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Verify/verify-yosupo-new/sum_of_multiplicative_function-black_algorithm.test.cpp
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- Last update: 2024-10-23 21:39:42+09:00
- Problem: https://judge.yosupo.jp/problem/sum_of_multiplicative_function
Depends on
- Math/EnumeratePrimes.hpp
- Math/MFPrefixSum.hpp
- Modint/Modint.hpp
- Template/InOut.hpp
- Template/Macro.hpp
- Template/Template.hpp
- Template/Util.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_multiplicative_function"
#include "../../Math/MFPrefixSum.hpp"
#include "../../Modint/Modint.hpp"
#include "../../Template/Template.hpp"
using mint = Modint<469762049>;
void solve() {
LL(T);
rep(_, T) {
LL(N, a, b);
MFPrefixSum<mint> mf(N);
vector<mint> pi = mf.pi_table();
vector<mint> prime_sum = mf.prime_sum_table();
vector<mint> table(len(pi));
rep(i, len(pi)) { table[i] = pi[i] * a + prime_sum[i] * b; }
out(mf.black_algorithm(table, [a, b](ll x, ll c) -> mint {
return a * c + b * x;
}));
}
}
int main() { solve(); }#line 1 "Verify/verify-yosupo-new/sum_of_multiplicative_function-black_algorithm.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_multiplicative_function"
#line 2 "Math/MFPrefixSum.hpp"
#include <math.h>
#include <cstdint>
#include <vector>
#include <stack>
#line 4 "Math/EnumeratePrimes.hpp"
std::vector<int32_t> enumerate_primes(int32_t n) {
std::vector<bool> flg((n + 1) >> 1, true);
std::vector<int32_t> ret = {2};
for (int32_t i = 3; i <= n; i += 2) {
if (!flg[i >> 1]) continue;
ret.emplace_back(i);
if (i * i > n) {
for (int32_t j = i + 2; j <= n; j += 2) {
if (flg[j >> 1]) ret.emplace_back(j);
}
break;
}
for (int32_t j = i * i; j <= n; j += i << 1) {
flg[j >> 1] = false;
}
}
while (!ret.empty() && ret.back() > n) ret.pop_back();
return ret;
}
#line 9 "Math/MFPrefixSum.hpp"
template <class T>
struct MFPrefixSum {
int64_t n;
int64_t sqrtN;
std::vector<int32_t> primes;
int32_t sz;
int32_t prisz;
MFPrefixSum(uint64_t N) {
n = N;
sqrtN = sqrt(n);
sz = sqrtN * 2;
if (n / sqrtN == sqrtN) sz--;
while ((sqrtN + 1) * (sqrtN + 1) <= n) sqrtN++;
while (sqrtN * sqrtN > n) sqrtN--;
primes = enumerate_primes(sqrtN);
prisz = primes.size();
}
std::vector<T> pi_table() {
std::vector<T> dp(sz);
for (int32_t i = 0; i < sqrtN; i++) {
dp[i] = i;
}
for (int32_t i = sqrtN; i < sz; i++) {
dp[i] = n / (sz - i) - 1;
}
for (int64_t x : primes) {
for (int32_t i = sz - 1; i >= sqrtN; i--) {
if (n < x * x * (sz - i)) break;
if (sz - (sz - i) * x < sqrtN) {
dp[i] -= (dp[n / (x * (sz - i)) - 1] - dp[x - 2]);
} else {
dp[i] -= (dp[sz - (sz - i) * x] - dp[x - 2]);
}
}
for (int32_t i = sqrtN - 1; i >= 0; i--) {
if (i + 1 < x * x) break;
dp[i] -= (dp[(i + 1) / x - 1] - dp[x - 2]);
}
}
return dp;
}
std::vector<T> prime_sum_table() {
std::vector<T> dp(sz);
for (int32_t i = 0; i < sqrtN; i++) {
dp[i] = T(i + 1) * T(i + 2) / 2 - 1;
}
for (int32_t i = sqrtN; i < sz; i++) {
dp[i] = T(n / (sz - i)) * T(n / (sz - i) + 1) / 2 - 1;
}
for (int64_t x : primes) {
for (int32_t i = sz - 1; i >= sqrtN; i--) {
if (n < x * x * (sz - i)) break;
if (sz - (sz - i) * x < sqrtN) {
dp[i] -= (dp[n / (x * (sz - i)) - 1] - dp[x - 2]) * x;
} else {
