結果
| 問題 | No.3670 Fast Knapsack |
| コンテスト | |
| ユーザー |
 miscalc
|
| 提出日時 | 2026-09-05 06:27:09 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 55,991 bytes |
| 記録 | |
| コンパイル時間 | 2,860 ms |
| コンパイル使用メモリ | 369,112 KB |
| 実行使用メモリ | 13,928 KB |
| 最終ジャッジ日時 | 2026-09-05 06:27:22 |
| 合計ジャッジ時間 | 12,129 ms |
|
ジャッジサーバーID （参考情報） |
judge2_1 / judge1_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 11 TLE * 1 -- * 13 |
ソースコード
#define INF 4'000'000'000'000'000'037LL
#define EPS 1e-11
// https://github.com/miscalculation53/library/tree/wip/template/template_all.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_all_but_modint.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_types.hpp
#include <bits/stdc++.h>
namespace {
using namespace std;
using ld = decltype(EPS);
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
using tllll = tuple<ll, ll, ll, ll>;
#define vc vector
template <class T>
using vvc = vc<vc<T>>;
using vstr = vc<string>;
using i128 = __int128_t;
using u128 = __uint128_t;
i128 stoi128(const string &s)
{
const bool neg = s.front() == '-';
u128 res = 0;
for (int i = neg; i < (int)s.size(); i++)
res = 10 * res + s[i] - '0';
if (neg)
return -i128(res - 1) - 1;
return i128(res);
}
string i128tos(i128 x)
{
if (x == 0) return "0";
string sign = "", res = "";
u128 ux;
if (x < 0)
ux = u128(-(x + 1)) + 1, sign = "-";
else
ux = x;
while (ux > 0)
{
res += '0' + ux % 10;
ux /= 10;
}
reverse(res.begin(), res.end());
return sign + res;
}
#define cauto const auto
// https://github.com/miscalculation53/library/tree/wip/template/template_rep.hpp
#define overload4(_1,_2,_3,_4,name,...) name
#define repi1(i,n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi2(i,l,r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)
#define repi3(i,l,r,d) for (int i = int(l), rrrrr = int(r), ddddd = int(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)
#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
#define fem(...) for (auto &__VA_ARGS__)
// https://github.com/miscalculation53/library/tree/wip/template/template_math.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/is_integral_ext.hpp
template <class T>
constexpr bool is_integral_ext = is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>;
template <class T>
constexpr bool is_signed_ext = is_signed_v<T> || is_same_v<T, i128>;
template <class T>
constexpr bool is_unsigned_ext = is_unsigned_v<T> || is_same_v<T, u128>;
template <class T, class U>
inline bool chmin(T &a, U b) { return a > b ? a = b, true : false; }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divround(U a, V b) { return divfloor<T>(2 * T(a) + T(b), 2 * T(b)); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T safemod(U a, V b) { return T(a) - T(b) * divfloor<T>(a, b); }
template <class T = ll, class U, class V>
constexpr T ipow(U a, V b)
{
assert(b >= 0);
if (b == 0)
return 1;
if (a == 0 || a == 1)
return a;
if (a < 0 && a == -1)
return b & 1 ? -1 : 1;
T res = 1, tmp = a;
while (true)
{
if (b & 1)
res *= tmp;
b >>= 1;
if (b == 0)
break;
tmp *= tmp;
}
return res;
}
template <class T = ll, class A, class B, class M>
T mul_limited(A a, B b, M m)
{
assert(a >= 0 && b >= 0 && m >= 0);
if (b == 0)
return 0;
return T(a) > T(m) / T(b) ? T(m) : T(a) * T(b);
}
template <class T = ll, class A, class B>
T mul_limited(A a, B b) { return mul_limited<T>(a, b, INF); }
template <class T = ll, class A, class B, class M>
T pow_limited(A a, B b, M m)
{
assert(a >= 0 && b >= 0 && m >= 0);
if (a <= 1 || b == 0)
return min(ipow<T>(a, b), T(m));
T res = 1, tmp = a;
while (true)
{
if (b & 1)
{
if (res > T(m) / tmp)
return m;
res *= tmp;
}
b >>= 1;
if (b == 0)
break;
if (tmp > T(m) / tmp)
return m;
tmp *= tmp;
}
return res;
}
template <class T = ll, class A, class B>
T pow_limited(A a, B b) { return pow_limited<T>(a, b, INF); }
template <class T = ll, class A, class K>
constexpr T iroot(A a, K k)
{
assert(a >= 0 && k >= 1);
if (a <= 1 || k == 1)
return a;
if (k == 2)
{
const T aa = T(a);
T x = T(sqrtl((long double)a));
while (x > aa / x)
x--;
while (x < numeric_limits<T>::max())
{
const T y = x + 1;
if (y > aa / y)
break;
x = y;
}
return x;
}
auto isok = [&](T x) -> bool
{
if (x == 0)
return true;
T res = 1, k2 = k;
while (true)
{
if (k2 & 1)
{
if (res > T(a) / x)
return false;
res *= x;
}
k2 >>= 1;
if (k2 == 0)
break;
if (x > T(a) / x)
return false;
x *= x;
}
return res <= T(a);
};
T x = pow(a, 1.0 / k);
bool up = true;
while (!isok(x))
up = false, x--;
if (up)
{
while (x < numeric_limits<T>::max() && isok(x + 1))
x++;
}
return x;
}
template <class T = ll, class U, class V>
vc<T> base_repr(U val, V base)
{
assert(val >= 0);
assert(base >= 2);
if (val == 0)
return {0};
vc<T> a;
while (val > 0)
{
a.emplace_back(val % base);
val /= base;
}
reverse(a.begin(), a.end());
return a;
}
template <class T = ll, class U, class V>
vc<T> base_repr(U val, V base, int n)
{
assert(val >= 0);
assert(base >= 2);
assert(n >= 0);
vc<T> a(n);
repi(i, n)
{
a[i] = val % base;
val /= base;
}
reverse(a.begin(), a.end());
return a;
}
template <const bool use_upper = true, class U>
string base_repr_str(U val, int base, int n)
{
assert(val >= 0);
assert(2 <= base && base <= 36);
assert(n >= 0);
auto a = base_repr(val, base, n);
string s = "";
for (cauto &ai : a)
s += (ai < 10 ? '0' + ai : (use_upper ? 'A' : 'a') + (ai - 10));
return s;
}
// https://github.com/miscalculation53/library/tree/wip/template/template_vector.hpp
#define ALL(a) (a).begin(), (a).end()
template <class T = ll, class V>
inline T SZ(const V &x) { return x.size(); }
#define eb emplace_back
template <class F>
auto gen_vec(int n, const F &f)
{
vc<decltype(f(0))> res(n);
repi(i, n) res[i] = f(i);
return res;
}
template <class T, size_t d, size_t i = 0, class V>
auto dvec(const V (&sz)[d], const T &init)
{
if constexpr (i < d)
return vc(sz[i], dvec<T, d, i + 1>(sz, init));
else
return init;
}
template <class T = ll>
T ctol(const char &c, const string &s)
{
repi(i, SZ<int>(s)) if (s[i] == c) return i;
return -1;
}
template <class T = ll>
vc<T> stov(const string &s, const string &t)
{
return gen_vec(SZ<int>(s), [&](int i) -> T
{ return ctol(s[i], t); });
}
template <class T>
string vtos(const vc<T> &v, const string &t)
{
string res = "";
fe(vi : v) res += t[vi];
return res;
}
template <class T>
vc<T> concat(const vc<T> &v) { return v; }
template <class T, class... Ts>
vc<T> concat(vc<T> v, const vc<Ts> &...vs)
{
(v.insert(v.end(), ALL(vs)), ...);
return v;
}
