This documentation is automatically generated by competitive-verifier/competitive-verifier
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/range_kth_smallest
#include "../template.hpp"
#include "../wavelet_matrix.hpp"
int main() {
int n, q;
cin >> n >> q;
vector<int> a(n);
for (int& e : a) cin >> e;
CompressedWaveletMatrix wm(a);
while (q--) {
int l, r, k;
cin >> l >> r >> k;
cout << wm.kth_smallest(l, r, k) << "\n";
}
}
#line 1 "test/lc_range_kth_smallest.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/range_kth_smallest
#line 1 "template.hpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#if __cplusplus >= 202002L
#include <bit>
#include <ranges>
#define TYPE(n) remove_cvref_t<decltype(n)>
#else
#define countl_zero __builtin_clzll
#define TYPE(n) remove_cv_t<remove_reference_t<decltype(n)>>
#endif
using namespace std;
using lint = long long;
using P = pair<lint, lint>;
using Pii = pair<int, int>;
using ull = unsigned long long;
struct FastIO {
FastIO() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(15);
}
} aaaAAAaaaAAA;
#define rep(i, n) for (TYPE(n) i = 0; i < (n); ++i)
#define repe(i, n) for (TYPE(n) i = 0; i <= (n); ++i)
#define rep1(i, n) for (TYPE(n) i = 1; i < (n); ++i)
#define rep1e(i, n) for (TYPE(n) i = 1; i <= (n); ++i)
#define repn(i, a, b) for (TYPE(a) i = (a); i < (b); ++i)
#define repne(i, a, b) for (TYPE(a) i = (a); i <= (b); ++i)
#define rrep(i, n) for (TYPE(n) i = (n); i >= 0; --i)
#define all(vec) begin(vec), end(vec)
#define rall(vec) rbegin(vec), rend(vec)
constexpr long long Mod = /** 1000'000'007LL /*/ 998244353LL /**/;
constexpr long long Inf = 2'000'000'000'000'000'010LL;
constexpr int IntInf = 1000'000'010;
constexpr double Pi = 3.141592653589793238;
constexpr double InvPi = 0.318309886183790671;
const int di[] = {0, -1, 0, 1, 0};
const int dj[] = {1, 0, -1, 0, 0};
pair<int, int> adj(int i, int j, int k) { return {i + di[k], j + dj[k]}; }
bool in(int i, int j, int h, int w) { return 0 <= i && i < h && 0 <= j && j < w; }
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
using mint = static_modint<Mod>;
template <int MOD>
inline istream &operator>>(istream &is, static_modint<MOD> &rhs) {
long long tmp;
is >> tmp;
rhs = tmp;
return is;
}
template <int ID>
inline istream &operator>>(istream &is, dynamic_modint<ID> &rhs) {
long long tmp;
is >> tmp;
rhs = tmp;
return is;
}
template <int MOD>
inline ostream &operator<<(ostream &os, const static_modint<MOD> &rhs) {
return os << rhs.val();
}
template <int ID>
inline ostream &operator<<(ostream &os, const dynamic_modint<ID> &rhs) {
return os << rhs.val();
}
// [0, n]
template <typename T>
auto enumerate_fact(int n) {
vector<T> fact(n + 1);
fact[0] = 1;
for (int i = 1; i <= n; ++i) fact[i] = i * fact[i - 1];
return fact;
}
// [0, n]
template <int MOD>
auto enumerate_inv(int n) {
vector<static_modint<MOD>> inv(n + 1);
inv[1] = 1;
for (int i = 2; i <= n; ++i) inv[i] = MOD - MOD / i * inv[MOD % i];
return inv;
}
// [0, n]
template <typename T>
auto enumerate_factinv(int n, vector<T> inv) {
vector<T> fact_inv(n + 1);
fact_inv[0] = 1;
for (int i = 1; i <= n; ++i) fact_inv[i] = fact_inv[i - 1] * inv[i];
return fact_inv;
}
// [0, n]
template <int MOD>