dp[i] -= (dp[sz - (sz - i) * x] - dp[x - 2]) * x;
}
}
for (int32_t i = sqrtN - 1; i >= 0; i--) {
if (i + 1 < x * x) break;
dp[i] -= (dp[(i + 1) / x - 1] - dp[x - 2]) * x;
}
}
return dp;
}
std::vector<T> prefix_prime_table(auto f) {
std::vector<T> dp(sz);
for (int32_t i = 0; i < sqrtN; i++) {
dp[i] = f(i + 1);
}
for (int32_t i = sqrtN; i < sz; i++) {
dp[i] = f(n / (sz - i));
}
for (int64_t x : primes) {
for (int32_t i = sz - 1; i >= sqrtN; i--) {
if (n < x * x * (sz - i)) break;
if (sz - (sz - i) * x < sqrtN) {
dp[i] -= (dp[n / (x * (sz - i)) - 1] - dp[x - 2]) *
(f(x) - f(x - 1));
} else {
dp[i] -=
(dp[sz - (sz - i) * x] - dp[x - 2]) * (f(x) - f(x - 1));
}
}
for (int32_t i = sqrtN - 1; i >= 0; i--) {
if (i + 1 < x * x) break;
dp[i] -= (dp[(i + 1) / x - 1] - dp[x - 2]) * (f(x) - f(x - 1));
}
}
return dp;
}
struct _Node{
int64_t x;
int32_t gpf;
int32_t c;
int32_t cnt;
T fx;
T ret;
};
T black_algorithm(std::vector<T> &table, auto f) {
//x,gpf(x),c,f(x),cnt,ret
if(n==1)return 1;
std::stack<_Node> dfs;
dfs.push({1,-1,0,0,1,0});
while(true){
_Node *tp=&dfs.top();
if(tp->cnt==tp->gpf){
if(tp->x*primes[tp->gpf]*primes[tp->gpf]<=n){
dfs.push({tp->x*primes[tp->gpf],tp->gpf,tp->c+1,tp->cnt,tp->fx,0});
}
tp->ret+=tp->fx*f(primes[tp->gpf],tp->c+1);
tp->fx*=f(primes[tp->gpf],tp->c);
tp->cnt++;
}
else{
if(tp->cnt<prisz&&tp->x*primes[tp->cnt]*primes[tp->cnt]<=n){
dfs.push({tp->x*primes[tp->cnt],tp->cnt,1,tp->cnt,tp->fx,0});
tp->cnt++;
}
else{
if(tp->gpf==-1){
if(sz-tp->x<sqrtN)return tp->ret+tp->fx*table[n/tp->x-1]+1;
else return tp->ret+tp->fx*table[sz-tp->x]+1;
}
T nret=tp->ret;
if(sz-tp->x<sqrtN)nret+=tp->fx*(table[n/tp->x-1]-table[primes[tp->gpf]-1]);
else nret+=tp->fx*(table[sz-tp->x]-table[primes[tp->gpf]-1]);
dfs.pop();
if(dfs.empty())return nret+1;
dfs.top().ret+=nret;
}
}
}
}
std::vector<T> min25_sieve(std::vector<T> &table, auto f) {
std::vector<T> dp = table;
for (auto it = primes.rbegin(); it != primes.rend(); it++) {
int64_t x = *it;
for (int32_t i = sz - 1; i >= sqrtN; i--) {
if (n < x * x * (sz - i)) break;
int64_t xp = x;
int32_t c = 1;
while (xp * x * (sz - i) <= n) {
if (sz - (sz - i) * xp < sqrtN) {
dp[i] += f(x, c) * (dp[n / (xp * (sz - i)) - 1] -
table[x - 1]) +
f(x, c + 1);
} else {
dp[i] +=
f(x, c) * (dp[sz - (sz - i) * xp] - table[x - 1]) +
f(x, c + 1);
}
c++;
xp *= x;
}
}
for (int32_t i = sqrtN - 1; i >= 0; i--) {
if (i + 1 < x * x) break;
int64_t xp = x;
int32_t c = 1;
while (xp * x <= i + 1) {
dp[i] += f(x, c) * (dp[(i + 1) / xp - 1] - table[x - 1]) +
f(x, c + 1);
c++;
xp *= x;
}
}
}
for (int32_t i = 0; i < sz; i++) {
dp[i] += 1;
}
return dp;
}
};
#line 2 "Modint/Modint.hpp"
#include <assert.h>
#line 5 "Modint/Modint.hpp"
#include <iostream>
template <uint64_t Mod>
struct Modint {
uint64_t x;
constexpr Modint() noexcept { x = 0; }
constexpr Modint(int64_t val) noexcept {
x = (val < 0 ? val % (int64_t)(Mod) + Mod : val % Mod);
}
inline uint64_t _get_mod(uint64_t val) noexcept {
const static uint64_t m_inv = (-1ULL) / Mod + 1;
uint64_t ret = ((unsigned __int128)(val)*m_inv) >> 64;
uint64_t pro = ret * Mod;
return (val - pro + (val < pro ? Mod : 0));
}
friend std::ostream &operator<<(std::ostream &os, Modint &b) noexcept {
return os << b.x;
}