// https://github.com/miscalculation53/library/tree/wip/template/template_algo.hpp
template <class T, class V>
T SUM(const V &v)
{
T s{};
fec(vi : v) s += vi;
return s;
}
template <class V>
auto MAX(const V &v) { return *max_element(ALL(v)); }
template <class T, class U>
vc<T> permuted(const vc<T> &a, const vc<U> &p)
{
const int n = p.size();
vc<T> res(n);
repi(i, n)
{
assert(0 <= p[i] && p[i] < U(a.size()));
res[i] = a[p[i]];
}
return res;
}
template <class T, class U, class... Ts>
vc<T> permuted(const vc<T> &p, const vc<U> &q, const vc<Ts> &...rs)
{
return permuted(permuted(p, q), rs...);
}
template <class V>
V reversed(const V &v) { return V(v.rbegin(), v.rend()); }
template <class V, class Equal = equal_to<>>
void unique(V &v, Equal equal = {}) { v.erase(std::unique(ALL(v), equal), v.end()); }
template <class V, class Compare = less<>, class Equal = equal_to<>>
void sortunique(V &v, Compare comp = {}, Equal equal = {})
{
sort(ALL(v), comp);
unique(v, equal);
}
template <class V, class U>
void rotate(V &v, U k)
{
const U n = v.size();
if (n == 0)
return;
k = (k % n + n) % n;
std::rotate(v.begin(), v.begin() + k, v.end());
}
template <class T>
vvc<T> top(const vvc<T> &a)
{
if (a.empty())
return {};
const int n = a.size(), m = a[0].size();
vvc<T> b(m, vc<T>(n));
repi(i, n)
{
assert(SZ<int>(a[i]) == m);
repi(j, m) b[j][i] = a[i][j];
}
return b;
}
template <class T, class = void>
struct has_e0 : false_type {};
template <class T>
struct has_e0<T, void_t<decltype(T::e0())>> : true_type {};
template <class T>
inline constexpr bool has_e0_v = has_e0<T>::value;
template <class T>
struct MonoidAdd
{
using S = T;
static constexpr S op(S a, S b) { return a + b; }
static constexpr S e()
{
if constexpr (has_e0_v<S>)
return S::e0();
else
return {};
}
template <class I, class = decltype(declval<S>() * declval<I>())>
static constexpr S pow(const S &a, I k) { return a * k; }
};
template <class T, const T infty = INF>
struct MonoidMin
{
using S = T;
static constexpr S op(S a, S b) { return min(a, b); }
static constexpr S e() { return infty; }
template <class I>
static constexpr S pow(const S &a, I k) { return k == 0 ? e() : a; }
};
template <class T, const T infty = INF>
struct MonoidMax
{
using S = T;
static constexpr S op(S a, S b) { return max(a, b); }
static constexpr S e() { return -infty; }
template <class I>
static constexpr S pow(const S &a, I k) { return k == 0 ? e() : a; }
};
namespace internal
{
template <class M, class I, class = void>
struct HasMonoidPow : false_type
{
};
template <class M, class I>
struct HasMonoidPow<M, I, void_t<decltype(M::pow(declval<const typename M::S &>(), declval<I>()))>> : true_type
{
};
}
template <class M, class I>
typename M::S pow_monoid(typename M::S a, I k)
{
if constexpr (is_signed_ext<I>)
assert(k >= 0);
if constexpr (internal::HasMonoidPow<M, I>::value)
return M::pow(a, k);
else
{
typename M::S c = M::e();
for (; k; k >>= 1)
{
if (k & 1)
c = M::op(c, a);
a = M::op(a, a);
}
return c;
}
}
template <class M>
vc<typename M::S> cuml(const vc<typename M::S> &v, int left_index = 0)
{
const int n = v.size();
vc<typename M::S> res(n + 1);
res[0] = M::e();
repi(i, n) res[i + 1] = M::op(res[i], v[i]);
res.erase(res.begin(), res.begin() + left_index);
return res;
}
template <class M>
vc<typename M::S> cumr(const vc<typename M::S> &v, int right_index = 0)
{ return reversed(cuml<M>(reversed(v), right_index)); }
constexpr array<pll, 4> DRULgrid = {{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}};
constexpr array<pll, 4> DRULplane = {{{0, -1}, {1, 0}, {0, 1}, {-1, 0}}};
// https://github.com/miscalculation53/library/tree/wip/template/template_binsearch.hpp
template <class T>
struct is_random_access_iterator
{
static constexpr bool value = is_same_v<
typename iterator_traits<T>::iterator_category,
random_access_iterator_tag
>;
};
template <class T>
constexpr bool is_random_access_iterator_v = is_random_access_iterator<T>::value;
template <class T = ll, class V, class Value, class Comp = ranges::less, class Proj = identity>
inline T LB(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
{ return ranges::lower_bound(v, val, comp, proj) - v.begin(); }
template <class T = ll, class V, class Value, class Comp = ranges::less, class Proj = identity>
inline T UB(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
{ return ranges::upper_bound(v, val, comp, proj) - v.begin(); }
#define DEFAULT_COMP ranges::less
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto lt_cnt(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>
{ return LB<T>(v, val, comp, proj); }
template <class V, class Value>
inline auto lt_max(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{
auto it = v.lower_bound(val);
return it == v.begin() ? v.end() : prev(it);
}
template <class V, class Value>
inline auto leq_max(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{
auto it = v.upper_bound(val);
return it == v.begin() ? v.end() : prev(it);
}
template <class V, class Value>
inline auto gt_min(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{ return v.upper_bound(val); }
template <class V, class Value>
inline auto geq_min(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>
{ return v.lower_bound(val); }
namespace internal
{
template <class T>
bool binsearch_adjacent(T a, T b)
{
if (a < b)
return a + 1 == b;
if (b < a)
return b + 1 == a;
return false;
}
};
template <class T = ll, class Judge, class InitOk, class InitNg>
pair<T, T> binsearch(const Judge &judge, InitOk init_ok, InitNg init_ng, bool check_ok = true, bool check_ng = true)
{
T ok(init_ok), ng(init_ng);
if (check_ok)
assert(judge(ok));
if (check_ng)
assert(!judge(ng));
while (!internal::binsearch_adjacent(ok, ng))
{
T mid = (ok & ng) + ((ok ^ ng) >> 1);
(judge(mid) ? ok : ng) = mid;
}
return {ok, ng};
}
// https://github.com/miscalculation53/library/tree/wip/template/template_bit.hpp
template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }
inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); }
inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); }
inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); }
inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); }
inline constexpr ll popcount(ll x) { return std::popcount((ull)x); }
inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); }
// https://github.com/miscalculation53/library/tree/wip/template/template_inout.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_dump.hpp
#define dump(...)
