#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <deque>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <random>
#include <iomanip>
#include <functional>
#include <cassert>
using namespace std;
typedef long long ll;
#include "doll.h"
void create_circuit(int m, vector <int> a) {
int n = a.size();
vector <vector <int>> where(m + 1);
for (int i = 0; i < n; ++i) {
where[a[i]].push_back(i);
}
a.push_back(0);
int uk = 0;
vector <int> c(m + 1);
c[0] = a[0];
vector <int> x, y;
auto new_node = [&] () {
x.push_back(-1);
y.push_back(-1);
return uk++;
};
int lg = 1;
while ((1 << lg) <= n) ++lg;
const int Inf = 1e9;
int root = new_node();
for (int v = 1; v <= m; ++v) {
if (!where[v].empty()) {
c[v] = -(root + 1);
}
}
//cout << "gogo " << v << endl;
function <void(int, int, int, int)> rec = [&] (int u, int lvl, int num, int skip) {
int sz = (1 << (lvl - 1));
int skip_l = min(sz, skip);
int skip_r = skip - skip_l;
int num_r = num | (1 << (lg - lvl));
int num_l = num;
if (skip_l == sz) {
x[u] = root + 1;
} else if (sz > 1) {
x[u] = new_node() + 1;
rec(x[u] - 1, lvl - 1, num_l, skip_l);
} else {
assert(sz == 1);
x[u] = Inf + num_l;
}
assert(skip_r < sz);
if (sz > 1) {
y[u] = new_node() + 1;
rec(y[u] - 1, lvl - 1, num_r, skip_r);
} else {
y[u] = Inf + num_r;
}
};
rec(root, lg, 0, (1 << lg) - n);
vector <pair <int, int>> cur;
for (int u = root; u < uk; ++u) {
if (x[u] >= Inf) {
cur.push_back({x[u], -u});
}
if (y[u] >= Inf) {
cur.push_back({y[u], u});
}
}
sort(cur.begin(), cur.end());
for (int i = 0; i < (int)cur.size(); ++i) {
if (cur[i].second < 0) {
x[-cur[i].second] = -a[i + 1];
} else {
y[cur[i].second] = -a[i + 1];
}
}
for (int i = 0; i < (int)x.size(); ++i) {
if (x[i] <= 0) {
x[i] *= -1;
} else {
x[i] *= -1;
}
}
for (int i = 0; i < (int)y.size(); ++i) {
if (y[i] <= 0) {
y[i] *= -1;
} else {
y[i] *= -1;
}
}
/*for (int i = 0; i <= m; ++i) {
cout << c[i] << '\n';
}
cout << "done\n";
for (int i = 0; i < (int)x.size(); ++i) {
cout << x[i] << ' ' << y[i] << endl;
}*/
answer(c, x, y);
}
#ifdef LOCAL
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;
cin >> x;
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);
}
} // 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() {
#ifdef LOCAL
freopen("input.txt", "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;
}
#endif
