/*
IOI 2011 Parrots
- Notice that there are (256 + N) choose 256 ways to make a non-decreasing
sequence of length N using numbers from the first 256 numbers
- There are 256^N permutations of length N from the first 256 numbers
- Since 570 choose 256 > 256^64, we can simply make each permutation to a
sequence and send that
- We need to use bigint for this
- Basically if we want a non-decreasing sequence of length N
- If the first integer is 0, there are none with first integer less
- If the first integer is 1, there are (N + 255) choose 256 with first integer less
- If the first integer is 2, there are (N + 255) choose 256 + (N + 254) choose 255 with first integer less
- etc.
*/
#include "encoder.h"
#include "encoderlib.h"
#include <bits/stdc++.h>
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("O3")
#pragma GCC target("sse4,avx2,fma,avx")
#define FOR(i, x, y) for (int i = x; i < y; i++)
typedef long long ll;
using namespace std;
/*
######################################################################
####################### THE BIG INT ##########################
*/
const int base = 1000000000;
const int base_digits = 9;
struct bigint {
vector<int> a;
int sign;
/*<arpa>*/
int size() {
if (a.empty()) return 0;
int ans = (a.size() - 1) * base_digits;
int ca = a.back();
while (ca) ans++, ca /= 10;
return ans;
}
bigint operator^(const bigint &v) {
bigint ans = 1, a = *this, b = v;
while (!b.isZero()) {
if (b % 2) ans *= a;
a *= a, b /= 2;
}
return ans;
}
string to_string() {
stringstream ss;
ss << *this;
string s;
ss >> s;
return s;
}
int sumof() {
string s = to_string();
int ans = 0;
for (auto c : s) ans += c - '0';
return ans;
}
/*</arpa>*/
bigint() : sign(1) {}
bigint(long long v) { *this = v; }
bigint(const string &s) { read(s); }
void operator=(const bigint &v) {
sign = v.sign;
a = v.a;
}
void operator=(long long v) {
sign = 1;
a.clear();
if (v < 0) sign = -1, v = -v;
for (; v > 0; v = v / base) a.push_back(v % base);
}
bigint operator+(const bigint &v) const {
if (sign == v.sign) {
bigint res = v;
for (int i = 0, carry = 0;
i < (int)max(a.size(), v.a.size()) || carry; ++i) {
if (i == (int)res.a.size()) res.a.push_back(0);
res.a[i] += carry + (i < (int)a.size() ? a[i] : 0);
carry = res.a[i] >= base;
if (carry) res.a[i] -= base;
}
return res;
}
return *this - (-v);
}
bigint operator-(const bigint &v) const {
if (sign == v.sign) {
if (abs() >= v.abs()) {
bigint res = *this;
for (int i = 0, carry = 0; i < (int)v.a.size() || carry; ++i) {
res.a[i] -= carry + (i < (int)v.a.size() ? v.a[i] : 0);
carry = res.a[i] < 0;
if (carry) res.a[i] += base;
}
res.trim();
return res;
}
return -(v - *this);
}
return *this + (-v);
}
void operator*=(int v) {
if (v < 0) sign = -sign, v = -v;
for (int i = 0, carry = 0; i < (int)a.size() || carry; ++i) {
if (i == (int)a.size()) a.push_back(0);
long long cur = a[i] * (long long)v + carry;
carry = (int)(cur / base);
a[i] = (int)(cur % base);
// asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur),
// "c"(base));
}
trim();
}
bigint operator*(int v) const {
bigint res = *this;
res *= v;
return res;
}
void operator*=(long long v) {
if (v < 0) sign = -sign, v = -v;
for (int i = 0, carry = 0; i < (int)a.size() || carry; ++i) {
if (i == (int)a.size()) a.push_back(0);
long long cur = a[i] * (long long)v + carry;
carry = (int)(cur / base);
a[i] = (int)(cur % base);
// asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur),
// "c"(base));
}
trim();
}
bigint operator*(long long v) const {
bigint res = *this;
res *= v;