#define local(...)
#define oj(...) __VA_ARGS__
template <class T, class Sequence>
vc<T> content(queue<T, Sequence> que)
{
vc<T> res;
while (!que.empty())
{
res.eb(que.front());
que.pop();
}
return res;
}
template <class T, class Sequence, class Compare>
vc<T> content(priority_queue<T, Sequence, Compare> pque)
{
vc<T> res;
while (!pque.empty())
{
res.eb(pque.top());
pque.pop();
}
return res;
}
template <class T>
auto content(const T &obj) { return obj.content(); }
namespace fastio {
template <class T>
struct unsigned_integer
{
using type = make_unsigned_t<T>;
};
template <>
struct unsigned_integer<i128>
{
using type = u128;
};
template <>
struct unsigned_integer<u128>
{
using type = u128;
};
template <class T>
using unsigned_integer_t = typename unsigned_integer<T>::type;
static constexpr uint32_t SIZ = 1 << 17;
char ibuf[SIZ];
char obuf[SIZ];
char out[100];
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SIZ - pir + pil, stdin);
pil = 0;
if (pir < SIZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd1(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd1_real(T &x) {
string s;
rd1(s);
if constexpr (is_same_v<T, long double>)
x = stold(s);
else
x = stod(s);
}
template <typename T>
void rd1_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
using U = unsigned_integer_t<T>;
U val = 0;
while ('0' <= c) { val = val * 10 + (c & 15), c = ibuf[pil++]; }
pil--;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (minus)
{
const U min_abs = U(numeric_limits<T>::max()) + 1;
assert(val <= min_abs);
x = val == min_abs ? numeric_limits<T>::lowest() : -T(val);
}
else
{
assert(val <= U(numeric_limits<T>::max()));
x = T(val);
}
}
else
x = T(val);
}
void rd1(ll &x) { rd1_integer(x); }
void rd1(uint &x) { rd1_integer(x); }
template <class T, class U>
void rd1(pair<T, U> &p) {
return rd1(p.first), rd1(p.second);
}
template <class... T>
void rd1(tuple<T...> &tpl) {
apply([](auto &...x) { (rd1(x), ...); }, tpl);
}
template <size_t N = 0, typename T>
void rd1(array<T, N> &x) {
for (auto &d: x) rd1(d);
}
template <class T>
void rd1(vc<T> &x) {
for (auto &d: x) rd1(d);
}
template <class... T>
void read(T &...x) {
(rd1(x), ...);
}
void wt1(const char c) {
if (por == SIZ) flush();
obuf[por++] = c;
}
void wt1(const string s) {
for (char c: s) wt1(c);
}
template <typename T>
void wt1_integer(T x) {
if (por > SIZ - 100) flush();
using U = unsigned_integer_t<T>;
U ux;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (x < 0)
obuf[por++] = '-', ux = U(0) - U(x);
else
ux = U(x);
}
else
ux = x;
int outi;
for (outi = 96; ux >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[ux % 10000], 4);
ux /= 10000;
}
if (ux >= 1000) {
memcpy(obuf + por, pre.num[ux], 4);
por += 4;
} else if (ux >= 100) {
memcpy(obuf + por, pre.num[ux] + 1, 3);
por += 3;
} else if (ux >= 10) {
int q = (ux * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (ux - q * 10) | '0';
por += 2;
} else
obuf[por++] = ux | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt1_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << x;
string s = oss.str();
wt1(s);
}
void wt1(int x) { wt1_integer(x); }
template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void wt1(T x) { wt1_integer(x); }
template <class T, class U>
void wt1(const pair<T, U> &val) {
wt1(val.first);
wt1(' ');
wt1(val.second);
}
template <class... T>
void wt1(const tuple<T...> &tpl) {
if constexpr (sizeof...(T))
{
int i = 0;
apply([&](const auto &...x)
{ ((i++ ? wt1(' ') : void(), wt1(x)), ...); }, tpl);
}
}
template <class T, size_t S>
void wt1(const array<T, S> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt1(' ');
wt1(val[i]);
}
}
template <class T>
void wt1(const vector<T> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt1(' ');
wt1(val[i]);
}
}
template <class... T>
void write(T &&...x) {
(wt1(std::forward<T>(x)), ...);
}
template <class... T>
void print(T &&...x) {
if constexpr (sizeof...(T))
{
int i = 0;
((i++ ? wt1(' ') : void(), wt1(std::forward<T>(x))), ...);
}
wt1('\n');
}
}
struct Dummy {
Dummy() { atexit(fastio::flush); }
} dummy;
namespace internal
{
template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }
template <class... T>
void READVECnodump(int n, vc<T> &...v)
{
(v.resize(n), ...);
READnodump(v...);
}
};
#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define IN(T,...) T __VA_ARGS__; READ(__VA_ARGS__)
#define LL(...) IN(ll, __VA_ARGS__)
#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define VEC(T,n,...) vc<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define PRINT fastio::print
template <class T, class U, class P>
pair<T, U> &operator+=(pair<T, U> &a, const P &b)
{
a.first += b.first;
a.second += b.second;
return a;
}
template <class T, class U, class P>
pair<T, U> operator+(pair<T, U> a, const P &b) { return a += b; }
template <class T, class U, class P>
pair<T, U> &operator-=(pair<T, U> &a, const P &b)
{
a.first -= b.first;
a.second -= b.second;
return a;
}
template <class T, class U, class P>
pair<T, U> operator-(pair<T, U> a, const P &b) { return a -= b; }
template <class T, class U>
pair<T, U> operator-(pair<T, U> a)
{
a.first = -a.first;
a.second = -a.second;
return a;
}
template <class T, size_t n, class A>
array<T, n> &operator+=(array<T, n> &a, const A &b)
{
for (size_t i = 0; i < n; i++)
a[i] += b[i];
return a;
}
template <class T, size_t n, class A>
array<T, n> operator+(array<T, n> a, const A &b) { return a += b; }
template <class T, size_t n, class A>
array<T, n> &operator-=(array<T, n> &a, const A &b)
{
for (size_t i = 0; i < n; i++)
a[i] -= b[i];
return a;
}
template <class T, size_t n, class A>
array<T, n> operator-(array<T, n> a, const A &b) { return a -= b; }
template <class T, size_t n>
array<T, n> operator-(array<T, n> a)
