結果
| 問題 | No.2724 Coprime Game 1 |
| ユーザー |
 Konton7
|
| 提出日時 | 2024-04-12 23:23:28 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 26,578 bytes |
| コンパイル時間 | 4,231 ms |
| コンパイル使用メモリ | 214,260 KB |
| 実行使用メモリ | 10,524 KB |
| 最終ジャッジ日時 | 2024-10-02 23:49:51 |
| 合計ジャッジ時間 | 7,841 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 31 ms
10,524 KB |
| testcase_01 | AC | 30 ms
5,272 KB |
| testcase_02 | AC | 44 ms
5,248 KB |
| testcase_03 | TLE | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
ソースコード
// #include <bits/stdc++.h>
#include <algorithm>
#include <atcoder/all>
#include <bitset>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <vector>
using namespace std;
using namespace atcoder;
using mint1 = modint1000000007;
using mint2 = modint998244353;
using ll = long long;
using VI = vector<int>;
using VL = vector<ll>;
using VD = vector<double>;
using VS = vector<string>;
using VB = vector<bool>;
using VVB = vector<vector<bool>>;
using VVI = vector<VI>;
using VVL = vector<VL>;
using VVD = vector<VD>;
using VVVI = vector<VVI>;
using VVVL = vector<VVL>;
using VVVD = vector<VVD>;
using PII = std::pair<int, int>;
using VPII = std::vector<std::pair<int, int>>;
using PLL = std::pair<ll, ll>;
using VPLL = std::vector<std::pair<ll, ll>>;
using TI3 = std::tuple<int, int, int>;
using TI4 = std::tuple<int, int, int, int>;
using TL3 = std::tuple<ll, ll, ll>;
using TL4 = std::tuple<ll, ll, ll, ll>;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep2(i, s, n) for (int i = (s); i < (int)(n); i++)
#define repr2(i, g, n) for (int i = (int)(n)-1; i >= (g); i--)
#define rep3(i, s, n, d) for (int i = (s); i < (int)(n); i += (d))
#define repr3(i, g, n, d) for (int i = (int)(n)-1; i >= (g); i -= (d))
#define allpt(v) (v).begin(), (v).end()
#define allpt_c(v) (v).cbegin(), (v).cend()
#define allpt_r(v) (v).rbegin(), (v).rend()
#define allpt_cr(v) (v).crbegin(), (v).crend()
constexpr int mod1 = 1e9 + 7, mod2 = 998244353, mod3 = 1e9 + 9;
constexpr int mod = mod1;
constexpr ll inf = 1e18;
constexpr int infint = 1e9;
constexpr double pi = 3.14159265359;
bool test;
const string wsp = " ";
const string tb = "\t";
const string rt = "\n";
const string alphabets = "abcdefghijklmnopqrstuvwxyz";
std::random_device seed_gen;
std::mt19937 engine(seed_gen());
// 乱数生成用メルセンヌ・ツイスタエンジン
template <typename T>
void operator++(vector<T> &v) {
for (auto &x : v) ++x;
}
template <typename T>
void operator--(vector<T> &v) {
for (auto &x : v) --x;
}
template <typename T, typename S>
void operator++(pair<T, S> &v) {
++v.first, ++v.second;
}
template <typename T, typename S>
void operator--(pair<T, S> &v) {
--v.first, --v.second;
}
int get1dcoodinate(int w, int i, int j) { return i * w + j; }
template <typename T, typename S>
istream &operator>>(istream &is, pair<T, S> &v) {
is >> v.first >> v.second;
return is;
}
template <typename T, typename S>
ostream &operator<<(ostream &os, pair<T, S> &v) {