auto enumerate_factinv(int n) {
return enumerate_factinv(n, enumerate_inv<MOD>(n));
}
template <int MOD>
struct Binomial {
using Fp = static_modint<MOD>;
vector<Fp> fact, inv, fact_inv;
explicit Binomial() = default;
// [0, n]
void build(int n) {
fact = enumerate_fact<Fp>(n);
inv = enumerate_inv<MOD>(n);
fact_inv = enumerate_factinv<Fp>(n, inv);
}
Fp comb(int n, int r) const {
if (n < 0 || r < 0 || n < r) return 0;
if (r == 0 || r == n) return 1;
return fact[n] * fact_inv[n - r] * fact_inv[r];
}
Fp perm(int n, int r) const {
if (n < 0 || r < 0 || n < r) return 0;
return fact[n] * fact_inv[n - r];
}
Fp multi(int n, int r) const {
if (n == 0 && r == 0) return 1;
if (n < 0 || r < 0) return 0;
return r == 0 ? 1 : comb(n + r - 1, r);
}
};
Binomial<Mod> binomial;
inline mint fact(int n) { return binomial.fact[n]; }
inline mint comb(int n, int r) { return binomial.comb(n, r); }
inline mint perm(int n, int r) { return binomial.perm(n, r); }
inline mint multi(int n, int r) { return binomial.multi(n, r); }
mint lagrange_interpolation(const vector<mint> &y, mint t) {
const int n = (int)y.size();
mint res = 0;
auto inv = enumerate_inv<Mod>(n - 1), fact_inv = enumerate_factinv(n - 1, inv);
vector<mint> prod2(n);
prod2.back() = 1;
for (int i = n - 1; i > 0; --i) {
prod2[i - 1] = (t - i) * prod2[i];
}
mint prod1 = 1;
for (int i = 0; i < n; ++i) {
mint a = y[i];
a *= fact_inv[i] * fact_inv[n - 1 - i];
if ((n - 1 - i) & 1) a = -a;
res += a * prod1 * prod2[i];
prod1 *= (t - i);
}
return res;
}
template <typename T>
lint inversion_number(const vector<T> vec) {
vector<T> v = vec;
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
const int n = vec.size();
lint res = 0;
fenwick_tree<int> b(n);
for (int i = 0; i < n; ++i) {
const int j = lower_bound(v.begin(), v.end(), vec[i]) - v.begin();
res += b.sum(j + 1, n);
b.add(j, 1);
}
return res;
}
#endif
// top = max
template <typename T>
using prique = priority_queue<T>;
// top = min
template <typename T>
using prique_inv = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
inline istream &operator>>(istream &is, pair<T, U> &rhs) {
return is >> rhs.first >> rhs.second;
}
template <typename T>
inline istream &operator>>(istream &is, complex<T> &c) {
T real, imag;
is >> real >> imag;
c.real(real);
c.imag(imag);
return is;
}
template <typename T, typename U>
inline ostream &operator<<(ostream &os, const pair<T, U> &rhs) {
return os << "{" << rhs.first << ", " << rhs.second << "}";
}
#if __cplusplus >= 202002L
template <class T>
concept Container = requires(const T &v) {
v.begin();
v.end();
} && !is_same_v<T, string>;
template <Container T>
inline istream &operator>>(istream &is, T &v) {
for (auto &e : v) is >> e;
return is;
}
template <Container T>
inline ostream &operator<<(ostream &os, const T &v) {
for (auto itr = v.begin(), end_itr = v.end(); itr != end_itr;) {
os << *itr;
if (++itr != end_itr) os << " ";
}
return os;
}
#else
template <typename T>
inline istream &operator>>(istream &is, vector<T> &v) {
for (auto &e : v) is >> e;
return is;
}
template <typename T>
inline ostream &operator<<(ostream &os, const vector<T> &v) {
for (auto itr = v.begin(), end_itr = v.end(); itr != end_itr;) {
os << *itr;
