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test/1_mytest/floor_sum_of_polynomial.test.cpp
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- Last update: 2024-12-26 06:32:57+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
alg/monoid/monoid_for_floor_sum.hpp
- alg/monoid_pow.hpp
- mod/floor_monoid_product.hpp
- mod/floor_sum_of_linear_polynomial.hpp
- mod/modint.hpp
- mod/modint_common.hpp
- my_template.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "mod/modint.hpp"
#include "mod/floor_sum_of_linear_polynomial.hpp"
using mint = modint998;
template <int K1, int K2>
void test_1() {
FOR(M, 1, 10) {
FOR(a, 10) {
FOR(b, 10) {
array<array<mint, K2 + 1>, K1 + 1> dp{};
FOR(N, 10) {
array<array<mint, K2 + 1>, K1 + 1> ans = floor_sum_of_linear_polynomial_nonnegative<mint, K1, K2, u64>(N, a, b, M);
assert(dp == ans);
mint y = floor(a * N + b, M);
FOR(i, K1 + 1) FOR(j, K2 + 1) dp[i][j] += mint(N).pow(i) * y.pow(j);
}
}
}
}
}
template <int K1, int K2>
void test_2() {
FOR(M, 1, 10) {
FOR(a, -5, 6) {
FOR(b, -5, 6) {
FOR(L, -5, 6) {
array<array<mint, K2 + 1>, K1 + 1> dp{};
FOR(R, L, 6) {
array<array<mint, K2 + 1>, K1 + 1> ans = floor_sum_of_linear_polynomial<mint, K1, K2, ll>(L, R, a, b, M);
assert(dp == ans);
mint y = floor(a * R + b, M);
FOR(i, K1 + 1) FOR(j, K2 + 1) dp[i][j] += mint(R).pow(i) * y.pow(j);
}
}
}
}
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test_1<0, 0>();
test_1<0, 1>();
test_1<0, 2>();
test_1<1, 0>();
test_1<1, 1>();
test_1<1, 2>();
test_1<2, 0>();
test_1<2, 1>();
test_1<2, 2>();
test_1<10, 10>();
test_2<0, 0>();
test_2<0, 1>();
test_2<0, 2>();
test_2<1, 0>();
test_2<1, 1>();
test_2<1, 2>();
test_2<2, 0>();
test_2<2, 1>();
test_2<2, 2>();
test_2<10, 10>();
solve();
return 0;
}#line 1 "test/1_mytest/floor_sum_of_polynomial.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T kth_bit(int k) {
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
struct iter {
UINT s;
iter(UINT s) : s(s) {}
int operator*() const { return lowbit(s); }
iter &operator++() {
s &= s - 1;
return *this;
}
bool operator!=(const iter) const { return s != 0; }
};
UINT s;
all_bit(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
struct iter {
UINT s, t;
bool ed;
iter(UINT s) : s(s), t(s), ed(0) {}
int operator*() const { return s ^ t; }
iter &operator++() {
(t == 0 ? ed = 1 : t = (t - 1) & s);
return *this;
}
bool operator!=(const iter) const { return !ed; }
};
UINT s;
all_subset(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 3 "test/1_mytest/floor_sum_of_polynomial.test.cpp"
#line 2 "mod/modint_common.hpp"
struct has_mod_impl {
template <class T>
static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n %= mod;
while (len(dat) <= n) {
int k = len(dat);
int q = (mod + k - 1) / k;
dat.eb(dat[k * q - mod] * mint::raw(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
assert(0 <= n && n < mod);
static vector<mint> dat = {1, 1};
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static vector<mint> dat = {1, 1};
if (n < 0) return mint(0);
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}
template <typename mint>
mint C_dense(int n, int k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
static vvc<mint> C;
static int H = 0, W = 0;
auto calc = [&](int i, int j) -> mint {
if (i == 0) return (j == 0 ? mint(1) : mint(0));
return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
};
if (W <= k) {
FOR(i, H) {
C[i].resize(k + 1);
FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
FOR(i, H, n + 1) {
C[i].resize(W);
FOR(j, W) { C[i][j] = calc(i, j); }
}
H = n + 1;
}
return C[n][k];
}
template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if constexpr (dense) return C_dense<mint>(n, k);
if constexpr (!large) return multinomial<mint>(n, k, n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) x *= mint(n - i);
return x * fact_inv<mint>(k);
}
template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