os << v.first << wsp << v.second << rt;
return os;
}
ostream &operator<<(ostream &os, modint &v) {
os << v.val();
return os;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
if (v.size() == 0) return os;
int n = (int)v.size() - 1;
rep(i, n) os << v[i] << wsp;
os << v[n] << rt;
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
if (v.size() == 0) return is;
int n = v.size();
rep(i, n) is >> v[i];
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<vector<T>> &v) {
if (v.size() == 0) return os;
int n = (int)v.size();
rep(i, n) os << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &v) {
if (v.size() == 0) return is;
int n = v.size();
rep(i, n) is >> v[i];
return is;
}
template <typename T, typename S>
istream &operator>>(istream &is, vector<pair<T, S>> &v) {
if (v.size() == 0) return is;
int n = v.size();
rep(i, n) is >> v[i].first >> v[i].second;
return is;
}
template <typename T, typename S>
ostream &operator<<(ostream &os, const vector<pair<T, S>> &v) {
if (v.size() == 0) return os;
int n = v.size();
rep(i, n) os << v[i].first << wsp << v[i].second << rt;
return os;
}
template <class T>
bool chmin(T &a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T>
bool chmax(T &a, T b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <typename T>
void range_sort(vector<T> &arr, int l, int r) {
sort(arr.begin() + l, arr.begin() + r);
}
template <typename T, typename S>
void pairzip(const vector<pair<T, S>> &v, vector<T> &t, vector<T> &s) {
int n = v.size();
rep(i, n) {
t.push_back(v[i].first);
s.push_back(v[i].second);
}
return;
}
template <typename T, typename S>
bool myfind(T t, S s) {
return find(t.cbegin(), t.cend(), s) != t.cend();
}
bool check(int y, int x, int h, int w) {
return 0 <= y && y < h && 0 <= x && x < w;
}
bool check(int y, int x, int h1, int h2, int w1, int w2) {
return h1 <= y && y < h2 && w1 <= x && x < w2;
}
bool iskadomatsu(int a, int b, int c) {
return (a != b && b != c && c != a) && ((a > b && b < c) || (a < b && b > c));
}
template <typename T>
bool iskadomatsu(vector<T> v) {
T a = v[0], b = v[1], c = v[2];
return (a != b && b != c && c != a) && ((a > b && b < c) || (a < b && b > c));
}
double euc_dist(PII a, PII b) {
return sqrt(pow(a.first - b.first, 2) + pow(a.second - b.second, 2));
}
// VS split(string s, char c) {
// VS ret;
// string part;
// s += c;
// rep(i, s.length()) {
// if (s[i] == c) {
// if (part != "") ret.emplace_back(part);
// part = "";
// } else if (s[i] != c) {
// part += s[i];
// }
// }
// return ret;
// }
VS split(string s, char c, char d = ' ') {
VS ret;
// reverse(allpt(s));
string part;
s += c;
rep(i, s.length()) {
if (s[i] == c) {
if (part != "") {
// string t;
// t += c;
// ret.emplace_back(t);
ret.emplace_back(part);
}
part = "";
} else {
part += s[i];
}
}
return ret;
}
template <typename T, typename S, typename R>
ll pow_mod(T p, S q, R _mod = 1ll) {
ll ret = 1, r = p % _mod;
while (q) {
if (q % 2) ret *= r, ret %= _mod;