if (++itr != end_itr) os << " ";
}
return os;
}
#endif
template <typename T, typename U>
inline bool chmin(T &a, const U b) {
return a > b ? a = b, true : false;
}
template <typename T, typename U>
inline bool chmax(T &a, const U b) {
return a < b ? a = b, true : false;
}
template <typename T, typename U, class Pr>
inline int getid(const vector<T> &v, const U &value, Pr pred) {
return lower_bound(v.begin(), v.end(), value, pred) - v.begin();
}
template <typename T, typename U>
inline int getid(const vector<T> &v, const U &value) {
return getid(v, value, less<>{});
}
template <typename T>
T gcd(const vector<T> &vec) {
T res = vec.front();
for (T e : vec) {
res = gcd(res, e);
if (res == 1) return 1;
}
return res;
}
template <typename T>
T gcd(initializer_list<T> init) {
auto first = init.begin(), last = init.end();
T res = *(first++);
for (auto itr = first; itr != last; ++itr) {
res = gcd(res, *itr);
if (res == 1) return 1;
}
return res;
}
template <typename T>
T lcm(const vector<T> &vec) {
T res = vec.front();
for (T e : vec) res = lcm(res, e);
return res;
}
template <typename T>
T lcm(initializer_list<T> init) {
auto first = init.begin(), last = init.end();
T res = *(first++);
for (auto itr = first; itr != last; ++itr) {
res = lcm(res, *itr);
}
return res;
}
inline void YesNo(bool b) { cout << (b ? "Yes\n" : "No\n"); }
inline void YESNO(bool b) { cout << (b ? "YES\n" : "NO\n"); }
inline void takaao(bool b) { cout << (b ? "Takahashi\n" : "Aoki\n"); }
inline void aotaka(bool b) { cout << (b ? "Aoki\n" : "Takahashi\n"); }
// [l, r]
template <typename T>
T rand(T l, T r) {
static mt19937 mt(random_device{}());
if constexpr (is_integral_v<T>) {
uniform_int_distribution<T> dist(l, r);
return dist(mt);
} else if constexpr (is_floating_point_v<T>) {
uniform_real_distribution<T> dist(l, r);
return dist(mt);
}
}
bool is_prime_naive(lint x) {
for (lint i = 2; i * i <= x; ++i) {
if (x % i == 0) return false;
}
return 1 < x;
}
vector<lint> divisors(lint n) {
vector<lint> f, l;
for (lint x = 1; x * x <= n; ++x) {
if (n % x == 0) {
f.push_back(x);
if (x * x != n) l.push_back(n / x);
}
}
f.reserve(f.size() + l.size());
copy(l.rbegin(), l.rend(), back_inserter(f));
return f;
}
lint phi(lint n) {
lint r = n;
for (lint i = 2; i * i <= n; ++i) {
if (n % i == 0) {
r -= r / i;
while (n % i == 0) n /= i;
}
}
if (n > 1) r -= r / n;
return r;
}
lint floor_sqrt(lint n) {
if (n == 0 || n == 1) return n;
lint x0 = 1LL << ((65 - countl_zero(static_cast<uint64_t>(n))) >> 1);
lint x1 = (x0 + n / x0) >> 1;
while (x1 < x0) {
x0 = x1;
x1 = (x0 + n / x0) >> 1;
}
return x0;
}
lint ceil_sqrt(lint n) {
const lint f = floor_sqrt(n);
if (f * f == n) return f;
return f + 1;
}
template <typename T>
constexpr bool is_intersect(T l1, T r1, T l2, T r2) {
return l1 <= r2 && l2 <= r1;
}
template <typename T>
constexpr bool is_intersect2(T l1, T r1, T l2, T r2) {
return l1 < r2 && l2 < r1;
}
lint modinv(lint a, lint m = Mod) {
lint b = m, u = 1, v = 0;
while (b != 0) {
lint t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
u %= m;
if (u < 0) u += m;
return u;
}
template <typename T>
T modpow(T x, T n, T m = Mod) {
if (m == 1) return 0;
T res = 1;
x %= m;
if (x < 0) x += m;
while (n > 0) {