friend std::istream &operator>>(std::istream &is, Modint &b) noexcept {
return is >> b.x;
}
constexpr uint64_t val() noexcept { return x; }
constexpr Modint operator+() noexcept { return (*this); }
constexpr Modint operator-() noexcept { return Modint() - (*this); }
friend Modint operator+(const Modint lhs, const Modint rhs) noexcept {
return Modint(lhs) += rhs;
}
friend Modint operator-(const Modint lhs, const Modint rhs) noexcept {
return Modint(lhs) -= rhs;
}
friend Modint operator*(const Modint lhs, const Modint rhs) noexcept {
return Modint(lhs) *= rhs;
}
friend Modint operator/(const Modint lhs, const Modint rhs) {
return Modint(lhs) /= rhs;
}
constexpr Modint &operator+=(const Modint rhs) noexcept {
x += rhs.x;
if (x >= Mod) x -= Mod;
return *this;
}
constexpr Modint &operator-=(const Modint rhs) noexcept {
if (x < rhs.x) x += Mod;
x -= rhs.x;
return *this;
}
constexpr Modint &operator*=(const Modint rhs) noexcept {
x = _get_mod(x * rhs.x);
return *this;
}
friend bool operator==(const Modint lhs, const Modint rhs) noexcept {
return lhs.x == rhs.x;
}
friend bool operator!=(const Modint lhs, const Modint rhs) noexcept {
return rhs.x != rhs.x;
}
constexpr Modint &operator/=(Modint rhs) { return (*this) *= rhs.inv(); }
constexpr Modint inv() {
int64_t a = (*this).x, b = get_mod();
assert(a != 0);
int64_t s = b, t = a;
int64_t m0 = 0, m1 = 1;
while (t) {
int64_t u = s / t;
s -= t * u;
m0 -= m1 * u;
int64_t tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
assert(s == 1);
if (m0 < 0) m0 += b;
return Modint(m0);
}
constexpr Modint pow(uint64_t x) noexcept {
Modint ret = 1;
Modint bin = (*this);
while (x) {
if (x & 1) ret *= bin;
bin *= bin;
x >>= 1;
}
return ret;
}
static uint64_t get_mod() noexcept { return Mod; }
};
template <int64_t id>
struct ArbitraryModint {
uint64_t x;
static uint64_t &mod() noexcept {
static uint64_t Mod = 0;
return Mod;
}
constexpr ArbitraryModint() noexcept { x = 0; }
constexpr ArbitraryModint(int64_t val) noexcept {
x = (val < 0 ? val % (int64_t)(get_mod()) + get_mod()
: val % get_mod());
}
inline uint64_t _get_mod(uint64_t val) noexcept {
const static uint64_t m_inv = (-1ULL) / get_mod() + 1;
uint64_t ret = ((unsigned __int128)(val)*m_inv) >> 64;
uint64_t pro = ret * get_mod();
return (val - pro + (val < pro ? get_mod() : 0));
}
friend std::ostream &operator<<(std::ostream &os,
ArbitraryModint &b) noexcept {
return os << b.x;
}
friend std::istream &operator>>(std::istream &is,
ArbitraryModint &b) noexcept {
return is >> b.x;
}
constexpr uint64_t val() noexcept { return x; }
constexpr ArbitraryModint operator+() noexcept { return (*this); }
constexpr ArbitraryModint operator-() noexcept {
return ArbitraryModint() - (*this);
}
friend ArbitraryModint operator+(const ArbitraryModint lhs,
const ArbitraryModint rhs) noexcept {
return ArbitraryModint(lhs) += rhs;
}
friend ArbitraryModint operator-(const ArbitraryModint lhs,
const ArbitraryModint rhs) noexcept {
return ArbitraryModint(lhs) -= rhs;
}
friend ArbitraryModint operator*(const ArbitraryModint lhs,
const ArbitraryModint rhs) noexcept {
return ArbitraryModint(lhs) *= rhs;
}
friend ArbitraryModint operator/(const ArbitraryModint lhs,
const ArbitraryModint rhs) {
