#include <bits/stdc++.h>
#ifndef LOCAL
#include "doll.h"
#endif
using namespace std;
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define Time (clock() * 1.0 / CLOCKS_PER_SEC)
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
using ld = long double;
template<typename T1, typename T2> bool chkmin(T1& x, T2 y) {
return y < x ? (x = y, true) : false;
}
template<typename T1, typename T2> bool chkmax(T1& x, T2 y) {
return y > x ? (x = y, true) : false;
}
void debug_out() {
cerr << endl;
}
template<typename T1, typename... T2> void debug_out(T1 A, T2... B) {
cerr << ' ' << A;
debug_out(B...);
}
template<typename T> void mdebug_out(T* a, int n) {
for (int i = 0; i < n; ++i)
cerr << a[i] << ' ';
cerr << endl;
}
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define mdebug(a, n) cerr << #a << ": ", mdebug_out(a, n)
#else
#define debug(...) 1337
#define mdebug(a, n) 1337
#endif
template<typename T> ostream& operator << (ostream& stream, const vector<T>& v) {
for (auto& x : v)
stream << x << ' ';
return stream;
}
template<typename T1, typename T2> ostream& operator << (ostream& stream, const pair<T1, T2>& p) {
return stream << p.first << ' ' << p.second;
}
const int INF32 = 1e9;
const int maxN = 4e5;
int X[maxN], Y[maxN];
int st[maxN];
int ord[maxN], pos[maxN];
void answer(std::vector<int> C, std::vector<int> X, std::vector<int> Y);
void create_circuit(int m, vector<int> a) {
int n = a.size();
a.push_back(0);
int S = 0;
auto newSwitch = [&]() -> int {
++S;
return -S;
};
vector<int> b(n + 1);
iota(all(b), 0);
while (b.size() > 1) {
if (b.size() & 1) {
int last = b.back();
b.pop_back();
b.push_back(INF32);
b.push_back(last);
}
vector<int> new_b;
for (int i = 0; i < b.size(); i += 2) {
int s = newSwitch();
int sid = -s - 1;
X[sid] = b[i];
Y[sid] = b[i + 1];
new_b.push_back(s);
}
swap(b, new_b);
}
int root = b[0];
for (int s = 0; s < S; ++s) {
if (X[s] == INF32) X[s] = root;
if (Y[s] == INF32) Y[s] = root;
}
int vis = 0;
int v = root;
while (vis < n + 1) {
if (v < 0) {
int sid = -v - 1;
if (!st[sid]) {
v = X[sid];
} else {
v = Y[sid];
}
st[sid] ^= 1;
} else {
pos[v] = vis;
++vis;
v = root;
}
}
// mdebug(pos, m + 1);
// mdebug(X, S);
// mdebug(Y, S);
for (int s = 0; s < S; ++s) {
if (X[s] >= 0) {
X[s] = a[pos[X[s]]];
}
if (Y[s] >= 0) {
Y[s] = a[pos[Y[s]]];
}
}
vector<int> x(S), y(S);
for (int i = 0; i < S; ++i) {
x[i] = X[i];
y[i] = Y[i];
}
// debug(root);
// debug(x);
// debug(y);
answer(vector<int>(m + 1, root), x, y);
}
#ifdef LOCAL
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");
}
if (pos != A[k++]) {
fclose(file_log);
wrong_answer("wrong motion");
}
pos = IC[pos];
}
}
fclose(file_log);
if (k != N) {
wrong_answer("wrong motion");
}
for (int j = 1; j <= S; ++j) {
if (state[j]) {
wrong_answer("state 'Y'");
}
}
printf("Accepted: %d %d\n", S, P);
}
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() {
#ifdef LOCAL
freopen("in", "r", stdin);
#endif
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;
}
// int32_t main() {
// #ifdef LOCAL
// freopen("in", "r", stdin);
// #endif
// ios::sync_with_stdio(0);
// cin.tie(0);
// return 0;
// }
#endif