if (n & 1) res = res * x % m;
x = x * x % m;
n >>= 1;
}
return res;
}
template <typename T>
T intpow(T x, T n) {
T res = 1;
while (n > 0) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
template <typename T>
vector<T> compressed(vector<T> v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
return v;
}
class Sieve {
private:
const int max_n;
vector<int> sieve;
public:
explicit Sieve(int max_n) : max_n(max_n), sieve(max_n + 1) {
iota(sieve.begin(), sieve.end(), 0);
for (int i = 2; i * i <= max_n; ++i) {
if (sieve[i] < i) continue;
for (int j = i * i; j <= max_n; j += i) {
if (sieve[j] == j) sieve[j] = i;
}
}
}
unordered_map<int, int> calc(int x) const {
assert(x <= max_n);
unordered_map<int, int> res;
while (x > 1) {
++res[sieve[x]];
x /= sieve[x];
}
return res;
}
vector<int> enumerate_prime(int x) const {
assert(x <= max_n);
vector<int> primes;
for (int i = 2; i <= x; ++i) {
if (sieve[i] == i) {
primes.push_back(i);
}
}
return primes;
}
};
struct UnionFind {
int n;
vector<int> par, rank, siz, es; // [root(i)]
int c;
UnionFind() = default;
explicit UnionFind(int _n) : n(_n), par(_n), rank(_n), siz(_n, 1), es(_n), c(_n) { iota(par.begin(), par.end(), 0); }
int root(int x) {
while (par[x] != x) x = par[x] = par[par[x]];
return x;
}
bool same(int x, int y) { return root(x) == root(y); }
void unite(int x, int y) {
if (x == y) return;
x = root(x);
y = root(y);
if (x == y)
++es[x];
else {
c--;
if (rank[x] < rank[y]) {
par[x] = y;
siz[y] += siz[x];
es[y] += es[x] + 1;
} else {
par[y] = x;
if (rank[x] == rank[y]) ++rank[x];
siz[x] += siz[y];
es[x] += es[y] + 1;
}
}
}
int size(int x) { return siz[root(x)]; }
vector<int> roots() {
vector<int> res;
res.reserve(c);
for (int i = 0; i < n; ++i) {
if (par[i] == i) {
res.push_back(i);
}
}
return res;
}
vector<vector<int>> groups() {
vector<vector<int>> res(n);
for (int i = 0; i < n; ++i)
if (par[i] == i) res[i].reserve(siz[i]);
for (int i = 0; i < n; ++i) res[root(i)].push_back(i);
res.erase(remove_if(res.begin(), res.end(), [](const vector<int> &v) { return v.empty(); }), res.end());
return res;
}
};
template <typename T>
class BinaryIndexedTree {
private:
int n;
vector<T> dat;
public:
BinaryIndexedTree() = default;
explicit BinaryIndexedTree(const int size) : n(size), dat(size + 1) {}
explicit BinaryIndexedTree(const vector<T> &vec) : n(vec.size()), dat(n + 1) {
for (int i = 0; i < n; ++i) dat[i + 1] = vec[i];
for (int i = 1; i <= n; ++i) {
const int j = i + (i & -i);
if (j <= n) dat[j] += dat[i];
}
}
// 0-indexed
void add(const int a, const T v) {
for (int x = a + 1; x <= n; x += (x & -x)) dat[x] += v;
}
// 0-indexed
void set(const int a, const T v) { add(a, v - get(a)); }
void reset() { fill(dat.begin(), dat.end(), T(0)); }
// [0, a)
T sum(const int a) const {
T res = 0;
for (int x = a; x > 0; x -= (x & -x)) res += dat[x];
return res;
}
// [a, b)
T sum(const int a, const int b) const { return sum(b) - sum(a); }
T get(const int i) const { return sum(i, i + 1); }
// min i s.t. sum(i) >= w
int lower_bound(T w) const {
int x = 0, r = 1;
while (r < n) r <<= 1;
for (int i = r; i > 0; i >>= 1) {
if (x + i <= n && dat[x + i] < w) {
w -= dat[x + i];
x += i;
}
}
return x + 1;
}
// min i s.t. sum(i) > w