return res;
}
friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
int norm = base / (b1.a.back() + 1);
bigint a = a1.abs() * norm;
bigint b = b1.abs() * norm;
bigint q, r;
q.a.resize(a.a.size());
for (int i = a.a.size() - 1; i >= 0; i--) {
r *= base;
r += a.a[i];
int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
int d = ((long long)base * s1 + s2) / b.a.back();
r -= b * d;
while (r < 0) r += b, --d;
q.a[i] = d;
}
q.sign = a1.sign * b1.sign;
r.sign = a1.sign;
q.trim();
r.trim();
return make_pair(q, r / norm);
}
bigint operator/(const bigint &v) const { return divmod(*this, v).first; }
bigint operator%(const bigint &v) const { return divmod(*this, v).second; }
void operator/=(int v) {
if (v < 0) sign = -sign, v = -v;
for (int i = (int)a.size() - 1, rem = 0; i >= 0; --i) {
long long cur = a[i] + rem * (long long)base;
a[i] = (int)(cur / v);
rem = (int)(cur % v);
}
trim();
}
bigint operator/(int v) const {
bigint res = *this;
res /= v;
return res;
}
int operator%(int v) const {
if (v < 0) v = -v;
int m = 0;
for (int i = a.size() - 1; i >= 0; --i)
m = (a[i] + m * (long long)base) % v;
return m * sign;
}
void operator+=(const bigint &v) { *this = *this + v; }
void operator-=(const bigint &v) { *this = *this - v; }
void operator*=(const bigint &v) { *this = *this * v; }
void operator/=(const bigint &v) { *this = *this / v; }
bool operator<(const bigint &v) const {
if (sign != v.sign) return sign < v.sign;
if (a.size() != v.a.size())
return a.size() * sign < v.a.size() * v.sign;
for (int i = a.size() - 1; i >= 0; i--)
if (a[i] != v.a[i]) return a[i] * sign < v.a[i] * sign;
return false;
}
bool operator>(const bigint &v) const { return v < *this; }
bool operator<=(const bigint &v) const { return !(v < *this); }
bool operator>=(const bigint &v) const { return !(*this < v); }
bool operator==(const bigint &v) const {
return !(*this < v) && !(v < *this);
}
bool operator!=(const bigint &v) const { return *this < v || v < *this; }
void trim() {
while (!a.empty() && !a.back()) a.pop_back();
if (a.empty()) sign = 1;
}
bool isZero() const { return a.empty() || (a.size() == 1 && !a[0]); }
bigint operator-() const {
bigint res = *this;
res.sign = -sign;
return res;
}
bigint abs() const {
bigint res = *this;
res.sign *= res.sign;
return res;
}
long long longValue() const {
long long res = 0;
for (int i = a.size() - 1; i >= 0; i--) res = res * base + a[i];
return res * sign;
}
friend bigint gcd(const bigint &a, const bigint &b) {
return b.isZero() ? a : gcd(b, a % b);
}
friend bigint lcm(const bigint &a, const bigint &b) {
return a / gcd(a, b) * b;
}
void read(const string &s) {
sign = 1;
a.clear();
int pos = 0;
while (pos < (int)s.size() && (s[pos] == '-' || s[pos] == '+')) {
if (s[pos] == '-') sign = -sign;
++pos;
}
for (int i = s.size() - 1; i >= pos; i -= base_digits) {
int x = 0;
for (int j = max(pos, i - base_digits + 1); j <= i; j++)
x = x * 10 + s[j] - '0';
a.push_back(x);
}
trim();
}
friend istream &operator>>(istream &stream, bigint &v) {
string s;
stream >> s;
v.read(s);
return stream;
}
friend ostream &operator<<(ostream &stream, const bigint &v) {
if (v.sign == -1) stream << '-';
stream << (v.a.empty() ? 0 : v.a.back());
for (int i = (int)v.a.size() - 2; i >= 0; --i)
stream << setw(base_digits) << setfill('0') << v.a[i];
return stream;
}
static vector<int> convert_base(const vector<int> &a, int old_digits,
int new_digits) {
vector<long long> p(max(old_digits, new_digits) + 1);
p[0] = 1;
for (int i = 1; i < (int)p.size(); i++) p[i] = p[i - 1] * 10;