r = (r * r) % _mod, q /= 2;
}
return ret % _mod;
}
template <typename T, typename S>
ll pow_no_mod(T p, S q) {
ll ret = 1, r = p;
while (q) {
if (q % 2) ret *= r;
r = (r * r), q /= 2;
}
return ret;
}
pair<VL, VL> make_frac_tables(int n) {
VL frac_list(n + 1, 1), frac_inv_list(n + 1, 1);
rep(i, n) {
frac_list[i + 1] *= frac_list[i] * (i + 1);
frac_list[i + 1] %= mod;
frac_inv_list[i + 1] *= frac_inv_list[i] * pow_mod(i + 1, mod - 2, mod);
frac_inv_list[i + 1] %= mod;
}
return make_pair(frac_list, frac_inv_list);
}
ll perm(int a, int b, const VL &frac_list, const VL &frac_inv_list) {
if (a < b) return 0;
if (b < 0) return 0;
ll ret = frac_list[a];
ret *= frac_inv_list[a - b];
ret %= mod;
return ret;
}
ll comb(int a, int b, const VL &frac_list, const VL &frac_inv_list) {
if (a < b) return 0;
if (b < 0) return 0;
ll ret = frac_list[a];
ret *= frac_inv_list[b];
ret %= mod;
ret *= frac_inv_list[a - b];
ret %= mod;
return ret;
}
struct vec2d {
ll x;
ll y;
vec2d(ll _x, ll _y) {
x = _x;
y = _y;
}
ll dot(vec2d p) { return x * p.x + y * p.y; }
vec2d diff(vec2d p) { return vec2d(x - p.x, y - p.y); }
};
struct node {
int parent = -1;
ll weight = 0;
int depth = 0;
int degree = 0;
int subtree = 0;
int check = 0;
int scc = -1;
VPLL children;
VI parent_list;
VPLL connect;
ll black_from_children;
ll black_from_parent;
node() {
parent = -1;
weight = 0;
depth = 0;
degree = 0;
subtree = 0;
check = 0;
black_from_children = 1;
black_from_parent = 1;
}
};
struct graph {
int _n;
int root = 0;
vector<node> nodes;
graph(int n) {
_n = n;
rep(i, _n) nodes.emplace_back(node());
}
void getconnect_nocost() {
ll a, b;
cin >> a >> b;
nodes[a].connect.emplace_back(b, 1);
nodes[b].connect.emplace_back(a, 1);
}
void getconnect_cost() {
ll a, b, c;
cin >> a >> b >> c;
nodes[a].connect.emplace_back(b, c);
nodes[b].connect.emplace_back(a, c);
}
void getconnect_increment_nocost() {
ll a, b;
cin >> a >> b;
a--, b--;
nodes[a].connect.emplace_back(b, 1);
nodes[b].connect.emplace_back(a, 1);
}
void getconnect_increment_cost() {
ll a, b, c;
cin >> a >> b >> c;
a--, b--;
nodes[a].connect.emplace_back(b, c);
nodes[b].connect.emplace_back(a, c);
}
void showparent() {
rep(i, _n - 1) cout << nodes[i].parent << wsp;
cout << nodes[_n - 1].parent << rt;
}
void showweight() {
rep(i, _n - 1) cout << nodes[i].weight << wsp;
cout << nodes[_n - 1].weight << rt;
}
void showsubtree() {
rep(i, _n - 1) cout << nodes[i].subtree << wsp;
cout << nodes[_n - 1].subtree << rt;
}
void showdepth() {
rep(i, _n - 1) cout << nodes[i].depth << wsp;
cout << nodes[_n - 1].depth << rt;
}
// pair<VL, VI> djcstra(int s = 0) {
// VL shortest(_n, inf);
// VI prev(_n, -1);
// shortest[s] = 0;
// priority_queue<pair<ll, int>> pq;
// pq.push(make_pair(0, s));
// while (!pq.empty()) {
// auto [t, u] = pq.top();
// pq.pop();
// t = -t;
// if (shortest[u] != t) continue;
// for (auto [v, c] : nodes[u].connect) {
// if (t + c < shortest[v]) {
