結果
| 問題 | No.2105 Avoid MeX |
| ユーザー |
 kuhaku
|
| 提出日時 | 2023-09-17 15:16:48 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 595 ms / 2,000 ms |
| コード長 | 23,627 bytes |
| コンパイル時間 | 3,420 ms |
| コンパイル使用メモリ | 225,108 KB |
| 実行使用メモリ | 19,096 KB |
| 最終ジャッジ日時 | 2023-09-17 15:16:57 |
| 合計ジャッジ時間 | 7,966 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge15 |
（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 | 1 ms
4,380 KB |
| testcase_01 | AC | 2 ms
4,380 KB |
| testcase_02 | AC | 2 ms
4,380 KB |
| testcase_03 | AC | 2 ms
4,376 KB |
| testcase_04 | AC | 239 ms
9,748 KB |
| testcase_05 | AC | 2 ms
4,376 KB |
| testcase_06 | AC | 74 ms
4,912 KB |
| testcase_07 | AC | 91 ms
5,420 KB |
| testcase_08 | AC | 10 ms
4,380 KB |
| testcase_09 | AC | 225 ms
9,140 KB |
| testcase_10 | AC | 2 ms
4,380 KB |
| testcase_11 | AC | 1 ms
4,380 KB |
| testcase_12 | AC | 25 ms
4,376 KB |
| testcase_13 | AC | 1 ms
4,376 KB |
| testcase_14 | AC | 60 ms
4,604 KB |
| testcase_15 | AC | 114 ms
6,364 KB |
| testcase_16 | AC | 2 ms
4,380 KB |
| testcase_17 | AC | 1 ms
4,376 KB |
| testcase_18 | AC | 1 ms
4,380 KB |
| testcase_19 | AC | 595 ms
18,824 KB |
| testcase_20 | AC | 575 ms
18,564 KB |
| testcase_21 | AC | 584 ms
19,096 KB |
| testcase_22 | AC | 579 ms
18,620 KB |
| testcase_23 | AC | 2 ms
4,380 KB |
| testcase_24 | AC | 2 ms
4,376 KB |
ソースコード
#line 1 "a.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/2105"
#line 2 "/home/kuhaku/atcoder/github/algo/lib/template/template.hpp"
#pragma GCC target("sse4.2,avx2,bmi2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
template <class T, class U>
bool chmax(T &a, const U &b) {
return a < (T)b ? a = (T)b, true : false;
}
template <class T, class U>
bool chmin(T &a, const U &b) {
return (T)b < a ? a = (T)b, true : false;
}
constexpr std::int64_t INF = 1000000000000000003;
constexpr int Inf = 1000000003;
constexpr int MOD = 1000000007;
constexpr int MOD_N = 998244353;
constexpr double EPS = 1e-7;
constexpr double PI = M_PI;
#line 3 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_math.hpp"
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr std::int64_t safe_mod(std::int64_t x, std::int64_t m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
std::uint64_t im;
// @param m `1 <= m`
explicit barrett(unsigned int m) : _m(m), im((std::uint64_t)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
std::uint64_t z = a;
z *= b;
std::uint64_t x = (std::uint64_t)(((__uint128_t)(z)*im) >> 64);
std::uint64_t y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
struct montgomery {
std::uint64_t _m;
std::uint64_t im;
std::uint64_t r2;
// @param m `1 <= m`
explicit constexpr montgomery(std::uint64_t m) : _m(m), im(m), r2(-__uint128_t(m) % m) {
for (int i = 0; i < 5; ++i) im = im * (2 - _m * im);
im = -im;
}
// @return m
constexpr std::uint64_t umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
constexpr std::uint64_t mul(std::uint64_t a, std::uint64_t b) const { return mr(mr(a, b), r2); }
constexpr std::uint64_t exp(std::uint64_t a, std::uint64_t b) const {
std::uint64_t res = 1, p = mr(a, r2);
while (b) {
if (b & 1) res = mr(res, p);
p = mr(p, p);
b >>= 1;
}
return res;
}
constexpr bool same_pow(std::uint64_t x, int s, std::uint64_t n) const {
x = mr(x, r2), n = mr(n, r2);
for (int r = 0; r < s; r++) {
if (x == n) return true;
x = mr(x, x);
}
return false;
}
private:
constexpr std::uint64_t mr(std::uint64_t x) const {
return ((__uint128_t)(x * im) * _m + x) >> 64;
}
constexpr std::uint64_t mr(std::uint64_t a, std::uint64_t b) const {