vector<int> res;
long long cur = 0;
int cur_digits = 0;
for (int i = 0; i < (int)a.size(); i++) {
cur += a[i] * p[cur_digits];
cur_digits += old_digits;
while (cur_digits >= new_digits) {
res.push_back(int(cur % p[new_digits]));
cur /= p[new_digits];
cur_digits -= new_digits;
}
}
res.push_back((int)cur);
while (!res.empty() && !res.back()) res.pop_back();
return res;
}
typedef vector<long long> vll;
static vll karatsubaMultiply(const vll &a, const vll &b) {
int n = a.size();
vll res(n + n);
if (n <= 32) {
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) res[i + j] += a[i] * b[j];
return res;
}
int k = n >> 1;
vll a1(a.begin(), a.begin() + k);
vll a2(a.begin() + k, a.end());
vll b1(b.begin(), b.begin() + k);
vll b2(b.begin() + k, b.end());
vll a1b1 = karatsubaMultiply(a1, b1);
vll a2b2 = karatsubaMultiply(a2, b2);
for (int i = 0; i < k; i++) a2[i] += a1[i];
for (int i = 0; i < k; i++) b2[i] += b1[i];
vll r = karatsubaMultiply(a2, b2);
for (int i = 0; i < (int)a1b1.size(); i++) r[i] -= a1b1[i];
for (int i = 0; i < (int)a2b2.size(); i++) r[i] -= a2b2[i];
for (int i = 0; i < (int)r.size(); i++) res[i + k] += r[i];
for (int i = 0; i < (int)a1b1.size(); i++) res[i] += a1b1[i];
for (int i = 0; i < (int)a2b2.size(); i++) res[i + n] += a2b2[i];
return res;
}
bigint operator*(const bigint &v) const {
vector<int> a6 = convert_base(this->a, base_digits, 6);
vector<int> b6 = convert_base(v.a, base_digits, 6);
vll a(a6.begin(), a6.end());
vll b(b6.begin(), b6.end());
while (a.size() < b.size()) a.push_back(0);
while (b.size() < a.size()) b.push_back(0);
while (a.size() & (a.size() - 1)) a.push_back(0), b.push_back(0);
vll c = karatsubaMultiply(a, b);
bigint res;
res.sign = sign * v.sign;
for (int i = 0, carry = 0; i < (int)c.size(); i++) {
long long cur = c[i] + carry;
res.a.push_back((int)(cur % 1000000));
carry = (int)(cur / 1000000);
}
res.a = convert_base(res.a, 6, base_digits);
res.trim();
return res;
}
};
/*
####################### THE BIG INT ##########################
######################################################################
*/
bigint factorial[576], pos[576][576];
bool visited[576][576];
inline bigint choose(int a, int b) {
return factorial[a] / factorial[b] / factorial[a - b];
}
inline bigint get_pos(int len, int mn) {
if (visited[len][mn]) return pos[len][mn];
visited[len][mn] = true;
pos[len][mn] = choose(len + 255 - mn, 255 - mn);
return pos[len][mn];
}
inline void get_seq_from_idx(bigint idx, int L) {
int prev = 0;
FOR(i, 0, L) {
FOR(j, prev, 256) {
bigint t = choose(L - i + 254 - j, 255 - j);
if (t <= idx) idx -= t;
else {
send(j);
prev = j;
break;
}
}
}
}
void encode(int N, int M[]) {
factorial[0] = 1;
FOR(i, 1, 576) factorial[i] = factorial[i - 1] * i;
bigint idx = 0, bs = 1;
FOR(i, 0, N) {
idx += bs * M[i];
bs *= 256;
}
get_seq_from_idx(idx, 5 * N);
}
/*
IOI 2011 Parrots
- Notice that there are (256 + N) choose 256 ways to make a non-decreasing
sequence of length N using numbers from the first 256 numbers
- There are 256^N permutations of length N from the first 256 numbers
- Since 570 choose 256 > 256^64, we can simply make each permutation to a
sequence and send that
- We need to use bigint for this
- Basically if we want a non-decreasing sequence of length N
- If the first integer is 0, there are none with first integer less
- If the first integer is 1, there are (N + 255) choose 256 with first integer less
- If the first integer is 2, there are (N + 255) choose 256 + (N + 254) choose 255 with first integer less
- etc.