// shortest[v] = t + c;
// prev[v] = u;
// pq.push(make_pair(-(t + c), v));
// }
// }
// }
// return make_pair(shortest, prev);
// }
pair<VL, VI> djcstra(int s = 0) {
VL shortest(_n, inf * 4);
VI prev(_n, -1);
shortest[s] = 0;
priority_queue<pair<ll, int>> pq;
pq.push(make_pair(0, s));
while (!pq.empty()) {
auto [t, u] = pq.top();
pq.pop();
t = -t;
if (shortest[u] != t) continue;
for (auto [v, c] : nodes[u].connect) {
if (t + c < shortest[v]) {
shortest[v] = t + c;
prev[v] = u;
pq.push(make_pair(-(t + c), v));
}
}
}
return make_pair(shortest, prev);
}
// pair<VL, VI> djcstra(VI s) {
// VL shortest(_n, inf);
// VI prev(_n, -1);
// priority_queue<pair<ll, int>> pq;
// for (auto x : s) {
// shortest[x] = 0;
// pq.push(make_pair(0, x));
// }
// while (!pq.empty()) {
// auto [t, u] = pq.top();
// pq.pop();
// t = -t;
// if (shortest[u] != t) continue;
// for (auto [v, c] : nodes[u].connect) {
// if (t + c < shortest[v]) {
// shortest[v] = t + c;
// prev[v] = u;
// pq.push(make_pair(-(t + c), v));
// }
// }
// }
// return make_pair(shortest, prev);
// }
// VI djcstra(VI s, const VI x_list) {
// VL shortest(_n, inf);
// VI prev(_n, -1);
// VI new_infection;
// priority_queue<pair<ll, PII>> pq;
// for (auto si : s) {
// shortest[si] = 0;
// pq.push(make_pair(0, make_pair(si, -x_list[si])));
// }
// while (!pq.empty()) {
// auto [t, p] = pq.top();
// auto [u, x] = p;
// pq.pop();
// t = -t, x = -x;
// if (shortest[u] != t) continue;
// for (auto [v, d] : nodes[u].connect) {
// if (t + d < shortest[v] && x >= d) {
// shortest[v] = t + d;
// prev[v] = u;
// pq.push(make_pair(-(t + d), make_pair(v, -(x - d))));
// }
// }
// }
// return new_infection;
// }
};
struct point {
int x;
int y;
point() {
x = 0;
y = 0;
}
point(int _x, int _y) {
x = _x;
y = _y;
}
void pointinput() {
int _x, _y;
cin >> _x >> _y;
x = _x;
y = _y;
}
void pointinv() { swap(x, y); }
};
istream &operator>>(istream &is, point &p) {
is >> p.x >> p.y;
return is;
}
ostream &operator<<(ostream &os, point &p) {
os << p.x << wsp << p.y << rt;
return os;
}
double pointseuc(point a, point b) {
ll ax = a.x, bx = b.x, ay = a.y, by = b.y;
return sqrt(pow(ax - bx, 2) + pow(ay - by, 2));
}
ll pointseucsquare(point a, point b) {
ll ax = a.x, bx = b.x, ay = a.y, by = b.y;
return (ax - bx) * (ax - bx) + (ay - by) * (ay - by);
}
int pointsmanhattan(point a, point b) {
return abs(a.x - b.x) + abs(a.y - b.y);
}
double dist_segment_point(TL3 segment, point p) {
double a = get<0>(segment);
double b = get<1>(segment);
double c = get<2>(segment);
return abs(a * p.x + b * p.y - c) / sqrt(a * a + b * b);
}
TL3 segment_parameter(point p, point q) {
ll a, b, c;
a = q.y - p.y;
b = p.x - q.x;
c = a * p.x + b * p.y;
TL3 ret = (TL3){a, b, c};
// cout << a << b << c << rt;
return ret;
}
int cross_check(TL3 segment, point p) {
ll a = get<0>(segment);
ll b = get<1>(segment);
ll c = get<2>(segment);
auto f = a * p.x + b * p.y - c;
int ret;