int upper_bound(T w) const {
int x = 0, r = 1;
while (r < n) r <<= 1;
for (int i = r; i > 0; i >>= 1) {
if (x + i <= n && dat[x + i] <= w) {
w -= dat[x + i];
x += i;
}
}
return x + 1;
}
};
constexpr int msb(long long x) { return 63 - countl_zero(static_cast<uint64_t>(x)); }
#line 4 "test/lc_range_kth_smallest.cpp"
#line 1 "bit_vector.hpp"
class BitVector {
int b;
vector<uint64_t> bit;
vector<uint32_t> sum;
public:
BitVector() = default;
BitVector(int n) : b((n + 63) >> 6) {
bit.assign(b, 0ull);
sum.assign(b, 0u);
}
void set(int p) { bit[p >> 6] |= 1ull << (p & 63); }
bool operator[](int p) { return bit[p >> 6] >> (p & 63) & 1; }
void build() {
for (int i = 1; i < b; ++i) sum[i] = sum[i - 1] + __builtin_popcountll(bit[i - 1]);
}
int rank1(int p) { return sum[p >> 6] + __builtin_popcountll(bit[p >> 6] & ~(0xffffffffffffffffull << (p & 63))); }
int rank0(int p) { return p - rank1(p); }
int rank(int p, bool b) { return b ? rank1(p) : rank0(p); }
};
#line 2 "wavelet_matrix.hpp"
template <typename T>
class CompressedWaveletMatrix {
class WaveletMatrix {
int n, ma, lg;
vector<BitVector> bits;
vector<int> mid, st;
public:
WaveletMatrix() = default;
WaveletMatrix(vector<int> v) : n(v.size()), ma(*max_element(v.begin(), v.end())) {
lg = 0;
while ((1 << lg) < ma + 1) ++lg;
bits.assign(lg, n + 1);
mid.resize(lg);
vector<int> l(n), r(n); // for sort
for (int i = lg - 1; i >= 0; --i) {
int li = 0, ri = 0;
for (int j = 0; j < n; ++j) {
if (v[j] >> i & 1) {
bits[i].set(j);
r[ri++] = v[j];
} else
l[li++] = v[j];
}
mid[i] = li;
bits[i].build();
v.swap(l);
for (int j = 0; j < ri; ++j) v[j + li] = r[j];
}
st.assign(ma + 1, -1);
for (int i = 0; i < n; ++i)
if (st[v[i]] == -1) st[v[i]] = i;
}
int access(int p) {
int res = 0;
for (int i = lg - 1; i >= 0; --i) {
const bool b = bits[i][p];
p = bits[i].rank(p, b);
if (b) res |= 1 << i, p += mid[i];
}
return res;
}
int operator[](int p) { return access(p); }
int rank(int x, int r) {
for (int i = lg - 1; i >= 0; --i) {
const bool b = x >> i & 1;
r = mid[i] * b + bits[i].rank(r, b);
}
return r - st[x];
}
int rank(int x, int l, int r) { return rank(x, r) - rank(x, l); }
int kth_smallest(int l, int r, int k) {
check(l, r);
int res = 0;
for (int i = lg - 1; i >= 0; --i) {
const int cnt = bits[i].rank0(r) - bits[i].rank0(l);
const bool b = cnt <= k;
if (b) {
res |= 1 << i;
k -= cnt;
}
tie(l, r) = nxt(l, r, b, i);
}
return res;
}
int kth_largest(int l, int r, int k) { return kth_smallest(l, r, r - l - k - 1); }
int range_freq(int l, int r, int upper) {
check(l, r);
int res = 0;
for (int i = lg - 1; i >= 0; --i) {
const bool b = upper >> i & 1;
if (b) {
res += bits[i].rank0(r) - bits[i].rank0(l);
}
tie(l, r) = nxt(l, r, b, i);
}
return res;
}
int range_freq(int l, int r, int lower, int upper) { return range_freq(l, r, upper) - range_freq(l, r, lower); }
private:
pair<int, int> nxt(int l, int r, bool b, int i) { return {bits[i].rank(l, b) + mid[i] * b, bits[i].rank(r, b) + mid[i] * b}; }
void check(int& l, int& r) {
if (l < 0) l = 0;
if (r > n) r = n;
}
};
WaveletMatrix wm;
vector<T> y;
public:
CompressedWaveletMatrix(vector<T> v) : y(v) {
sort(y.begin(), y.end());
y.erase(unique(y.begin(), y.end()), y.end());