{
for (auto &ai : a)
ai = -ai;
return a;
}
namespace internal
{
template <size_t... I, class A, class B>
auto &tuple_add_impl(A &a, const B &b, const index_sequence<I...>)
{
((get<I>(a) += get<I>(b)), ...);
return a;
}
template <size_t... I, class A, class B>
auto &tuple_sub_impl(A &a, const B &b, const index_sequence<I...>)
{
((get<I>(a) -= get<I>(b)), ...);
return a;
}
template <size_t... I, class A>
auto &tuple_neg_impl(A &a, const index_sequence<I...>)
{
((get<I>(a) = -get<I>(a)), ...);
return a;
}
};
template <class... Ts, class Tp>
tuple<Ts...> &operator+=(tuple<Ts...> &a, const Tp &b)
{ return internal::tuple_add_impl(a, b, make_index_sequence<tuple_size_v<tuple<Ts...>>>{}); }
template <class... Ts, class Tp>
tuple<Ts...> operator+(tuple<Ts...> a, const Tp &b) { return a += b; }
template <class... Ts, class Tp>
tuple<Ts...> &operator-=(tuple<Ts...> &a, const Tp &b)
{ return internal::tuple_sub_impl(a, b, make_index_sequence<tuple_size_v<tuple<Ts...>>>{}); }
template <class... Ts, class Tp>
tuple<Ts...> operator-(tuple<Ts...> a, const Tp &b) { return a -= b; }
template <class... Ts>
tuple<Ts...> operator-(tuple<Ts...> a)
{
internal::tuple_neg_impl(a, make_index_sequence<sizeof...(Ts)>{});
return a;
}
template <class T, class Add>
void offset(vvc<T> &v, const Add &add) { for (auto &vi : v) for (auto &vij : vi) vij += add; }
template <class T, class U>
pair<vc<T>, vc<U>> unzip(const vc<pair<T, U>> &vt)
{
const size_t n = vt.size();
pair<vc<T>, vc<U>> tv;
tv.first.resize(n), tv.second.resize(n);
for (size_t i = 0; i < n; i++)
tie(tv.first[i], tv.second[i]) = vt[i];
return tv;
}
template <class T, class U>
vc<pair<T, U>> zip(const pair<vc<T>, vc<U>> &tv)
{
const size_t n = tv.first.size();
assert(n == tv.second.size());
vc<pair<T, U>> vt(n);
for (size_t i = 0; i < n; i++)
vt[i] = make_pair(tv.first[i], tv.second[i]);
return vt;
}
namespace internal
{
template <size_t... I, class V, class Tp>
auto vt_to_tv_impl(V &tv, const Tp &t, index_sequence<I...>, size_t index)
{ ((get<I>(tv)[index] = get<I>(t)), ...); }
template <size_t... I, class Tp>
auto tv_to_vt_impl(const Tp &tv, index_sequence<I...>, size_t index)
{ return make_tuple(get<I>(tv)[index]...); }
};
template <class... Ts>
auto unzip(const vc<tuple<Ts...>> &vt)
{
const size_t n = vt.size();
tuple<vc<Ts>...> tv;
apply([&](auto &...v)
{ ((v.resize(n)), ...); }, tv);
for (size_t i = 0; i < n; i++)
internal::vt_to_tv_impl(tv, vt[i], make_index_sequence<tuple_size_v<decltype(tv)>>{}, i);
return tv;
}
template <class... Ts>
auto zip(const tuple<vc<Ts>...> &tv)
{
size_t n = get<0>(tv).size();
apply([&](auto &...v)
{ ((void(v), assert(v.size() == n)), ...); }, tv);
vc<tuple<Ts...>> vt(n);
for (size_t i = 0; i < n; i++)
vt[i] = internal::tv_to_vt_impl(tv, index_sequence_for<Ts...>{}, i);
return vt;
}
// https://github.com/miscalculation53/library/tree/wip/template/template_random.hpp
mt19937_64 mt;
template <class T = ll, class U1, class U2>
T randint(U1 l, U2 r)
{
assert(T(l) <= T(r));
return uniform_int_distribution<T>(T(l), T(r))(mt);
}
namespace internal
{
template <bool does_sort, class V, class T>
void random_sample_range(V &res, T l, T r)
{
int k = res.size();
T n = r - l;
if (k <= 256)
{
repi(i, k)
{
T j = n - T(k) + T(i), x = randint<T>(0, j);
if (find(res.begin(), res.begin() + i, x) != res.begin() + i)
x = j;
res[i] = x;
}
}
else
{
unordered_set<T> used;
used.reserve(2 * size_t(k));
repi(i, k)
{
T j = n - T(k) + T(i), x = randint<T>(0, j);
if (!used.insert(x).second)
x = j, used.insert(x);
res[i] = x;
}
}
for (T &x : res) x += l;
if constexpr (does_sort)
sort(res.begin(), res.end());
else
shuffle(res.begin(), res.end(), mt);
}
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/template_modint.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_static.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/larger_int.hpp
template <class T>
struct larger_int
{
using type = T;
};
#define LARGER_INT(T,U) template <> struct larger_int<T> { using type = U; };
LARGER_INT(signed char, short)
LARGER_INT(short, int)
LARGER_INT(int, long long)
LARGER_INT(long, __int128_t)
LARGER_INT(long long, __int128_t)
LARGER_INT(unsigned char, unsigned short)
LARGER_INT(unsigned short, unsigned int)
LARGER_INT(unsigned int, unsigned long long)
LARGER_INT(unsigned long, __uint128_t)
LARGER_INT(unsigned long long, __uint128_t)
#undef LARGER_INT
template <class T>
using larger_int_t = typename larger_int<T>::type;
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_isprime.hpp
namespace internal
{
template <class T>
constexpr ll powmod_constexpr(ll x, ll n, T m)
{
if (m == 1)
return 0;
using U = make_unsigned_t<T>;
using L = larger_int_t<U>;
U r = 1, y = safemod(x, m);
while (n)
{
if (n & 1)
r = L(r) * y % m;
y = L(y) * y % m;
n >>= 1;
}
return r;
}
template <class T>
constexpr bool isprime_constexpr(T n)
{
if constexpr (sizeof(T) > 4)
{
if (n <= INT_MAX)
return isprime_constexpr<int>(n);
}
if (n <= 1)
return false;
if (n == 2 || n == 7 || n == 61)
return true;
if (n % 2 == 0)
return false;
ll d = n - 1;
while (d % 2 == 0)
d /= 2;
using U = make_unsigned_t<T>;
using L = larger_int_t<U>;
auto miller_rabin = [&](const auto &bases) constexpr
{
for (ll a : bases)
{
ll t = d, y = powmod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1)
{
y = L(y) * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0)
return false;
}
return true;
};
if constexpr(sizeof(T) <= 4)
{
constexpr ll bases[3] = {2, 7, 61};
return miller_rabin(bases);
}
else
{
constexpr ll bases[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
return miller_rabin(bases);
}
}
template <auto n>
constexpr bool isprime = isprime_constexpr(n);
};
namespace internal
{
template <auto M>
struct policy_static
{