assert(n >= 0);
if (d < 0) return mint(0);
if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
return C<mint, large, dense>(n + d - 1, d);
}
#line 3 "mod/modint.hpp"
template <int mod>
struct modint {
static constexpr u32 umod = u32(mod);
static_assert(umod < u32(1) << 31);
u32 val;
static modint raw(u32 v) {
modint x;
x.val = v;
return x;
}
constexpr modint() : val(0) {}
constexpr modint(u32 x) : val(x % umod) {}
constexpr modint(u64 x) : val(x % umod) {}
constexpr modint(u128 x) : val(x % umod) {}
constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
bool operator<(const modint &other) const { return val < other.val; }
modint &operator+=(const modint &p) {
if ((val += p.val) >= umod) val -= umod;
return *this;
}
modint &operator-=(const modint &p) {
if ((val += umod - p.val) >= umod) val -= umod;
return *this;
}
modint &operator*=(const modint &p) {
val = u64(val) * p.val % umod;
return *this;
}
modint &operator/=(const modint &p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return val == p.val; }
bool operator!=(const modint &p) const { return val != p.val; }
modint inverse() const {
int a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint(u);
}
modint pow(ll n) const {
assert(n >= 0);
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
static constexpr int get_mod() { return mod; }
// (n, r), r は 1 の 2^n 乗根
static constexpr pair<int, int> ntt_info() {
if (mod == 120586241) return {20, 74066978};
if (mod == 167772161) return {25, 17};
if (mod == 469762049) return {26, 30};
if (mod == 754974721) return {24, 362};
if (mod == 880803841) return {23, 211};
if (mod == 943718401) return {22, 663003469};
if (mod == 998244353) return {23, 31};
if (mod == 1004535809) return {21, 582313106};
if (mod == 1012924417) return {21, 368093570};
return {-1, -1};
}
static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};
#ifdef FASTIO
template <int mod>
void rd(modint<mod> &x) {
fastio::rd(x.val);
x.val %= mod;
// assert(0 <= x.val && x.val < mod);
}
template <int mod>
void wt(modint<mod> x) {
fastio::wt(x.val);
}
#endif
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 1 "mod/floor_sum_of_linear_polynomial.hpp"
#line 2 "alg/monoid_pow.hpp"
// chat gpt
template <typename U, typename Arg1, typename Arg2>
struct has_power_method {
private:
// ヘルパー関数の実装
template <typename V, typename A1, typename A2>
static auto check(int)
-> decltype(std::declval<V>().power(std::declval<A1>(),
std::declval<A2>()),
std::true_type{});
template <typename, typename, typename>
static auto check(...) -> std::false_type;
public:
// メソッドの有無を表す型
static constexpr bool value = decltype(check<U, Arg1, Arg2>(0))::value;
};
template <typename Monoid>
typename Monoid::X monoid_pow(typename Monoid::X x, ll exp) {
using X = typename Monoid::X;
if constexpr (has_power_method<Monoid, X, ll>::value) {
return Monoid::power(x, exp);
} else {
assert(exp >= 0);
X res = Monoid::unit();
while (exp) {
if (exp & 1) res = Monoid::op(res, x);
x = Monoid::op(x, x);
exp >>= 1;
}
return res;
}
}
#line 2 "mod/floor_monoid_product.hpp"
// https://yukicoder.me/submissions/883884
// https://qoj.ac/contest/1411/problem/7620
// U は範囲内で ax+b がオーバーフローしない程度
// yyy x yyyy x ... yyy x yyy (x を N 個)
// k 個目の x までに floor(ak+b,m) 個の y がある
// my<=ax+b における lattice path における辺の列と見なせる
template <typename Monoid, typename X, typename U>
X floor_monoid_product(X x, X y, U N, U a, U b, U m) {
U c = (a * N + b) / m;
X pre = Monoid::unit(), suf = Monoid::unit();
while (1) {
const U p = a / m, q = b / m;
a %= m, b %= m;
x = Monoid::op(x, monoid_pow<Monoid>(y, p));
pre = Monoid::op(pre, monoid_pow<Monoid>(y, q));
c -= (p * N + q);
if (c == 0) break;
const U d = (m * c - b - 1) / a + 1;
suf = Monoid::op(y, Monoid::op(monoid_pow<Monoid>(x, N - d), suf));
b = m - b - 1 + a, N = c - 1, c = d;
swap(m, a), swap(x, y);
}
x = monoid_pow<Monoid>(x, N);
return Monoid::op(Monoid::op(pre, x), suf);