*/
#include <bits/stdc++.h>
#include "decoder.h"
#include "decoderlib.h"
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("O3")
#pragma GCC target("sse4,avx2,fma,avx")
#define FOR(i, x, y) for (int i = x; i < y; i++)
typedef long long ll;
using namespace std;
/*
######################################################################
####################### THE BIG INT ##########################
*/
const int base = 1000000000;
const int base_digits = 9;
struct bigint {
vector<int> a;
int sign;
/*<arpa>*/
int size() {
if (a.empty()) return 0;
int ans = (a.size() - 1) * base_digits;
int ca = a.back();
while (ca) ans++, ca /= 10;
return ans;
}
bigint operator^(const bigint &v) {
bigint ans = 1, a = *this, b = v;
while (!b.isZero()) {
if (b % 2) ans *= a;
a *= a, b /= 2;
}
return ans;
}
string to_string() {
stringstream ss;
ss << *this;
string s;
ss >> s;
return s;
}
int sumof() {
string s = to_string();
int ans = 0;
for (auto c : s) ans += c - '0';
return ans;
}
/*</arpa>*/
bigint() : sign(1) {}
bigint(long long v) { *this = v; }
bigint(const string &s) { read(s); }
void operator=(const bigint &v) {
sign = v.sign;
a = v.a;
}
void operator=(long long v) {
sign = 1;
a.clear();
if (v < 0) sign = -1, v = -v;
for (; v > 0; v = v / base) a.push_back(v % base);
}
bigint operator+(const bigint &v) const {
if (sign == v.sign) {
bigint res = v;
for (int i = 0, carry = 0;
i < (int)max(a.size(), v.a.size()) || carry; ++i) {
if (i == (int)res.a.size()) res.a.push_back(0);
res.a[i] += carry + (i < (int)a.size() ? a[i] : 0);
carry = res.a[i] >= base;
if (carry) res.a[i] -= base;
}
return res;
}
return *this - (-v);
}
bigint operator-(const bigint &v) const {
if (sign == v.sign) {
if (abs() >= v.abs()) {
bigint res = *this;
for (int i = 0, carry = 0; i < (int)v.a.size() || carry; ++i) {
res.a[i] -= carry + (i < (int)v.a.size() ? v.a[i] : 0);
carry = res.a[i] < 0;
if (carry) res.a[i] += base;
}
res.trim();
return res;
}
return -(v - *this);
}
return *this + (-v);
}
void operator*=(int v) {
if (v < 0) sign = -sign, v = -v;
for (int i = 0, carry = 0; i < (int)a.size() || carry; ++i) {
if (i == (int)a.size()) a.push_back(0);
long long cur = a[i] * (long long)v + carry;
carry = (int)(cur / base);
a[i] = (int)(cur % base);
// asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur),
// "c"(base));
}
trim();
}
bigint operator*(int v) const {
bigint res = *this;
res *= v;
return res;
}
void operator*=(long long v) {
if (v < 0) sign = -sign, v = -v;
for (int i = 0, carry = 0; i < (int)a.size() || carry; ++i) {
if (i == (int)a.size()) a.push_back(0);
long long cur = a[i] * (long long)v + carry;
carry = (int)(cur / base);
a[i] = (int)(cur % base);
// asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur),
// "c"(base));
}
trim();
}
bigint operator*(long long v) const {
bigint res = *this;
res *= v;
return res;
}
friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
int norm = base / (b1.a.back() + 1);
bigint a = a1.abs() * norm;