return ArbitraryModint(lhs) /= rhs;
}
constexpr ArbitraryModint &operator+=(const ArbitraryModint rhs) noexcept {
x += rhs.x;
if (x >= mod()) x -= mod();
return *this;
}
constexpr ArbitraryModint &operator-=(const ArbitraryModint rhs) noexcept {
if (x < rhs.x) x += mod();
x -= rhs.x;
return *this;
}
constexpr ArbitraryModint &operator*=(const ArbitraryModint rhs) noexcept {
x = _get_mod(x * rhs.x);
return *this;
}
friend bool operator==(const ArbitraryModint lhs,
const ArbitraryModint rhs) noexcept {
return lhs.x == rhs.x;
}
friend bool operator!=(const ArbitraryModint lhs,
const ArbitraryModint rhs) noexcept {
return rhs.x != rhs.x;
}
constexpr ArbitraryModint &operator/=(ArbitraryModint rhs) {
return (*this) *= rhs.inv();
}
constexpr ArbitraryModint inv() {
int64_t a = (*this).x, b = get_mod();
assert(a != 0);
int64_t s = b, t = a;
int64_t m0 = 0, m1 = 1;
while (t) {
int64_t u = s / t;
s -= t * u;
m0 -= m1 * u;
int64_t tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
assert(s == 1);
if (m0 < 0) m0 += b;
return ArbitraryModint(m0);
}
constexpr ArbitraryModint pow(uint64_t x) noexcept {
ArbitraryModint ret = 1;
ArbitraryModint bin = (*this);
while (x) {
if (x & 1) ret *= bin;
bin *= bin;
x >>= 1;
}
return ret;
}
static void set_mod(const uint64_t x) noexcept { mod() = x; }
static uint64_t get_mod() noexcept { return mod(); }
};
template <uint64_t N>
inline void scan(Modint<N> &a) {
std::cin >> a.x;
}
template <int64_t id>
inline void scan(ArbitraryModint<id> &a) {
std::cin >> a.x;
}
template <uint64_t N>
inline void print(Modint<N> a) {
std::cout << a.x;
}
template <int64_t id>
inline void print(ArbitraryModint<id> a) {
std::cout << a.x;
}
#line 2 "Template/Template.hpp"
#include <bits/stdc++.h>
using namespace std;
#line 8 "Template/InOut.hpp"
inline void scan() {}
inline void scan(int32_t &a) { std::cin >> a; }
inline void scan(uint32_t &a) { std::cin >> a; }
inline void scan(int64_t &a) { std::cin >> a; }
inline void scan(uint64_t &a) { std::cin >> a; }
inline void scan(char &a) { std::cin >> a; }
inline void scan(float &a) { std::cin >> a; }
inline void scan(double &a) { std::cin >> a; }
inline void scan(long double &a) { std::cin >> a; }
inline void scan(std::vector<bool> &vec) {
for (int32_t i = 0; i < vec.size(); i++) {
int a;
scan(a);
vec[i] = a;
}
}
inline void scan(std::string &a) { std::cin >> a; }
template <class T>
inline void scan(std::vector<T> &vec);
template <class T, size_t size>
inline void scan(std::array<T, size> &vec);
template <class T, class L>
inline void scan(std::pair<T, L> &p);
template <class T, size_t size>
inline void scan(T (&vec)[size]);
template <class T>
inline void scan(std::vector<T> &vec) {
for (auto &i : vec) scan(i);
}
template <class T>
inline void scan(std::deque<T> &vec) {
for (auto &i : vec) scan(i);
}
template <class T, size_t size>
inline void scan(std::array<T, size> &vec) {
for (auto &i : vec) scan(i);
}
template <class T, class L>
inline void scan(std::pair<T, L> &p) {
scan(p.first);
scan(p.second);
}
template <class T, size_t size>
inline void scan(T (&vec)[size]) {
for (auto &i : vec) scan(i);
}
template <class T>
inline void scan(T &a) {
std::cin >> a;
}
inline void in() {}