if (f > 0) ret = 1;
if (f == 0) ret = 0;
if (f < 0) ret = -1;
return ret;
}
VI shave(int n) {
VI v;
if (n <= 1) return v;
vector<bool> w(n + 1, true);
int x;
w[0] = w[1] = false;
rep2(i, 2, n + 1) {
if (w[i]) {
x = i * 2;
while (x <= n) {
w[x] = false;
x += i;
}
}
}
rep(i, n + 1) if (w[i]) v.emplace_back(i);
return v;
}
bool iscross(point p1, point p2, point p3, point p4) {
auto segment_1 = segment_parameter(p1, p2);
auto segment_2 = segment_parameter(p3, p4);
const double eps = 1e-6;
bool ans{false};
if (cross_check(segment_1, p3) * cross_check(segment_1, p4) == 0 &&
cross_check(segment_2, p1) * cross_check(segment_2, p2) == 0) {
auto xmin_1 = min(p1.x, p2.x) - eps;
auto xmin_2 = min(p3.x, p4.x) - eps;
auto xmax_1 = max(p1.x, p2.x) + eps;
auto xmax_2 = max(p3.x, p4.x) + eps;
auto ymin_1 = min(p1.y, p2.y) - eps;
auto ymin_2 = min(p3.y, p4.y) - eps;
auto ymax_1 = max(p1.y, p2.y) + eps;
auto ymax_2 = max(p3.y, p4.y) + eps;
if (xmin_1 <= p3.x && p3.x <= xmax_1 && ymin_1 <= p3.y && p3.y <= ymax_1)
ans = true;
if (xmin_1 <= p4.x && p4.x <= xmax_1 && ymin_1 <= p4.y && p4.y <= ymax_1)
ans = true;
if (xmin_2 <= p1.x && p1.x <= xmax_2 && ymin_2 <= p1.y && p1.y <= ymax_2)
ans = true;
if (xmin_2 <= p2.x && p2.x <= xmax_2 && ymin_2 <= p2.y && p2.y <= ymax_2)
ans = true;
} else if (cross_check(segment_1, p3) * cross_check(segment_1, p4) <= 0 &&
cross_check(segment_2, p1) * cross_check(segment_2, p2) <= 0) {
ans = true;
}
return ans;
}
// int on_the_segment(point p, point q1, point q2) {
// auto [a, b, c] = segment_parameter(q1, q2);
// if (p.x < min(q1.x, q2.x) || max(q1.x, q2.x) < p.x) return 0;
// if (p.y < min(q1.y, q2.y) || max(q1.y, q2.y) < p.y) return 0;
// auto f = a * p.x + b * p.y - c;
// return f == 0;
// }
void shave(vector<int> &v, int n) {
if (n <= 1) return;
vector<bool> w(n + 1, true);
int x;
w[0] = w[1] = false;
rep2(i, 2, n + 1) {
if (w[i]) {
x = i * 2;
while (x <= n) {
w[x] = false;
x += i;
}
}
}
rep(i, n + 1) if (w[i]) v.emplace_back(i);
}
template <typename T>
void sort_and_unique(vector<T> &x) {
sort(x.begin(), x.end());
x.erase(unique(x.begin(), x.end()), x.end());
}
template <typename T>
void coordinate_compress(vector<T> &x, map<T, int> &zip, int &xs) {
sort_and_unique(x);
xs = x.size();
for (int i = 0; i < xs; i++) zip[x[i]] = i;
}
template <typename T>
pair<map<T, int>, int> coordinate_compress(vector<T> &x) {
map<T, int> zip;
sort_and_unique(x);
int xs = x.size();
for (int i = 0; i < xs; i++) zip[x[i]] = i;
return make_pair(zip, xs);
}
template <typename T>
pair<map<T, int>, int> copy_coordinate_compress(vector<T> &x) {
VI x_copy = x;
auto [x_zip, xl] = coordinate_compress(x_copy);
for (auto &v : x) v = x_zip[v];
return make_pair(x_zip, xl);
}
// ll getpalindrome(int l, int r, const string &s, VL &memo) {
// if (r - l <= 1) return 1;
// if (memo[l] != -1) return memo[l];
// ll ret{1};
// int n = (r - l) / 2;
// string sl, sr;
// rep(i, n) {
// sl += s[l + i];
