/*************************************
* author: marvinthang *
* created: 26.06.2023 22:53:11 *
*************************************/
#include "doll.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i--; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
// end of template
int N, M;
vector <int> A, X, Y;
void gen_tree(int cur, int k, int v) {
if (k == 1) {
X[cur] = 0;
Y[cur] = v == 2 ? 0 : -1;
return;
}
int r;
if (v <= MASK(k - 1)) {
r = 0;
} else {
r = X.size();
X.push_back(0);
Y.push_back(0);
gen_tree(r, k - 1, MASK(k - 1));
v -= MASK(k - 1);
}
int l = X.size();
X.push_back(0);
Y.push_back(0);
gen_tree(l, k - 1, v);
X[cur] = -1 - l;
Y[cur] = -1 - r;
}
void dfs(int u) {
if (A.empty()) return;
u = -u - 1;
swap(X[u], Y[u]);
if (!Y[u]) {
Y[u] = A.back();
A.pop_back();
dfs(-1);
} else dfs(Y[u]);
}
void create_circuit(int m, vector<int> a) {
A = a; M = m;
A.push_back(0);
reverse(ALL(A));
N = A.size();
int k = 1;
while (MASK(k) < N) ++k;
X.push_back(0);
Y.push_back(0);
gen_tree(0, k, N);
vector <int> C(M + 1, -1);
dfs(-1);
answer(C, X, Y);
}
#ifdef LOCAL
#include <cstdio>
#include <cstdlib>
#include "doll.h"
namespace {
constexpr int P_MAX = 20000000;
constexpr int S_MAX = 400000;
int ___M, ___N;
std::vector<int> ___A;
bool answered;
int S;
std::vector<int> IC, IX, IY;
int read_int() {
int x;
if (scanf("%d", &x) != 1) {
fprintf(stderr, "Error while reading input\n");
exit(1);
}
return x;
}
void wrong_answer(const char *MSG) {
printf("Wrong Answer: %s\n", MSG);
exit(0);
}
void simulate() {
if (S > S_MAX) {
char str[50];
sprintf(str, "over %d switches", S_MAX);
wrong_answer(str);
}
for (int i = 0; i <= ___M; ++i) {
if (!(-S <= IC[i] && IC[i] <= ___M)) {
wrong_answer("wrong serial number");
}
}
for (int j = 1; j <= S; ++j) {
if (!(-S <= IX[j - 1] && IX[j - 1] <= ___M)) {
wrong_answer("wrong serial number");
}
if (!(-S <= IY[j - 1] && IY[j - 1] <= ___M)) {
wrong_answer("wrong serial number");
}
}
int P = 0;
std::vector<bool> state(S + 1, false);
int pos = IC[0];
int k = 0;
FILE *file_log = fopen("log.txt", "w");
fprintf(file_log, "0\n");
for (;;) {
fprintf(file_log, "%d\n", pos);
if (pos < 0) {
if (++P > P_MAX) {
fclose(file_log);
char str[50];
sprintf(str, "over %d inversions", P_MAX);
wrong_answer(str);
}
state[-pos] = !state[-pos];
pos = state[-pos] ? IX[-(1 + pos)] : IY[-(1 + pos)];
} else {
if (pos == 0) {
break;
}
if (k >= ___N) {
fclose(file_log);
wrong_answer("wrong motion 1");
}
if (pos != ___A[k++]) {
fclose(file_log);
wrong_answer("wrong motion 2");
}
pos = IC[pos];
}
}
fclose(file_log);
if (k != ___N) {
wrong_answer("wrong motion 3");
}
for (int j = 1; j <= S; ++j) {
if (state[j]) {
wrong_answer("state 'Y'");
}
}
printf("Accepted: %d %d\n", S, P);
}
} // namespace
void answer(std::vector<int> C, std::vector<int> X, std::vector<int> Y) {
if (answered) {
wrong_answer("answered not exactly once");
}
answered = true;
// check if input format is correct
if ((int)C.size() != ___M + 1) {
wrong_answer("wrong array length");
}
if (X.size() != Y.size()) {
wrong_answer("wrong array length");
}
S = X.size();
IC = C;
IX = X;
IY = Y;
}
int main() {
file("doll");
___M = read_int();
___N = read_int();
___A.resize(___N);
for (int k = 0; k < ___N; ++k) {
___A[k] = read_int();
}
answered = false;
create_circuit(___M, ___A);
if (!answered) {
wrong_answer("answered not exactly once");
}
FILE *file_out = fopen("out.txt", "w");
fprintf(file_out, "%d\n", S);
for (int i = 0; i <= ___M; ++i) {
fprintf(file_out, "%d\n", IC[i]);
}
for (int j = 1; j <= S; ++j) {
fprintf(file_out, "%d %d\n", IX[j - 1], IY[j - 1]);
}
fclose(file_out);
simulate();
return 0;
}
#endif