bigint b = b1.abs() * norm;
bigint q, r;
q.a.resize(a.a.size());
for (int i = a.a.size() - 1; i >= 0; i--) {
r *= base;
r += a.a[i];
int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
int d = ((long long)base * s1 + s2) / b.a.back();
r -= b * d;
while (r < 0) r += b, --d;
q.a[i] = d;
}
q.sign = a1.sign * b1.sign;
r.sign = a1.sign;
q.trim();
r.trim();
return make_pair(q, r / norm);
}
bigint operator/(const bigint &v) const { return divmod(*this, v).first; }
bigint operator%(const bigint &v) const { return divmod(*this, v).second; }
void operator/=(int v) {
if (v < 0) sign = -sign, v = -v;
for (int i = (int)a.size() - 1, rem = 0; i >= 0; --i) {
long long cur = a[i] + rem * (long long)base;
a[i] = (int)(cur / v);
rem = (int)(cur % v);
}
trim();
}
bigint operator/(int v) const {
bigint res = *this;
res /= v;
return res;
}
int operator%(int v) const {
if (v < 0) v = -v;
int m = 0;
for (int i = a.size() - 1; i >= 0; --i)
m = (a[i] + m * (long long)base) % v;
return m * sign;
}
void operator+=(const bigint &v) { *this = *this + v; }
void operator-=(const bigint &v) { *this = *this - v; }
void operator*=(const bigint &v) { *this = *this * v; }
void operator/=(const bigint &v) { *this = *this / v; }
bool operator<(const bigint &v) const {
if (sign != v.sign) return sign < v.sign;
if (a.size() != v.a.size())
return a.size() * sign < v.a.size() * v.sign;
for (int i = a.size() - 1; i >= 0; i--)
if (a[i] != v.a[i]) return a[i] * sign < v.a[i] * sign;
return false;
}
bool operator>(const bigint &v) const { return v < *this; }
bool operator<=(const bigint &v) const { return !(v < *this); }
bool operator>=(const bigint &v) const { return !(*this < v); }
bool operator==(const bigint &v) const {
return !(*this < v) && !(v < *this);
}
bool operator!=(const bigint &v) const { return *this < v || v < *this; }
void trim() {
while (!a.empty() && !a.back()) a.pop_back();
if (a.empty()) sign = 1;
}
bool isZero() const { return a.empty() || (a.size() == 1 && !a[0]); }
bigint operator-() const {
bigint res = *this;
res.sign = -sign;
return res;
}
bigint abs() const {
bigint res = *this;
res.sign *= res.sign;
return res;
}
long long longValue() const {
long long res = 0;
for (int i = a.size() - 1; i >= 0; i--) res = res * base + a[i];
return res * sign;
}
friend bigint gcd(const bigint &a, const bigint &b) {
return b.isZero() ? a : gcd(b, a % b);
}
friend bigint lcm(const bigint &a, const bigint &b) {
return a / gcd(a, b) * b;
}
void read(const string &s) {
sign = 1;
a.clear();
int pos = 0;
while (pos < (int)s.size() && (s[pos] == '-' || s[pos] == '+')) {
if (s[pos] == '-') sign = -sign;
++pos;
}
for (int i = s.size() - 1; i >= pos; i -= base_digits) {
int x = 0;
for (int j = max(pos, i - base_digits + 1); j <= i; j++)
x = x * 10 + s[j] - '0';
a.push_back(x);
}
trim();
}
friend istream &operator>>(istream &stream, bigint &v) {
string s;
stream >> s;
v.read(s);
return stream;
}
friend ostream &operator<<(ostream &stream, const bigint &v) {