// sr += s[r - 1 - i];
// string rsr(i + 1, '0');
// reverse_copy(allpt_c(sr), rsr.begin());
// // cout << sl << wsp << sr << wsp << rsr << rt;
// if (sl == rsr) {
// ret += getpalindrome(l + i + 1, r - i - 1, s, memo);
// ret %= mod;
// }
// }
// memo[l] = ret;
// return ret;
// }
// void getpalindrome(int l, int r, int n, const string &s, VVB &memo) {
// if (r - l <= 1 || s[l] == s[r - 1]) {
// memo[l][r] = true;
// if (l > 0 && r < n) {
// getpalindrome(l - 1, r + 1, n, s, memo);
// }
// }
// return;
// }
class Unionfind {
vector<int> p;
vector<int> w;
public:
Unionfind(int n, int _w = 1) {
for (int i = 0; i < n; i++) {
p.emplace_back(i);
w.emplace_back(_w);
}
}
int find(int x) {
while (p[x] != x) {
p[x] = p[p[x]];
x = p[x];
}
return x;
}
int getval(int x) { return p[x]; }
int getweight(int x) { return w[find(x)]; }
void setweight(int x, int _w) { w[find(x)] += _w; }
void unite(int x, int y) {
x = find(x);
y = find(y);
if (x != y) {
p[x] = min(x, y);
p[y] = min(x, y);
w[min(x, y)] += w[max(x, y)];
w[max(x, y)] = 0;
}
}
bool isunion(int x, int y) { return find(x) == find(y); }
void showtree() { cout << p << w; }
};
template <typename T>
class RangeMinorMaxorSumQuery // 0-index
{
T const intmax = inf;
T const intmin = 0;
vector<T> sgt;
int n;
int k;
public:
RangeMinorMaxorSumQuery(int n1, T f) {
int na = 1;
int ka = 0;
while (na < n1) {
na *= 2;
ka++;
}
for (int i = 0; i < 2 * na; i++) sgt.push_back(f);
n = na;
k = ka;
}
void update_min(int i, T x) {
i += n;
sgt[i] = x;
while (i > 1) {
i /= 2;
sgt[i] = min(sgt[2 * i], sgt[2 * i + 1]);
}
}
void update_max(int i, T x) {
i += n;
sgt[i] = x;
while (i > 1) {
i /= 2;
sgt[i] = max(sgt[2 * i], sgt[2 * i + 1]);
}
}
void update_sum(int i, T x) {
i += n;
sgt[i] = x;
while (i > 1) {
i /= 2;
sgt[i] = sgt[2 * i] + sgt[2 * i + 1];
}
}
void update_gcd(int i, T x) {
i += n;
sgt[i] = x;
while (i > 1) {
i /= 2;
sgt[i] = gcd(sgt[2 * i], sgt[2 * i + 1]);
}
}
void add_sum(int i, T x) {
i += n;
sgt[i] += x;
while (i > 1) {
i /= 2;
sgt[i] = sgt[2 * i] + sgt[2 * i + 1];
}
}
void add_min(int i, T x) {
i += n;
sgt[i] += x;
while (i > 1) {
i /= 2;
sgt[i] = min(sgt[2 * i], sgt[2 * i + 1]);
}
}
void add_max(int i, T x) {
i += n;
sgt[i] += x;
while (i > 1) {
i /= 2;
sgt[i] = max(sgt[2 * i], sgt[2 * i + 1]);
}
}
T get_min(int a, int b, int k = 1, int l = 0,
int r = -1) // 閉区間 l <= x < r とする
{
if (r == -1) r = n;
if (r <= a || b <= l) return inf;
if (a == l && b == r)
return sgt[k];
else
return min(get_min(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2),
get_min(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r));
}
T get_max(int a, int b, int k = 1, int l = 0,
int r = -1) // 閉区間 l <= x < r とする
{
if (r == -1) r = n;
if (r <= a || b <= l) return 0;
if (a == l && b == r)
return sgt[k];
else
return max(get_max(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2),
get_max(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r));