__uint128_t t = (__uint128_t)a * b;
std::uint64_t inc = std::uint64_t(t) != 0;
std::uint64_t x = t >> 64, y = ((__uint128_t)(a * b * im) * _m) >> 64;
unsigned long long z = 0;
bool f = __builtin_uaddll_overflow(x, y, &z);
z += inc;
return f ? z - _m : z;
}
};
constexpr bool is_SPRP32(std::uint32_t n, std::uint32_t a) {
std::uint32_t d = n - 1, s = 0;
while ((d & 1) == 0) ++s, d >>= 1;
std::uint64_t cur = 1, pw = d;
while (pw) {
if (pw & 1) cur = (cur * a) % n;
a = (std::uint64_t)a * a % n;
pw >>= 1;
}
if (cur == 1) return true;
for (std::uint32_t r = 0; r < s; r++) {
if (cur == n - 1) return true;
cur = cur * cur % n;
}
return false;
}
// given 2 <= n,a < 2^64, a prime, check whether n is a-SPRP
constexpr bool is_SPRP64(const montgomery &m, std::uint64_t a) {
auto n = m.umod();
if (n == a) return true;
if (n % a == 0) return false;
std::uint64_t d = n - 1;
int s = 0;
while ((d & 1) == 0) ++s, d >>= 1;
std::uint64_t cur = m.exp(a, d);
if (cur == 1) return true;
return m.same_pow(cur, s, n - 1);
}
constexpr bool is_prime_constexpr(std::uint64_t x) {
if (x == 2 || x == 3 || x == 5 || x == 7) return true;
if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
if (x < 121) return (x > 1);
montgomery m(x);
constexpr std::uint64_t bases[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
for (auto a : bases) {
if (!is_SPRP64(m, a)) return false;
}
return true;
}
constexpr bool is_prime_constexpr(std::int64_t x) {
if (x < 0) return false;
return is_prime_constexpr(std::uint64_t(x));
}
constexpr bool is_prime_constexpr(std::uint32_t x) {
if (x == 2 || x == 3 || x == 5 || x == 7) return true;
if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
if (x < 121) return (x > 1);
std::uint64_t h = x;
h = ((h >> 16) ^ h) * 0x45d9f3b;
h = ((h >> 16) ^ h) * 0x45d9f3b;
h = ((h >> 16) ^ h) & 255;
constexpr uint16_t bases[] = {
15591, 2018, 166, 7429, 8064, 16045, 10503, 4399, 1949, 1295, 2776, 3620, 560,
3128, 5212, 2657, 2300, 2021, 4652, 1471, 9336, 4018, 2398, 20462, 10277, 8028,
2213, 6219, 620, 3763, 4852, 5012, 3185, 1333, 6227, 5298, 1074, 2391, 5113,
7061, 803, 1269, 3875, 422, 751, 580, 4729, 10239, 746, 2951, 556, 2206,
3778, 481, 1522, 3476, 481, 2487, 3266, 5633, 488, 3373, 6441, 3344, 17,
15105, 1490, 4154, 2036, 1882, 1813, 467, 3307, 14042, 6371, 658, 1005, 903,
737, 1887, 7447, 1888, 2848, 1784, 7559, 3400, 951, 13969, 4304, 177, 41,
19875, 3110, 13221, 8726, 571, 7043, 6943, 1199, 352, 6435, 165, 1169, 3315,
978, 233, 3003, 2562, 2994, 10587, 10030, 2377, 1902, 5354, 4447, 1555, 263,
27027, 2283, 305, 669, 1912, 601, 6186, 429, 1930, 14873, 1784, 1661, 524,
3577, 236, 2360, 6146, 2850, 55637, 1753, 4178, 8466, 222, 2579, 2743, 2031,
2226, 2276, 374, 2132, 813, 23788, 1610, 4422, 5159, 1725, 3597, 3366, 14336,
579, 165, 1375, 10018, 12616, 9816, 1371, 536, 1867, 10864, 857, 2206, 5788,
434, 8085, 17618, 727, 3639, 1595, 4944, 2129, 2029, 8195, 8344, 6232, 9183,
8126, 1870, 3296, 7455, 8947, 25017, 541, 19115, 368, 566, 5674, 411, 522,
1027, 8215, 2050, 6544, 10049, 614, 774, 2333, 3007, 35201, 4706, 1152, 1785,
1028, 1540, 3743, 493, 4474, 2521, 26845, 8354, 864, 18915, 5465, 2447, 42,
4511, 1660, 166, 1249, 6259, 2553, 304, 272, 7286, 73, 6554, 899, 2816,
5197, 13330, 7054, 2818, 3199, 811, 922, 350, 7514, 4452, 3449, 2663, 4708,
418, 1621, 1171, 3471, 88, 11345, 412, 1559, 194};
return is_SPRP32(x, bases[h]);
}
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr std::int64_t pow_mod_constexpr(std::int64_t x, std::int64_t n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
std::uint64_t r = 1;