template <class Head, class... Tail>
inline void in(Head &head, Tail &...tail) {
scan(head);
in(tail...);
}
inline void print() { std::cout << ' '; }
inline void print(const bool &a) { std::cout << a; }
inline void print(const int32_t &a) { std::cout << a; }
inline void print(const uint32_t &a) { std::cout << a; }
inline void print(const int64_t &a) { std::cout << a; }
inline void print(const uint64_t &a) { std::cout << a; }
inline void print(const char &a) { std::cout << a; }
inline void print(const char a[]) { std::cout << a; }
inline void print(const float &a) { std::cout << a; }
inline void print(const double &a) { std::cout << a; }
inline void print(const long double &a) { std::cout << a; }
inline void print(const std::string &a) {
for (auto &&i : a) print(i);
}
template <class T>
inline void print(const std::vector<T> &vec);
template <class T, size_t size>
inline void print(const std::array<T, size> &vec);
template <class T, class L>
inline void print(const std::pair<T, L> &p);
template <class T, size_t size>
inline void print(const T (&vec)[size]);
template <class T>
inline void print(const std::vector<T> &vec) {
if (vec.empty()) return;
print(vec[0]);
for (auto i = vec.begin(); ++i != vec.end();) {
std::cout << ' ';
print(*i);
}
}
template <class T>
inline void print(const std::deque<T> &vec) {
if (vec.empty()) return;
print(vec[0]);
for (auto i = vec.begin(); ++i != vec.end();) {
std::cout << ' ';
print(*i);
}
}
template <class T, size_t size>
inline void print(const std::array<T, size> &vec) {
print(vec[0]);
for (auto i = vec.begin(); ++i != vec.end();) {
std::cout << ' ';
print(*i);
}
}
template <class T, class L>
inline void print(const std::pair<T, L> &p) {
print(p.first);
std::cout << ' ';
print(p.second);
}
template <class T, size_t size>
inline void print(const T (&vec)[size]) {
print(vec[0]);
for (auto i = vec; ++i != end(vec);) {
std::cout << ' ';
print(*i);
}
}
template <class T>
inline void print(const T &a) {
std::cout << a;
}
inline void out() { std::cout << '\n'; }
template <class T>
inline void out(const T &t) {
print(t);
std::cout << '\n';
}
template <class Head, class... Tail>
inline void out(const Head &head, const Tail &...tail) {
print(head);
std::cout << ' ';
out(tail...);
}
inline void Yes(bool i = true) { out(i ? "Yes" : "No"); }
inline void No(bool i = true) { out(i ? "No" : "Yes"); }
inline void Takahashi(bool i = true) { out(i ? "Takahashi" : "Aoki"); }
inline void Aoki(bool i = true) { out(i ? "Aoki" : "Takahashi"); }
inline void Alice(bool i = true) { out(i ? "Alice" : "Bob"); }
inline void Bob(bool i = true) { out(i ? "Bob" : "Alice"); }
inline void First(bool i = true) { out(i ? "First" : "Second"); }
inline void Second(bool i = true) { out(i ? "Second" : "First"); }
inline void Possible(bool i = true) { out(i ? "Possible" : "Impossible"); }
inline void Impossible(bool i = true) { out(i ? "Impossible" : "Possible"); }
inline void fls() { std::flush(std::cout); }
struct IOsetup {
IOsetup() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(16);
}
} iosetup;
#line 9 "Template/Util.hpp"
using ll = int64_t;
using ld = long double;
using ull = uint64_t;
using uint = uint32_t;
using pll = std::pair<ll, ll>;