}
T get_sum(int a, int b, int k = 1, int l = 0,
int r = -1) // 閉区間 l <= x < r とする
{
if (r == -1) r = n;
if (r <= a || b <= l) return intmin;
if (a == l && b == r)
return sgt[k];
else
return get_sum(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2) +
get_sum(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r);
}
T get_gcd(int a, int b, int k = 1, int l = 0,
int r = -1) // 閉区間 l <= x < r とする
{
if (r == -1) r = n;
if (r <= a || b <= l) return 0;
if (a == l && b == r)
return sgt[k];
else
return gcd(get_gcd(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2),
get_gcd(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r));
}
void update_xor(int i, T x) {
i += n;
sgt[i] = x;
while (i > 1) {
i /= 2;
sgt[i] = sgt[2 * i] ^ sgt[2 * i + 1];
}
}
T get_xor(int a, int b, int k = 1, int l = 0,
int r = -1) // 閉区間 l <= x < r とする
{
if (r == -1) r = n;
if (r <= a || b <= l) return 0;
if (a == l && b == r)
return sgt[k];
else
return get_xor(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2) ^
get_xor(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r);
}
T operator[](int i) { return sgt[i + n]; }
void printsegtree() {
for (int i = 0; i < 2 * n; i++) {
cout << sgt[i] << " ";
}
cout << endl;
}
};
template <typename T>
class Bit_Index_Tree // 1-index
{
int n = 0;
vector<T> v;
public:
void add(int i, T x) {
while (i <= n) {
v[i] += x;
i += i & -i;
}
}
Bit_Index_Tree(int _n, T x = 0) {
n = _n;
v.resize(n + 1);
fill(allpt(v), x);
}
Bit_Index_Tree(vector<T> _v) {
n = _v.size();
v.resize(n + 1);
fill(allpt(v), 0);
rep(i, n) add(i, v[i]);
}
T get_sum(int i) {
T ret = 0;
while (i > 0) {
ret += v[i];
i -= i & -i;
}
return ret;
}
T get_range_sum(int l, int r) { // 半開区間 l <= x < r
return get_sum(r) - get_sum(l);
}
};
// #define DEBUG
VI smallest_prime_factors(int n) {
VI ret(n + 1);
iota(allpt(ret), 0);
for (int i = 2; i * i <= n; i++) {
if (ret[i] == i) {
for (int j = i * i; j <= n; j += i) {
if (ret[j] == j) ret[j] = i;
}
}
}
return ret;
}
// void dfs_1(graph &tree, int u)
// {
// cout << u << rt;
// for (auto [v, _] : tree.nodes[u].connect)
// if (v != tree.root && tree.nodes[v].parent == -1)
// {
// tree.nodes[v].parent = u;
// dfs_1(tree, v);
// tree.nodes[u].subtree += tree.nodes[v].subtree;
// tree.nodes[u].children.emplace_back(PII(tree.nodes[v].subtree,
// v));
// }
// }
// void dfs_2(graph &tree, int u, int d)
// {
// cout << u << wsp << d << rt;
// sort(allpt_r(tree.nodes[u].children));
// rep(j, tree.nodes[u].children.size())
// {
// auto [_, v] = tree.nodes[u].children[j];
// cout << (VI){u, (int)v, j};
// dfs_2(tree, v, j == 0 ? d : d + 1);
// }
// }
template <typename T>
class Matrix_n {
int matsize;
vector<vector<T>> mat;
public:
Matrix_n() {
matsize = 0;
vector<vector<T>> mat;
}
Matrix_n(int n) {
matsize = n;
mat.resize(n);
rep(i, n) rep(j, n) mat[i].emplace_back(0);
}
Matrix_n(const vector<vector<T>> &inmat) {
int n = inmat.size();
matsize = n;