std::uint64_t y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
std::int64_t d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr std::int64_t bases[3] = {2, 7, 61};
for (std::int64_t a : bases) {
std::int64_t t = d;
std::int64_t y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<std::int64_t, std::int64_t> inv_gcd(std::int64_t a, std::int64_t b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
std::int64_t s = b, t = a;
std::int64_t m0 = 0, m1 = 1;
while (t) {
std::int64_t u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (std::int64_t)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
std::uint64_t floor_sum_unsigned(std::uint64_t n, std::uint64_t m, std::uint64_t a,
std::uint64_t b) {
std::uint64_t ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
std::uint64_t y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (std::uint64_t)(y_max / m);
b = (std::uint64_t)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
#line 3 "/home/kuhaku/atcoder/github/algo/lib/internal/internal_type_traits.hpp"
namespace internal {
template <class T>
using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type, std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;
template <class T>
using is_integral =
typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_signed_int =
typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value, make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
std::common_type<T>>::type>::type;
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
#line 5 "/home/kuhaku/atcoder/github/algo/lib/math/modint.hpp"
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static constexpr mint raw(int v) {
mint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
constexpr static_modint(T v) : _v(0) {
std::int64_t x = (std::int64_t)(v % (std::int64_t)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
constexpr static_modint(T v) : _v(0) {
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const { return _v; }
constexpr mint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr mint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr mint operator++(int) {
mint result = *this;
++*this;
return result;
}
constexpr mint operator--(int) {
mint result = *this;
--*this;
return result;
}
constexpr mint &operator+=(const mint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr mint &operator-=(const mint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr mint &operator*=(const mint &rhs) {
std::uint64_t z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
constexpr mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return mint() - *this; }
constexpr mint pow(std::int64_t n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend constexpr mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend constexpr mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend constexpr mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend constexpr bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend constexpr bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
friend std::istream &operator>>(std::istream &is, mint &rhs) {
std::int64_t t;
is >> t;
rhs = mint(t);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const mint &rhs) {
return os << rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id>
struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
dynamic_modint(T v) {