using mod_type = decltype(M);
using value_type = make_unsigned_t<mod_type>;
using calc_type = larger_int_t<value_type>;
static constexpr bool is_prime = isprime_constexpr(M);
static constexpr mod_type mod() { return M; }
static constexpr value_type umod() { return M; }
static constexpr value_type init(value_type v) { return v; }
static constexpr mod_type val(value_type v) { return v; }
static constexpr value_type mul(value_type a, value_type b)
{
return (value_type)((calc_type(a) * b) % M);
}
};
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_barrett32.hpp
namespace internal
{
struct barrett32
{
uint m;
ull im;
explicit barrett32(uint m) : m(m), im((ull)(-1) / m + 1) {}
uint umod() const { return m; }
uint mul(uint a, uint b) const
{
ull z = a;
z *= b;
ull x = ull((u128(z) * im) >> 64);
ull y = x * m;
return uint(z - y + (z < y ? m : 0));
}
};
template <int id>
struct policy_barrett32
{
using value_type = uint;
using calc_type = ull;
using mod_type = int;
static constexpr bool is_prime = false;
static inline barrett32 reducer{998244353};
static void set_mod(mod_type m) { reducer = barrett32(m); }
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return v; }
static mod_type val(value_type v) { return v; }
static value_type mul(value_type a, value_type b) { return reducer.mul(a, b); }
};
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_montgomery64.hpp
namespace internal
{
inline constexpr ull inv64(ull a)
{
ull x = a;
while (a * x != 1) x *= 2 - a * x;
return x;
}
struct montgomery64odd
{
ull m, im, sq;
explicit montgomery64odd(ull m) : m(m), im(inv64(m)), sq(-u128(m) % m) {}
ull umod() const { return m; }
ull reduce(u128 x) const
{
auto t = (x + u128(m) * (-im * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * sq); }
};
struct montgomery64
{
ull m, mx, imx, d, q;
uint b;
explicit montgomery64(ull m) : m(m)
{
b = countr_zero(m), mx = m >> b;
imx = inv64(mx);
d = powmod_constexpr((mx + 1) / 2, b, mx);
u128 sq = -u128(mx) % mx;
q = (1 + (((sq - 1) * d) << b)) % m;
}
ull umod() const { return m; }
ull reduce(u128 x) const
{
if (b == 0)
{
auto t = (x + u128(mx) * (-imx * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull p = x & MASK(b);
x = (x >> b) + p * d;
ull y = p << (64 - b);
auto t = (x + u128(mx) * (imx * (y - ull(x)))) >> (64 - b);
if (t >= m) { t -= m; if (t >= m) t -= m; }
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * q); }
};
template <int id>
struct policy_montgomery64_odd
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64odd reducer{(1LL << 61) - 1};
static void set_mod(mod_type m) { reducer = montgomery64odd(m); }
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v) { return reducer.reduce(v); }
static value_type mul(value_type a, value_type b) { return reducer.reduce((calc_type)a * b); }
};
template <int id>
struct policy_montgomery64
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64 reducer{(1LL << 61) - 1};
static void set_mod(mod_type m) { reducer = montgomery64(m); }
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v) { return reducer.reduce(v); }
static value_type mul(value_type a, value_type b) { return reducer.reduce((calc_type)a * b); }
};
};
// https://github.com/miscalculation53/library/tree/wip/math/extgcd.hpp
template <class T = ll>
constexpr tuple<T, T, T> extgcd(T a, T b)
{
if (a == 0 && b == 0)
return {0, 0, 0};
T x1 = 1, y1 = 0, z1 = a;
T x2 = 0, y2 = 1, z2 = b;
while (z2 != 0)
{
T q = z1 / z2;
tie(x1, x2) = make_pair(x2, x1 - q * x2);
tie(y1, y2) = make_pair(y2, y1 - q * y2);
tie(z1, z2) = make_pair(z2, z1 - q * z2);
}
if (z1 < 0)
x1 = -x1, y1 = -y1, z1 = -z1;
return {z1, x1, y1};
}
namespace internal
{
template <class Policy>
struct modint_impl
{
using V = typename Policy::value_type;
using M = typename Policy::mod_type;
using mint = modint_impl;
private:
V _v;
public:
static constexpr M mod() { return Policy::mod(); }
template <class T = Policy>
static auto set_mod(M m) -> decltype(T::set_mod(m)) { return T::set_mod(m); }
static mint raw(V v)
{
mint x;
x._v = v;
return x;
}
modint_impl() : _v(0) {}
template <class T, typename = enable_if_t<is_integral_ext<T>>>
modint_impl(T v)
{
V rem;
if constexpr (is_signed_ext<T>)
{
using S = make_signed_t<V>;
S x = v % S(Policy::umod());
if (x < 0)
x += Policy::umod();
rem = x;
}
else
rem = V(v % Policy::umod());
_v = Policy::init(rem);
};
M val() const { return Policy::val(_v); }
mint &operator+=(const mint &rhs)
{
_v += rhs._v;
if (_v >= Policy::umod())
_v -= Policy::umod();
return *this;
}
mint &operator-=(const mint &rhs)
{
_v -= rhs._v;
if (_v >= Policy::umod())
_v += Policy::umod();
return *this;
}
mint &operator*=(const mint &rhs)
{
_v = Policy::mul(_v, rhs._v);
return *this;
}
mint &operator/=(const mint &rhs)
{
return *this *= rhs.inv();
}
mint &operator++()
{
_v++;
if (_v == Policy::umod())
_v = 0;
return *this;
}
mint &operator--()
{
if (_v == 0)
_v = Policy::umod();
_v--;
return *this;
}
mint operator++(int)
{
mint res = *this;
++(*this);
return res;
}
mint operator--(int)
{
mint res = *this;
--(*this);
return res;
}
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
template <class T>
mint pow(T n) const
{
assert(n >= 0);
mint x = *this, r = 1;
while (n)
{
if (n & 1)
r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const
{
if constexpr (Policy::is_prime)
{
return pow(mod() - 2);
}
else
{
auto [g, x, y] = extgcd<M>(val(), mod());
assert(g == 1);
return mint(x);
}
}
friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
friend void rd1(mint &x)
{
long long a;
fastio::rd1(a);
x = a;
}
friend void wt1(const mint &x)
{
fastio::wt1(x.val());
}
};
};
template <int mod>
using static_modint32 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint32 = internal::modint_impl<internal::policy_barrett32<id>>;