const int n = v.size();
vector<int> t(n);
for (int i = 0; i < n; ++i) t[i] = get(v[i]);
wm = WaveletMatrix(t);
}
T access(int p) { return y[wm.access(p)]; }
T operator[](int p) { return access(p); }
int count(T x, int r) {
int p = get(x);
if (p == y.size() || y[p] != x) return 0;
return wm.rank(p, r);
}
int count(T x, int l, int r) { return count(x, r) - count(x, l); }
// k=0: min
T kth_smallest(int l, int r, int k) { return y[wm.kth_smallest(l, r, k)]; }
// k=0: max
T kth_largest(int l, int r, int k) { return y[wm.kth_largest(l, r, k)]; }
int range_freq(int l, int r, T upper) { return wm.range_freq(l, r, get(upper)); }
int range_freq(int l, int r, T lower, T upper) { return wm.range_freq(l, r, get(lower), get(upper)); }
private:
int get(T x) { return lower_bound(y.begin(), y.end(), x) - y.begin(); }
};
#line 6 "test/lc_range_kth_smallest.cpp"
int main() {
int n, q;
cin >> n >> q;
vector<int> a(n);
for (int& e : a) cin >> e;
CompressedWaveletMatrix wm(a);
while (q--) {
int l, r, k;
cin >> l >> r >> k;
cout << wm.kth_smallest(l, r, k) << "\n";
}
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | all_zero_00 |
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6 ms | 4 MB |
g++ | dense_large_a_00 |
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51 ms | 4 MB |
g++ | dense_small_a_00 |
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44 ms | 4 MB |
g++ | example_00 |
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4 ms | 4 MB |
g++ | max_random_00 |
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196 ms | 10 MB |
g++ | max_random_01 |
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197 ms | 10 MB |
g++ | max_random_02 |
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197 ms | 10 MB |
g++ | max_random_03 |
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197 ms | 10 MB |
g++ | max_random_04 |
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198 ms | 10 MB |
g++ | random_00 |
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129 ms | 8 MB |
g++ | random_01 |
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144 ms | 8 MB |
g++ | random_02 |
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74 ms | 5 MB |
g++ | random_03 |
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72 ms | 9 MB |
g++ | random_04 |
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48 ms | 4 MB |
g++ | small_00 |
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5 ms | 4 MB |
g++ | small_01 |
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5 ms | 4 MB |
g++ | small_02 |
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5 ms | 4 MB |
g++ | small_03 |
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4 ms | 4 MB |
g++ | small_04 |
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5 ms | 4 MB |
g++ | small_05 |
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5 ms | 4 MB |
g++ | small_06 |
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5 ms | 4 MB |
g++ | small_07 |
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5 ms | 4 MB |
g++ | small_08 |
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5 ms | 4 MB |
g++ | small_09 |
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5 ms | 4 MB |