This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include "bits/stdc++.h"
using namespace std;
const int mod = (int) 1e9 + 7;
const int N = (int) 5e3;
int mem[N][N];
int get(int a, int b) {
if (a > b) {
swap(a, b);
}
if (a < 0 || b < 0) {
return -1;
}
if (a == 0 && b == 0) {
return 0;
}
if (a == b) {
return -1;
}
if (a < N && b < N && mem[a][b]) {
return mem[a][b];
}
int add = b / (a + 1);
b %= (a + 1);
int res = get(a, b);
if (res == -1) {
if (a < N && b < N) {
mem[a][b] = -1;
}
return -1;
}
if (a < N && b < N) {
mem[a][b] = res + add;
}
return res + add;
}
int phi(int x) {
int res = x;
for (int i = 2; i <= x; i++) {
if (x % i == 0) {
res -= res / i;
while (x % i == 0) {
x /= i;
}
}
}
return res;
}
void solve() {
int k;
cin >> k;
cout << phi(k + 2) << '\n';
k++;
int optj = -1;
for (int j = 0; j < min(k, 400000); j++) {
int res = get(j, k - j - 1);
if (res != -1) {
if (optj == -1 || res < get(optj, k - optj - 1)) {
optj = j;
}
}
}
// cout << optj << endl;
// return;
// cout << ans << '\n';
// exit(0);
{
int a = optj, b = k - optj - 1, x = 0;
while (a + b) {
if (a > b) {
x ^= 1;
swap(a, b);
}
while (b >= a + 1) {
cout << x << " ";
b -= a + 1;
}
}
}
cout << '\n';
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int t = 1;
cin >> t;
while (t--) {
solve();
}
}
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