template <ll mod>
using static_modint64 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint64_odd = internal::modint_impl<internal::policy_montgomery64_odd<id>>;
template <int id>
using dynamic_modint64 = internal::modint_impl<internal::policy_montgomery64<id>>;
using modint998244353 = static_modint32<998244353>;
template <class T>
struct is_modint : std::false_type
{
};
template <class Policy>
struct is_modint<internal::modint_impl<Policy>> : std::true_type
{
};
template <class T>
inline constexpr bool is_modint_v = is_modint<T>::value;
template <class T>
struct is_static_modint : false_type {};
template <int m>
struct is_static_modint<static_modint32<m>> : true_type {};
template <ll m>
struct is_static_modint<static_modint64<m>> : true_type {};
template <class T>
inline constexpr bool is_static_modint_v = is_static_modint<T>::value;
template <class T>
struct is_dynamic_modint : false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint32<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64_odd<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64<id>> : true_type {};
template <class T>
inline constexpr bool is_dynamic_modint_v = is_dynamic_modint<T>::value;
template <typename, typename = void>
struct has_mod : std::false_type
{
};
template <typename T>
struct has_mod<T, std::void_t<decltype(T::mod())>> : std::true_type
{
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/power_table.hpp
template <class mint>
struct PowerTable
{
private:
decltype(mint::mod()) mod;
mint base;
vc<mint> pw;
public:
PowerTable() {}
PowerTable(const mint &base) : mod(mint::mod()), base(base), pw(1, 1) {}
void reserve(int n)
{
if (mod != mint::mod())
{
mod = mint::mod();
pw = {1};
}
int i = pw.size();
if (n < i)
return;
pw.resize(n + 1);
for (; i <= n; i++)
pw[i] = pw[i - 1] * base;
}
mint pow(int n)
{
reserve(n);
return pw[n];
}
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/binomial.hpp
template <class T>
struct Binomial
{
private:
inline static decltype(T::mod()) mod;
public:
inline static vc<T> fac_, finv_, inv_;
static void reserve(int n)
{
if constexpr (is_dynamic_modint_v<T>)
{
if (mod != T::mod())
{
mod = T::mod();
fac_ = {1, 1}, finv_ = {1, 1}, inv_ = {0, 1};
}
}
else
{
if (fac_.empty())
fac_ = {1, 1}, finv_ = {1, 1}, inv_ = {0, 1};
}
if (n < SZ(fac_))
return;
chmin(n, T::mod() - 1);
int si = fac_.size();
fac_.resize(n + 1), finv_.resize(n + 1), inv_.resize(n + 1);
repi(i, si, n + 1)
{
fac_[i] = fac_[i - 1] * T::raw(i);
inv_[i] = -inv_[T::mod() % i] * T::raw(T::mod() / i);
finv_[i] = finv_[i - 1] * inv_[i];
}
}
static T inv(int n)
{
n %= T::mod();
if (n < 0)
n += T::mod();
assert(n != 0);
reserve(n);
return inv_[n];
}
static T C(int n, int k)
{
if (n < k)
return 0;
if (n < 0 || k < 0)
return 0;
if (n >= T::mod())
return 0;
reserve(n);
return fac_[n] * finv_[k] * finv_[n - k];
}
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/stom.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/to_rational.hpp
// https://github.com/miscalculation53/library/tree/wip/math/svp2d.hpp
template <class T = ll, class U = larger_int_t<T>>
pair<T, T> svp2d(const pair<T, T> &a, const pair<T, T> &b)
{
assert((a != pair<T, T>{0, 0} && b != pair<T, T>{0, 0}));
auto [a1, a2] = a;
auto [b1, b2] = b;
if ((U)a1 * a1 + (U)a2 * a2 < (U)b1 * b1 + (U)b2 * b2)
swap(a1, b1), swap(a2, b2);
while ((U)a1 * a1 + (U)a2 * a2 > (U)b1 * b1 + (U)b2 * b2)
{
swap(a1, b1), swap(a2, b2);
T k = divround<U>((U)a1 * b1 + (U)a2 * b2, (U)a1 * a1 + (U)a2 * a2);
b1 -= k * a1, b2 -= k * a2;
if (b1 == 0 && b2 == 0)
return {a1, a2};
}
return {a1, a2};
}
template <class mint>
pair<decltype(mint(0).val()), decltype(mint(0).val())>
mint_to_rat(const mint &x)
{
auto [p, q] = svp2d({x.val(), 1}, {mint::mod(), 0});
if (q < 0)
p = -p, q = -q;
return {p, q};
}
namespace cpp_dump
{
struct mint_to_rat_fn
{
template <class T>
constexpr auto operator()(const T &x) const -> decltype(mint_to_rat(x))
{
return mint_to_rat(x);
}
};
struct rat_closure : std::ranges::range_adaptor_closure<rat_closure>
{
template <typename T>
constexpr auto operator()(T &&t) const
{
if constexpr (!std::ranges::range<T> && std::invocable<mint_to_rat_fn, decltype(std::forward<T>(t))>)
{
return mint_to_rat_fn{}(std::forward<T>(t));
}
else if constexpr (std::ranges::range<T>)
{
using Ref = std::ranges::range_reference_t<T>;
if constexpr (std::invocable<mint_to_rat_fn, decltype(std::forward<Ref>(std::declval<Ref>()))>)
{
return std::forward<T>(t) | std::views::transform(mint_to_rat_fn{});
}
else if constexpr (std::ranges::range<Ref>)
{
return std::forward<T>(t) | std::views::transform([this](auto &&inner)
{ return (*this)(std::forward<decltype(inner)>(inner)); });
}
else
{
static_assert(false);
}
}
else
{
static_assert(false);
}
}
};
template <typename T>
requires(!std::ranges::range<T> && std::invocable<mint_to_rat_fn, T>)
constexpr auto operator|(T &&t, const rat_closure &c)
{
return c(std::forward<T>(t));
}
}
using mint = modint998244353;
using bi = Binomial<mint>;
void init()
{
oj(mt.seed(random_device()()));
}
// https://github.com/miscalculation53/library/tree/wip/algo/subset_sum.hpp
// https://github.com/miscalculation53/library/tree/wip/ds/dynamic_bitset.hpp
struct DynamicBitset
{
using Word = ull;
static constexpr int word_bits = numeric_limits<Word>::digits;
private:
int n;
vc<Word> dat;
static int word_size(int n) { return (n + word_bits - 1) / word_bits; }
static Word low_mask(int k)
{
return k == word_bits ? ~Word(0) : (Word(1) << k) - 1;
}
Word last_mask() const
{
return n % word_bits == 0 ? ~Word(0) : low_mask(n % word_bits);
}
void trim()
{
if (!dat.empty())
dat.back() &= last_mask();
}
Word get_word(int i) const
{
int w = i / word_bits, b = i % word_bits;