mat.resize(n);
rep(i, n) {
mat[i].resize(n);
rep(j, n) { mat[i][j] = inmat[i][j]; }
}
}
void identify() {
rep(i, matsize) rep(j, matsize) { mat[i][j] = i == j ? 1 : 0; }
}
T getone(const int &i, const int &j) { return mat[i][j]; }
int getsize() { return matsize; }
const Matrix_n operator+(const Matrix_n &b) {
Matrix_n ret(matsize);
rep(i, matsize) rep(j, matsize) { ret.mat[i][j] = mat[i][j] + b.mat[i][j]; }
return ret;
}
const Matrix_n operator-(const Matrix_n &b) {
Matrix_n ret(matsize);
rep(i, matsize) rep(j, matsize) { ret.mat[i][j] = mat[i][j] - b.mat[i][j]; }
return ret;
}
const Matrix_n operator*(const Matrix_n &b) {
Matrix_n ret(matsize);
rep(i, matsize) rep(j, matsize) rep(k, matsize) {
ret.mat[i][j] += mat[i][k] * b.mat[k][j];
ret.mat[i][j] %= mod;
}
return ret;
}
const Matrix_n operator%(const int &b) {
Matrix_n ret(matsize);
rep(i, matsize) rep(j, matsize) { ret.mat[i][j] = mat[i][j] % b; }
return ret;
}
const Matrix_n operator+() { return *this; }
const Matrix_n operator-() {
Matrix_n ret(matsize);
rep(i, matsize) rep(j, matsize) { ret.mat[i][j] = -mat[i][j]; }
return ret;
}
Matrix_n &operator+=(const Matrix_n &b) {
rep(i, matsize) rep(j, matsize) { mat[i][j] += b.mat[i][j]; }
return *this;
}
Matrix_n &operator-=(const Matrix_n &b) {
rep(i, matsize) rep(j, matsize) { mat[i][j] -= b.mat[i][j]; }
return *this;
}
Matrix_n &operator%=(const int &b) {
rep(i, matsize) rep(j, matsize) { mat[i][j] %= b; }
return *this;
}
void showmat() { cout << mat; }
};
template <typename T>
Matrix_n<T> mat_pow_mod(Matrix_n<T> a, ll p, ll m = mod) {
const int n = a.getsize();
Matrix_n<T> b(n);
b.identify();
while (p > 0) {
if (p % 2) {
b = b * a;
b %= m;
}
p /= 2;
a = a * a;
a %= m;
}
return b;
}
template <typename T>
Matrix_n<T> mat_pow_no_mod(Matrix_n<T> a, ll p) {
const int n = a.getsize();
Matrix_n<T> b(n);
b.identify();
while (p > 0) {
if (p % 2) {
b = b * a;
}
p /= 2;
a = a * a;
}
return b;
}
VL make_frac_k(int k, int l) {
VL ret(l + 1, 1);
rep(i, l) {
ret[i + 1] = ret[i] * k;
ret[i + 1] %= mod;
}
return ret;
}
template <typename T, typename S>
void ans_print(T ans, T nodata, S printdata) {
if (ans == nodata) {
cout << printdata;
} else {
cout << ans;
}
cout << endl;
}
int mex(VI v) {
sort_and_unique(v);
int n = v.size();
rep(i, n) {
if (v[i] != i) return i;
}
return n;
}
VI primes;
void solve() {
int n;
cin >> n;
// cout << *lower_bound(allpt_c(primes), n) << rt;
// cout << *lower_bound(allpt_c(primes), n / 2) << rt;
// cout << n - 1 - (lower_bound(allpt_c(primes), n) - upper_bound(allpt_c(primes), n / 2)) << rt << rt;
if (myfind(primes, n)) {
cout << 'P' << rt;
return;
}
int s = n - 1 - (lower_bound(allpt_c(primes), n) - upper_bound(allpt_c(primes), n / 2));
cout << (s % 2 == 0 ? "K" : "P" ) << rt;
}
int main(int argc, char *argv[]) {
// cin.tie(0);
// ios::sync_with_stdio(false);
// リアクティブ問題のときはコメントアウト
primes = shave(3000000);
int q;
cin >> q;
rep(_, q) solve();
return 0;
}