (long long)(res.d.size() > i ? res.d[i] : 0) + carry + d[i];
d[i] = cur % 1000000000;
carry = cur / 1000000000;
}
}
void remove(const bigint& res) {
int borrow = 0;
for (int i = 0; i < res.d.size() || borrow; i++) {
long long cur = (long long)d[i] - (res.d.size() > i ? res.d[i] : 0) - borrow;
if (cur < 0) { borrow = 1; cur += 1000000000; }
else borrow = 0;
d[i] = (int)cur;
}
while (d.size() > 1 && d.back() == 0) d.pop_back();
}
void multily(int res) {
if (res == 0) { d = {0}; return; }
long long carry = 0;
for (int i = 0; i < d.size() || carry; i++) {
if (i == d.size()) d.emplace_back(0);
long long cur = (long long)d[i] * res + carry;
d[i] = cur % 1000000000;
carry = cur / 1000000000;
}
while (d.size() > 1 && d.back() == 0) d.pop_back();
}
int divide(int res) {
long long rem = 0;
for (int i = (int)d.size() - 1; i >= 0; i--) {
long long cur = d[i] + rem * 1000000000;
d[i] = (int)(cur / res);
rem = cur % res;
}
while (d.size() > 1 && d.back() == 0) d.pop_back();
return (int)rem;
}
bool operator<(const bigint& res) const {
if (d.size() != res.d.size()) return d.size() < res.d.size();
for (int i = (int)d.size() - 1; i >= 0; i--)
if (d[i] != res.d[i]) return d[i] < res.d[i];
return false;
}
};
bigint c[700][300];
bool done_pre = false;
void precomp(int n) {
if (done_pre) return;
c[0][0] = bigint(1);
for (int i = 1; i <= 650; i++) {
c[i][0] = bigint(1);
for (int j = 1; j <= 260 && j <= i; j++) {
c[i][j] = c[i-1][j];
c[i][j].add(c[i-1][j-1]);
}
}
done_pre = true;
}
void encode(int N, int M[]) {
precomp(N);
bigint res_limit(1);
for (int i = 0; i < N; i++) res_limit.multily(256);
int L = 0;
while (c[L + 256][256] < res_limit) L++;
bigint val(0);
for (int i = N - 1; i >= 0; i--) {
val.multily(256);
val.add(bigint(M[i]));
}
int cur = L;
for (int x = 0; x <= 255; x++) {
int rem = 255-x;
for (int k = 0; k <= cur; k++) {
int nn = (cur - k) + rem-x-1;
int kk = rem-x;
if (val < c[nn][kk]) {
for (int i = 0; i < k; i++) send(x);
cur -= k;
break;
} else {
val.remove(c[nn][kk]);
}
}
}
}
#include <bits/stdc++.h>
#include "decoder.h"
#include "decoderlib.h"
using namespace std;
int base = 1e9;
struct bigint {
vector<int> d;
bigint() {}
bigint(long long res) {
if (res == 0) d.emplace_back(0);
while (res > 0) {
d.emplace_back(res % 1000000000);
res /= 1000000000;
}
}
void add(const bigint& res) {
int carry = 0;
for (int i = 0; i < max(res.d.size(), d.size()) || carry; i++) {
if (i == d.size()) d.emplace_back(0);
long long cur = (long long)(res.d.size() > i ? res.d[i] : 0) + carry + d[i];
d[i] = cur % 1000000000;
carry = cur / 1000000000;
}
}
void remove(const bigint& res) {
int borrow = 0;
for (int i = 0; i < res.d.size() || borrow; i++) {
long long cur = (long long)d[i] - (res.d.size() > i ? res.d[i] : 0) - borrow;
if (cur < 0) { borrow = 1; cur += 1000000000; }
else borrow = 0;
d[i] = (int)cur;
}
while (d.size() > 1 && d.back() == 0) d.pop_back();
}
void multily(int res) {
if (res == 0) { d = {0}; return; }
long long carry = 0;
for (int i = 0; i < d.size() || carry; i++) {
if (i == d.size()) d.emplace_back(0);
long long cur = (long long)d[i] * res + carry;
d[i] = cur % 1000000000;
carry = cur / 1000000000;
}
while (d.size() > 1 && d.back() == 0) d.pop_back();
}
int divide(int res) {
long long rem = 0;
for (int i = (int)d.size() - 1; i >= 0; i--) {
long long cur = d[i] + rem * 1000000000;
d[i] = (int)(cur / res);
rem = cur % res;
}
while (d.size() > 1 && d.back() == 0) d.pop_back();
return (int)rem;
}
bool operator<(const bigint& res) const {
if (d.size() != res.d.size()) return d.size() < res.d.size();
for (int i = (int)d.size() - 1; i >= 0; i--)
if (d[i] != res.d[i]) return d[i] < res.d[i];
return false;
}
};
bigint c[700][300];
bool done_pre = false;
void precomp(int n) {
if (done_pre) return;
c[0][0] = bigint(1);
for (int i = 1; i <= 650; i++) {
c[i][0] = bigint(1);
for (int j = 1; j <= 260 && j <= i; j++) {
c[i][j] = c[i-1][j];
c[i][j].add(c[i-1][j-1]);
}
}
done_pre = true;
}
void decode(int N, int L, int X[]) {
precomp(N);
int cnt[256] = {0};
for (int i = 0; i < L; i++) cnt[X[i]]++;
bigint v(0);
int cur = L;
for (int x = 0; x <= 255; x++) {
int k = cnt[x];
int rem_types = 255 - x;
for (int i = 0; i < k; i++) {
int nn = (cur - i) + rem_types - 1;
int kk = rem_types - 1;
v.add(c[nn][kk]);
}
cur -= k;
}
for (int i = 0; i < N; i++) {
output(v.divide(256));
}
}