Word x = dat[w] >> b;
if (b && w + 1 < SZ(dat))
x |= dat[w + 1] << (word_bits - b);
return x;
}
template <int op, class F>
DynamicBitset &apply_slice(int l, int r, const DynamicBitset &b, int bl, const F &f)
{
assert(0 <= l && l <= r && r <= n);
assert(0 <= bl && bl + r - l <= b.n);
if (l == r)
return *this;
auto apply_word = [&](int w)
{
int lo = max(l, w * word_bits), hi = min(r, (w + 1) * word_bits);
int len = hi - lo, shift = lo % word_bits;
Word mask = low_mask(len) << shift;
Word x = (b.get_word(bl + lo - l) & low_mask(len)) << shift;
Word old = dat[w], y;
if constexpr (op == 0)
y = x;
else if constexpr (op == 1)
y = old & x;
else if constexpr (op == 2)
y = old | x;
else
y = old ^ x;
dat[w] = (old & ~mask) | (y & mask);
if constexpr (!is_same_v<F, nullptr_t>)
{
Word added = dat[w] & ~old & mask;
while (added)
{
f(w * word_bits + __builtin_ctzll(added));
added &= added - 1;
}
}
};
int lw = l / word_bits, rw = (r - 1) / word_bits;
if (this == &b && bl < l && l < bl + r - l)
repi(w, rw, lw - 1, -1) apply_word(w);
else
repi(w, lw, rw + 1) apply_word(w);
return *this;
}
public:
struct Reference
{
DynamicBitset *bs;
int pos;
operator bool() const { return bs->test(pos); }
Reference &operator=(bool value)
{
bs->set(pos, value);
return *this;
}
Reference &operator=(const Reference &ref) { return *this = bool(ref); }
Reference &flip()
{
bs->flip(pos);
return *this;
}
};
DynamicBitset() : n(0) {}
DynamicBitset(int n, bool value = false) : n(n), dat(n < 0 ? 0 : word_size(n), value ? ~Word(0) : 0)
{
assert(n >= 0);
trim();
}
explicit DynamicBitset(const string &s, char zero = '0', char one = '1') : n(0)
{
assign(s, zero, one);
}
int size() const { return n; }
bool empty() const { return n == 0; }
int capacity() const { return int(dat.capacity()) * word_bits; }
void reserve(int n)
{
assert(n >= 0);
dat.reserve(word_size(n));
}
void resize(int n, bool value = false)
{
assert(n >= 0);
int old = this->n;
dat.resize(word_size(n));
this->n = n;
if (value && old < n)
set_range(old, n);
trim();
}
DynamicBitset &assign(const string &s, char zero = '0', char one = '1')
{
assert(zero != one);
assert(s.size() <= size_t(numeric_limits<int>::max()));
n = int(s.size());
dat.assign(word_size(n), 0);
repi(i, n)
{
char c = s[n - 1 - i];
assert(c == zero || c == one);
if (c == one)
dat[i / word_bits] |= Word(1) << (i % word_bits);
}
return *this;
}
bool test(int i) const
{
assert(0 <= i && i < n);
return dat[i / word_bits] >> (i % word_bits) & 1;
}
bool operator[](int i) const { return test(i); }
Reference operator[](int i)
{
assert(0 <= i && i < n);
return {this, i};
}
DynamicBitset &set(int i, bool value = true)
{
assert(0 <= i && i < n);
Word mask = Word(1) << (i % word_bits);
if (value)
dat[i / word_bits] |= mask;
else
dat[i / word_bits] &= ~mask;
return *this;
}
DynamicBitset &reset(int i) { return set(i, false); }
DynamicBitset &flip(int i)
{
assert(0 <= i && i < n);
dat[i / word_bits] ^= Word(1) << (i % word_bits);
return *this;
}
DynamicBitset &set()
{
fill(ALL(dat), ~Word(0));
trim();
return *this;
}
DynamicBitset &reset()
{
fill(ALL(dat), 0);
return *this;
}
DynamicBitset &flip()
{
fem(x : dat) x = ~x;
trim();
return *this;
}
DynamicBitset &set_range(int l, int r, bool value = true)
{
assert(0 <= l && l <= r && r <= n);
if (!value)
return reset_range(l, r);
if (l == r)
return *this;
int lw = l / word_bits, rw = (r - 1) / word_bits;
if (lw == rw)
dat[lw] |= low_mask((r - 1) % word_bits + 1) & ~low_mask(l % word_bits);
else
{
dat[lw] |= ~low_mask(l % word_bits);
fill(dat.begin() + lw + 1, dat.begin() + rw, ~Word(0));
dat[rw] |= low_mask((r - 1) % word_bits + 1);
}
trim();
return *this;
}
DynamicBitset &reset_range(int l, int r)
{
assert(0 <= l && l <= r && r <= n);
if (l == r)
return *this;
int lw = l / word_bits, rw = (r - 1) / word_bits;
if (lw == rw)
dat[lw] &= ~(low_mask((r - 1) % word_bits + 1) & ~low_mask(l % word_bits));
else
{
dat[lw] &= low_mask(l % word_bits);
fill(dat.begin() + lw + 1, dat.begin() + rw, 0);
dat[rw] &= ~low_mask((r - 1) % word_bits + 1);
}
return *this;
}
int count() const
{
int res = 0;
fec(x : dat) res += __builtin_popcountll(x);
return res;
}
int count(int l, int r) const
{
assert(0 <= l && l <= r && r <= n);
if (l == r)
return 0;
int lw = l / word_bits, rw = (r - 1) / word_bits;
if (lw == rw)
return __builtin_popcountll(dat[lw] & low_mask((r - 1) % word_bits + 1) & ~low_mask(l % word_bits));
int res = __builtin_popcountll(dat[lw] & ~low_mask(l % word_bits));
repi(w, lw + 1, rw) res += __builtin_popcountll(dat[w]);
return res + __builtin_popcountll(dat[rw] & low_mask((r - 1) % word_bits + 1));
}
bool any() const
{
fec(x : dat) if (x) return true;
return false;
}
bool any(int l, int r) const { return count(l, r) != 0; }
bool none(int l, int r) const { return !any(l, r); }
bool all(int l, int r) const { return count(l, r) == r - l; }
int find_next(int i, bool value = true) const
{
assert(-1 <= i && i < n);
i++;
if (i == n)
return n;
int w = i / word_bits, b = i % word_bits;
Word x = (value ? dat[w] : ~dat[w]) & (~Word(0) << b);
while (true)
{
if (x)
{
int res = w * word_bits + __builtin_ctzll(x);
return min(res, n);
}
if (++w == SZ(dat))
return n;
x = value ? dat[w] : ~dat[w];
}
}
int find_last(bool value = true) const { return find_prev(n, value); }
int find_prev(int i, bool value = true) const
{
assert(0 <= i && i <= n);
if (i == 0)
return -1;
i--;
int w = i / word_bits, b = i % word_bits;
Word x = (value ? dat[w] : ~dat[w]) & low_mask(b + 1);
while (true)
{
if (x)
return w * word_bits + 63 - __builtin_clzll(x);
if (w-- == 0)
return -1;
x = value ? dat[w] : ~dat[w];
}
}
DynamicBitset &operator&=(const DynamicBitset &b)
{
assert(n == b.n);
repi(i, SZ(dat)) dat[i] &= b.dat[i];
return *this;
}