if (v.sign == -1) stream << '-';
stream << (v.a.empty() ? 0 : v.a.back());
for (int i = (int)v.a.size() - 2; i >= 0; --i)
stream << setw(base_digits) << setfill('0') << v.a[i];
return stream;
}
static vector<int> convert_base(const vector<int> &a, int old_digits,
int new_digits) {
vector<long long> p(max(old_digits, new_digits) + 1);
p[0] = 1;
for (int i = 1; i < (int)p.size(); i++) p[i] = p[i - 1] * 10;
vector<int> res;
long long cur = 0;
int cur_digits = 0;
for (int i = 0; i < (int)a.size(); i++) {
cur += a[i] * p[cur_digits];
cur_digits += old_digits;
while (cur_digits >= new_digits) {
res.push_back(int(cur % p[new_digits]));
cur /= p[new_digits];
cur_digits -= new_digits;
}
}
res.push_back((int)cur);
while (!res.empty() && !res.back()) res.pop_back();
return res;
}
typedef vector<long long> vll;
static vll karatsubaMultiply(const vll &a, const vll &b) {
int n = a.size();
vll res(n + n);
if (n <= 32) {
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) res[i + j] += a[i] * b[j];
return res;
}
int k = n >> 1;
vll a1(a.begin(), a.begin() + k);
vll a2(a.begin() + k, a.end());
vll b1(b.begin(), b.begin() + k);
vll b2(b.begin() + k, b.end());
vll a1b1 = karatsubaMultiply(a1, b1);
vll a2b2 = karatsubaMultiply(a2, b2);
for (int i = 0; i < k; i++) a2[i] += a1[i];
for (int i = 0; i < k; i++) b2[i] += b1[i];
vll r = karatsubaMultiply(a2, b2);
for (int i = 0; i < (int)a1b1.size(); i++) r[i] -= a1b1[i];
for (int i = 0; i < (int)a2b2.size(); i++) r[i] -= a2b2[i];
for (int i = 0; i < (int)r.size(); i++) res[i + k] += r[i];
for (int i = 0; i < (int)a1b1.size(); i++) res[i] += a1b1[i];
for (int i = 0; i < (int)a2b2.size(); i++) res[i + n] += a2b2[i];
return res;
}
bigint operator*(const bigint &v) const {
vector<int> a6 = convert_base(this->a, base_digits, 6);
vector<int> b6 = convert_base(v.a, base_digits, 6);
vll a(a6.begin(), a6.end());
vll b(b6.begin(), b6.end());
while (a.size() < b.size()) a.push_back(0);
while (b.size() < a.size()) b.push_back(0);
while (a.size() & (a.size() - 1)) a.push_back(0), b.push_back(0);
vll c = karatsubaMultiply(a, b);
bigint res;
res.sign = sign * v.sign;
for (int i = 0, carry = 0; i < (int)c.size(); i++) {
long long cur = c[i] + carry;
res.a.push_back((int)(cur % 1000000));
carry = (int)(cur / 1000000);
}
res.a = convert_base(res.a, 6, base_digits);
res.trim();
return res;
}
};
/*
####################### THE BIG INT ##########################
######################################################################
*/
bigint factorial[576];
inline bigint choose(int a, int b) {
return factorial[a] / factorial[b] / factorial[a - b];
}
inline bigint get_seq_idx(int L, int X[]) {
bigint ans = 0;
int prev = 0;
FOR(i, 0, L) {
FOR(j, prev, X[i]) {
ans += choose(L - i + 254 - j, 255 - j);
}
prev = X[i];
}
return ans;
}
void decode(int N, int L, int X[]) {
factorial[0] = 1;
FOR(i, 1, 576) factorial[i] = factorial[i - 1] * i;
sort(X, X + L);
bigint idx = get_seq_idx(L, X);
FOR(i, 0, N) {
output(idx % 256);
idx /= 256;
}
}