}
#line 1 "alg/monoid/monoid_for_floor_sum.hpp"
// sum i^k1floor^k2: floor path で (x,y) から x 方向に進むときに x^k1y^k2 を足す
template <typename T, int K1, int K2>
struct Monoid_for_floor_sum {
using ARR = array<array<T, K2 + 1>, K1 + 1>;
struct Data {
ARR dp;
T dx, dy;
};
using value_type = Data;
using X = value_type;
static X op(X a, X b) {
static constexpr int n = max(K1, K2);
static T comb[n + 1][n + 1];
if (comb[0][0] != T(1)) {
comb[0][0] = T(1);
FOR(i, n) FOR(j, i + 1) { comb[i + 1][j] += comb[i][j], comb[i + 1][j + 1] += comb[i][j]; }
}
array<T, K1 + 1> pow_x;
array<T, K2 + 1> pow_y;
pow_x[0] = 1, pow_y[0] = 1;
FOR(i, K1) pow_x[i + 1] = pow_x[i] * a.dx;
FOR(i, K2) pow_y[i + 1] = pow_y[i] * a.dy;
// +dy
FOR(i, K1 + 1) {
FOR_R(j, K2 + 1) {
T x = b.dp[i][j];
FOR(k, j + 1, K2 + 1) b.dp[i][k] += comb[k][j] * pow_y[k - j] * x;
}
}
// +dx
FOR(j, K2 + 1) {
FOR_R(i, K1 + 1) { FOR(k, i, K1 + 1) a.dp[k][j] += comb[k][i] * pow_x[k - i] * b.dp[i][j]; }
}
a.dx += b.dx, a.dy += b.dy;
return a;
}
static X to_x() {
X x = unit();
x.dp[0][0] = 1, x.dx = 1;
return x;
}
static X to_y() {
X x = unit();
x.dy = 1;
return x;
}
static constexpr X unit() { return {ARR{}, T(0), T(0)}; }
static constexpr bool commute = 0;
};
#line 4 "mod/floor_sum_of_linear_polynomial.hpp"
// 全部非負, T は答, U は ax+b がオーバーフローしない
template <typename T, int K1, int K2, typename U>
array<array<T, K2 + 1>, K1 + 1> floor_sum_of_linear_polynomial_nonnegative(U N, U a, U b, U mod) {
static_assert(is_same_v<U, u64> || is_same_v<U, u128>);
assert(a == 0 || N < (U(-1) - b) / a);
using Mono = Monoid_for_floor_sum<T, K1, K2>;
auto x = floor_monoid_product<Mono>(Mono::to_x(), Mono::to_y(), N, a, b, mod);
return x.dp;
};
// sum_{L<=x<R} x^i floor(ax+b,mod)^j
// a+bx が I, U でオーバーフローしない
template <typename T, int K1, int K2, typename I>
array<array<T, K2 + 1>, K1 + 1> floor_sum_of_linear_polynomial(I L, I R, I a, I b, I mod) {
static_assert(is_same_v<I, ll> || is_same_v<I, i128>);
assert(L <= R && mod > 0);
if (a < 0) {
auto ANS = floor_sum_of_linear_polynomial<T, K1, K2, I>(-R + 1, -L + 1, -a, b, mod);
FOR(i, K1 + 1) {
if (i % 2 == 1) { FOR(j, K2 + 1) ANS[i][j] = -ANS[i][j]; }
}
return ANS;
}
assert(a >= 0);
I ADD_X = L;
I N = R - L;
b += a * L;
I ADD_Y = floor<I>(b, mod);
b -= ADD_Y * mod;
assert(a >= 0 && b >= 0);
using Mono = Monoid_for_floor_sum<T, K1, K2>;
using Data = typename Mono::Data;
using U = std::conditional_t<is_same_v<I, ll>, i128, u128>;
Data A = floor_monoid_product<Mono, Data, U>(Mono::to_x(), Mono::to_y(), N, a, b, mod);
Data offset = Mono::unit();
offset.dx = T(ADD_X), offset.dy = T(ADD_Y);
A = Mono::op(offset, A);
return A.dp;
};
#line 6 "test/1_mytest/floor_sum_of_polynomial.test.cpp"
using mint = modint998;
template <int K1, int K2>
void test_1() {
FOR(M, 1, 10) {
FOR(a, 10) {
FOR(b, 10) {
array<array<mint, K2 + 1>, K1 + 1> dp{};
FOR(N, 10) {
array<array<mint, K2 + 1>, K1 + 1> ans = floor_sum_of_linear_polynomial_nonnegative<mint, K1, K2, u64>(N, a, b, M);
assert(dp == ans);
mint y = floor(a * N + b, M);
FOR(i, K1 + 1) FOR(j, K2 + 1) dp[i][j] += mint(N).pow(i) * y.pow(j);
}
}
}
}
}
template <int K1, int K2>
void test_2() {
FOR(M, 1, 10) {
FOR(a, -5, 6) {
FOR(b, -5, 6) {
FOR(L, -5, 6) {
array<array<mint, K2 + 1>, K1 + 1> dp{};
FOR(R, L, 6) {
array<array<mint, K2 + 1>, K1 + 1> ans = floor_sum_of_linear_polynomial<mint, K1, K2, ll>(L, R, a, b, M);
assert(dp == ans);
mint y = floor(a * R + b, M);
FOR(i, K1 + 1) FOR(j, K2 + 1) dp[i][j] += mint(R).pow(i) * y.pow(j);
}
}
}
}
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test_1<0, 0>();
test_1<0, 1>();
test_1<0, 2>();
test_1<1, 0>();
test_1<1, 1>();
test_1<1, 2>();
test_1<2, 0>();
test_1<2, 1>();
test_1<2, 2>();
test_1<10, 10>();
test_2<0, 0>();
test_2<0, 1>();
test_2<0, 2>();
test_2<1, 0>();
test_2<1, 1>();
test_2<1, 2>();
test_2<2, 0>();
test_2<2, 1>();
test_2<2, 2>();
test_2<10, 10>();
solve();
return 0;
}