DynamicBitset &operator|=(const DynamicBitset &b)
{
assert(n == b.n);
repi(i, SZ(dat)) dat[i] |= b.dat[i];
return *this;
}
DynamicBitset &operator^=(const DynamicBitset &b)
{
assert(n == b.n);
repi(i, SZ(dat)) dat[i] ^= b.dat[i];
return *this;
}
friend DynamicBitset operator&(DynamicBitset a, const DynamicBitset &b) { return a &= b; }
friend DynamicBitset operator|(DynamicBitset a, const DynamicBitset &b) { return a |= b; }
friend DynamicBitset operator^(DynamicBitset a, const DynamicBitset &b) { return a ^= b; }
DynamicBitset operator~() const { return DynamicBitset(*this).flip(); }
DynamicBitset &operator<<=(int k)
{
assert(k >= 0);
if (k >= n)
return reset();
if (k == 0)
return *this;
int dw = k / word_bits, db = k % word_bits;
repi(i, SZ(dat) - 1, dw - 1, -1)
{
Word x = dat[i - dw] << db;
if (db && i > dw)
x |= dat[i - dw - 1] >> (word_bits - db);
dat[i] = x;
}
fill(dat.begin(), dat.begin() + dw, 0);
trim();
return *this;
}
DynamicBitset &operator>>=(int k)
{
assert(k >= 0);
if (k >= n)
return reset();
if (k == 0)
return *this;
int dw = k / word_bits, db = k % word_bits, m = SZ(dat);
repi(i, m - dw)
{
Word x = dat[i + dw] >> db;
if (db && i + dw + 1 < m)
x |= dat[i + dw + 1] << (word_bits - db);
dat[i] = x;
}
fill(dat.end() - dw, dat.end(), 0);
trim();
return *this;
}
DynamicBitset operator<<(int k) const { return DynamicBitset(*this) <<= k; }
DynamicBitset operator>>(int k) const { return DynamicBitset(*this) >>= k; }
DynamicBitset &or_slice(int l, int r, const DynamicBitset &b, int bl)
{
return apply_slice<2>(l, r, b, bl, nullptr);
}
template <class F>
DynamicBitset &or_slice(int l, int r, const DynamicBitset &b, int bl, const F &f)
{
return apply_slice<2>(l, r, b, bl, f);
}
string to_string(char zero = '0', char one = '1') const
{
assert(zero != one);
string res(n, zero);
repi(i, n) if (test(i)) res[n - 1 - i] = one;
return res;
}
friend bool operator==(const DynamicBitset &a, const DynamicBitset &b)
{
return a.n == b.n && a.dat == b.dat;
}
friend bool operator!=(const DynamicBitset &a, const DynamicBitset &b) { return !(a == b); }
friend bool operator<(const DynamicBitset &a, const DynamicBitset &b)
{
assert(a.n == b.n);
repi(i, SZ(a.dat) - 1, -1, -1)
if (a.dat[i] != b.dat[i])
return a.dat[i] < b.dat[i];
return false;
}
friend bool operator>(const DynamicBitset &a, const DynamicBitset &b) { return b < a; }
friend bool operator<=(const DynamicBitset &a, const DynamicBitset &b) { return !(b < a); }
friend bool operator>=(const DynamicBitset &a, const DynamicBitset &b) { return !(a < b); }
};
struct SubsetSumFromFrequency
{
private:
int s;
vc<pair<int, int>> val_cnt;
DynamicBitset dp;
vc<int> time;
public:
SubsetSumFromFrequency() : s(0), dp(1), time(1, 0) { dp.set(0); }
template <class T>
SubsetSumFromFrequency(const vc<T> &freq, int smax) : s(smax), dp(s + 1)
{
static_assert(is_integral_ext<T>);
assert(s >= 0);
time.assign(s + 1, -1);
time[0] = 0;
dp.set(0);
int vmax = min(s, SZ<int>(freq) - 1);
repi(v, 1, vmax + 1)
{
assert(freq[v] >= 0);
int c = freq[v] < T(s / v) ? int(freq[v]) : s / v;
for (ll k = 1; c > 0; k *= 2)
{
int x = int(min<ll>(c, k));
c -= x;
int t = val_cnt.size();
val_cnt.eb(v, x);
int w = v * x;
dp.or_slice(w, s + 1, dp, 0, [&](int i) { time[i] = t + 1; });
}
}
}
bool exists(int x) const
{
return 0 <= x && x <= s && time[x] != -1;
}
const DynamicBitset &reachable() const { return dp; }
pair<bool, vc<pair<int, int>>> answer(int x) const
{
if (!exists(x))
return {false, {}};
vc<pair<int, int>> res;
int y = x;
repi(t, SZ(val_cnt) - 1, -1, -1)
{
auto [v, c] = val_cnt[t];
int w = v * c;
if (y >= w && time[y - w] != -1 && time[y - w] <= t)
{
y -= w;
if (res.empty() || res.back().first != v)
res.eb(v, 0);
res.back().second += c;
}
}
return {true, res};
}
};
struct SubsetSum
{
private:
int n, s, xmax;
ll negsum;
vc<bool> isneg;
vvc<int> ids;
SubsetSumFromFrequency ss;
public:
SubsetSum() : n(0), s(-1), xmax(-1), negsum(0) {}
template <class T>
SubsetSum(const vc<T> &a, int smax) : n(SZ<int>(a)), xmax(smax), negsum(0)
{
static_assert(is_integral_ext<T>);
isneg.assign(n, false);
repi(i, n) if (a[i] < 0)
{
isneg[i] = true;
negsum += ll(a[i]);
}
ll shifted_s = ll(smax) - negsum;
assert(shifted_s <= numeric_limits<int>::max());
if (shifted_s < 0)
{
s = -1;
return;
}
s = int(shifted_s);
ids.resize(s + 1);
vc<int> freq(s + 1);
repi(i, n)
{
ll x = ll(a[i]);
if (x < 0)
{
if (x < -ll(s))
continue;
x = -x;
}
if (x <= s)
{
int v = int(x);
ids[v].eb(i);
freq[v]++;
}
}
ss = SubsetSumFromFrequency(freq, s);
}
bool exists(int x) const
{
ll y = ll(x) - negsum;
return x <= xmax && 0 <= y && y <= s && ss.exists(int(y));
}
const DynamicBitset &reachable() const
{
static const DynamicBitset empty;
return s < 0 ? empty : ss.reachable();
}
pair<bool, vc<bool>> answer(int x) const
{
ll y = ll(x) - negsum;
if (x > xmax || !(0 <= y && y <= s))
return {false, {}};
auto [ok, cnt] = ss.answer(int(y));
if (!ok)
return {false, {}};
vc<bool> res(n, false);
for (auto [v, c] : cnt)
{
assert(c <= SZ(ids[v]));
repi(k, c) res[ids[v][k]] = true;
}
repi(i, n) if (isneg[i]) res[i] = !res[i];
return {true, res};
}
};
void main2()
{
LL(N, S);
VEC(ll, N, A);
SubsetSum ss(A, S);
auto res = ss.reachable();
PRINT(res.find_last());
}
void test()
{
}
// https://github.com/miscalculation53/library/tree/wip/template/template_main.hpp
template <auto init, auto main2, auto test>
struct Main
{
Main()
{
cauto CERR = [](string val, string color)
{
string s = "\033[" + color + "m" + val + "\033[m";
};
CERR("\n[FAST_IO]\n\n", "32");
cout << fixed << setprecision(20);
init();
CERR("\n[MULTI_TESTCASE]\n\n", "33");
local(while (true))
{
dump("T");
IN(uint, T);
while (T--)
{
dump("new testcase");
main2();
}
}
}
};
Main<init, main2, test> main_dummy;
}
int main() {}