using pii = std::pair<int32_t, int32_t>;
using vl = std::vector<ll>;
using vvl = std::vector<std::vector<ll>>;
using pdd = std::pair<ld, ld>;
using tuplis = std::array<ll, 3>;
template <class T>
using pq = std::priority_queue<T, std::vector<T>, std::greater<T>>;
constexpr ll LINF = (1LL << 62) - (1LL << 31);
constexpr int32_t INF = INT_MAX >> 1;
constexpr ll MINF = 1LL << 40;
constexpr ld DINF = std::numeric_limits<ld>::infinity();
constexpr int32_t MODD = 1000000007;
constexpr int32_t MOD = 998244353;
constexpr ld EPS = 1e-9;
constexpr ld PI = 3.1415926535897932;
const ll four[] = {0, 1, 0, -1, 0};
const ll eight[] = {0, 1, 1, 0, -1, -1, 1, -1, 0};
template <class T>
bool chmin(T &a, const T &b) {
if (a > b) {
a = b;
return true;
} else
return false;
}
template <class T>
bool chmax(T &a, const T &b) {
if (a < b) {
a = b;
return true;
} else
return false;
}
template <class T>
ll sum(const T &a) {
return accumulate(std::begin(a), std::end(a), 0LL);
}
template <class T>
ld dsum(const T &a) {
return accumulate(std::begin(a), std::end(a), 0.0L);
}
template <class T>
auto min(const T &a) {
return *min_element(std::begin(a), std::end(a));
}
template <class T>
auto max(const T &a) {
return *max_element(std::begin(a), std::end(a));
}
#line 1 "Template/Macro.hpp"
#define _overload3(_1, _2, _3, name, ...) name
#define _overload4(_1, _2, _3, _4, name, ...) name
#define _rep1(i, n) for (int64_t i = 0; i < (n); i++)
#define _rep2(i, a, b) for (int64_t i = (a); i < (b); i++)
#define _rep3(i, a, b, c) for (int64_t i = (a); i < (b); i += (c))
#define rep(...) _overload4(__VA_ARGS__, _rep3, _rep2, _rep1)(__VA_ARGS__)
#define _rrep1(i, n) for (int64_t i = (n) - 1; i >= 0; i--)
#define _rrep2(i, a, b) for (int64_t i = (b) - 1; i >= (a); i--)
#define rrep(...) _overload3(__VA_ARGS__, _rrep2, _rrep1)(__VA_ARGS__)
#define each(i, ...) for (auto&& i : __VA_ARGS__)
#define all(i) std::begin(i), std::end(i)
#define rall(i) std::rbegin(i), std::rend(i)
#define len(x) ((int64_t)(x).size())
#define fi first
#define se second
#define uniq(x) x.erase(unique(all(x)), std::end(x))
#define vec(type, name, ...) vector<type> name(__VA_ARGS__);
#define vv(type, name, h, ...) std::vector<std::vector<type>> name(h, std::vector<type>(__VA_ARGS__));
#define INT(...) int32_t __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) int64_t __VA_ARGS__; in(__VA_ARGS__)
#define ULL(...) uint64_t __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) std::string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) long double __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) std::vector<type> name(size); in(name)
#define VV(type, name, h, w) std::vector<std::vector<type>> name(h, std::vector<type>(w)); in(name)
#line 5 "Verify/verify-yosupo-new/sum_of_multiplicative_function-black_algorithm.test.cpp"
using mint = Modint<469762049>;
void solve() {
LL(T);
rep(_, T) {
LL(N, a, b);
MFPrefixSum<mint> mf(N);
vector<mint> pi = mf.pi_table();
vector<mint> prime_sum = mf.prime_sum_table();
vector<mint> table(len(pi));
rep(i, len(pi)) { table[i] = pi[i] * a + prime_sum[i] * b; }
out(mf.black_algorithm(table, [a, b](ll x, ll c) -> mint {
return a * c + b * x;
}));
}
}
int main() { solve(); }