std::int64_t x = (std::int64_t)(v % (std::int64_t)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint &operator+=(const mint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint &operator-=(const mint &rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint &operator*=(const mint &rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(std::int64_t n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
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 std::istream &operator>>(std::istream &is, mint &rhs) {
std::int64_t t;
is >> t;
rhs = mint(t);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const mint &rhs) {
return os << rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt(998244353);
using modint998 = static_modint<998244353>;
using modint107 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
#line 3 "/home/kuhaku/atcoder/github/algo/lib/template/macro.hpp"
#define FOR(i, m, n) for (int i = (m); i < int(n); ++i)
#define FORR(i, m, n) for (int i = (m)-1; i >= int(n); --i)
#define FORL(i, m, n) for (int64_t i = (m); i < int64_t(n); ++i)
#define rep(i, n) FOR (i, 0, n)
#define repn(i, n) FOR (i, 1, n + 1)
#define repr(i, n) FORR (i, n, 0)
#define repnr(i, n) FORR (i, n + 1, 1)
#define all(s) (s).begin(), (s).end()
#line 3 "/home/kuhaku/atcoder/github/algo/lib/template/sonic.hpp"
struct Sonic {
Sonic() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
}
constexpr void operator()() const {}
} sonic;
#line 5 "/home/kuhaku/atcoder/github/algo/lib/template/atcoder.hpp"
using namespace std;
using ll = std::int64_t;
using ld = long double;
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
return is >> p.first >> p.second;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
for (T &i : v) is >> i;
return is;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
return os << '(' << p.first << ',' << p.second << ')';
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
for (auto it = v.begin(); it != v.end(); ++it) {
os << (it == v.begin() ? "" : " ") << *it;
}
return os;
}
template <class Head, class... Tail>
void co(Head &&head, Tail &&...tail) {
if constexpr (sizeof...(tail) == 0) std::cout << head << '\n';
else std::cout << head << ' ', co(std::forward<Tail>(tail)...);
}
template <class Head, class... Tail>
void ce(Head &&head, Tail &&...tail) {
if constexpr (sizeof...(tail) == 0) std::cerr << head << '\n';
else std::cerr << head << ' ', ce(std::forward<Tail>(tail)...);
}
template <typename T, typename... Args>
auto make_vector(T x, int arg, Args... args) {
if constexpr (sizeof...(args) == 0) return std::vector<T>(arg, x);
else return std::vector(arg, make_vector<T>(x, args...));
}
void setp(int n) {
std::cout << std::fixed << std::setprecision(n);
}
void Yes(bool is_correct = true) {
std::cout << (is_correct ? "Yes" : "No") << '\n';
}
void No(bool is_not_correct = true) {
Yes(!is_not_correct);
}
void YES(bool is_correct = true) {
std::cout << (is_correct ? "YES" : "NO") << '\n';
}
void NO(bool is_not_correct = true) {
YES(!is_not_correct);
}
void Takahashi(bool is_correct = true) {
std::cout << (is_correct ? "Takahashi" : "Aoki") << '\n';
}
void Aoki(bool is_not_correct = true) {
Takahashi(!is_not_correct);
}
#line 4 "a.cpp"
using Mint = modint998;
int main(void) {
int c, x;
cin >> c >> x;
if (c == 0 && x == 0) {
co(1);
return 0;
}
if (x == 0) {
co(Mint(1) / (c + 1));
return 0;
}
if (c >= x) {
co(Mint(x) / (x + 1));
return 0;
}
vector dp(x - c + 1, vector(x - c + 1, Mint()));
dp[0][0] = 1;
rep (i, x - c) {
rep (j, x - c) {
if (dp[i][j] == 0)
continue;
dp[i + 1][j] += dp[i][j] * (j) / (c + i + 1);
dp[i + 1][j + 1] += dp[i][j] * (c + i + 1 - j) / (c + i + 1);
}
}
Mint ans = 0;
rep (i, x - c + 1) {
ans += dp[x - c][i] * (x - i) / (x + 1 - i);
}
co(ans);
return 0;
}