結果
| 問題 | No.1781 LCM |
| ユーザー |
 hotman78
|
| 提出日時 | 2021-12-10 17:52:05 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 4,114 ms / 5,000 ms |
| コード長 | 26,963 bytes |
| コンパイル時間 | 4,011 ms |
| コンパイル使用メモリ | 238,948 KB |
| 実行使用メモリ | 15,592 KB |
| 最終ジャッジ日時 | 2024-09-25 17:05:05 |
| 合計ジャッジ時間 | 30,526 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（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 | 3 ms
6,812 KB |
| testcase_01 | AC | 4 ms
6,940 KB |
| testcase_02 | AC | 4 ms
6,940 KB |
| testcase_03 | AC | 4 ms
6,944 KB |
| testcase_04 | AC | 4 ms
6,940 KB |
| testcase_05 | AC | 4 ms
6,940 KB |
| testcase_06 | AC | 4 ms
6,940 KB |
| testcase_07 | AC | 3 ms
6,944 KB |
| testcase_08 | AC | 3 ms
6,940 KB |
| testcase_09 | AC | 3 ms
6,944 KB |
| testcase_10 | AC | 3 ms
6,944 KB |
| testcase_11 | AC | 2 ms
6,940 KB |
| testcase_12 | AC | 3 ms
6,944 KB |
| testcase_13 | AC | 3 ms
6,940 KB |
| testcase_14 | AC | 3 ms
6,944 KB |
| testcase_15 | AC | 2 ms
6,944 KB |
| testcase_16 | AC | 2 ms
6,940 KB |
| testcase_17 | AC | 2 ms
6,944 KB |
| testcase_18 | AC | 3 ms
6,940 KB |
| testcase_19 | AC | 2 ms
6,940 KB |
| testcase_20 | AC | 3 ms
6,944 KB |
| testcase_21 | AC | 4,114 ms
15,468 KB |
| testcase_22 | AC | 4,105 ms
15,412 KB |
| testcase_23 | AC | 3 ms
6,944 KB |
| testcase_24 | AC | 2 ms
6,944 KB |
| testcase_25 | AC | 4,094 ms
15,592 KB |
| testcase_26 | AC | 4,084 ms
15,348 KB |
| testcase_27 | AC | 4,052 ms
15,176 KB |
| testcase_28 | AC | 3,432 ms
13,752 KB |
| testcase_29 | AC | 904 ms
8,044 KB |
| testcase_30 | AC | 969 ms
8,168 KB |
| testcase_31 | AC | 3 ms
6,940 KB |
| testcase_32 | AC | 3 ms
6,940 KB |
ソースコード
#line 2 "cpplib/util/template.hpp"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")
#include<bits/stdc++.h>
using namespace std;
struct __INIT__{__INIT__(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}}__INIT__;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define EPS (1e-10)
#define endl ('\n')
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>using V=vector<T>;
template<typename T>using VV=V<V<T>>;
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void debug(T t){bool f=0;for(auto i:t){cerr<<(f?" ":"")<<i;f=1;}cerr<<endl;}
template<typename T>inline void debug2(T t){for(auto i:t)debug(i);}
#define loop(n) for(long long _=0;_<(long long)(n);++_)
#define _overload4(_1,_2,_3,_4,name,...) name
#define __rep(i,a) repi(i,0,a,1)
#define _rep(i,a,b) repi(i,a,b,1)
#define repi(i,a,b,c) for(long long i=(long long)(a);i<(long long)(b);i+=c)
#define rep(...) _overload4(__VA_ARGS__,repi,_rep,__rep)(__VA_ARGS__)
#define _overload3_rev(_1,_2,_3,name,...) name
#define _rep_rev(i,a) repi_rev(i,0,a)
#define repi_rev(i,a,b) for(long long i=(long long)(b)-1;i>=(long long)(a);--i)
#define rrep(...) _overload3_rev(__VA_ARGS__,repi_rev,_rep_rev)(__VA_ARGS__)
// #define rep(i,...) for(auto i:range(__VA_ARGS__))
// #define rrep(i,...) for(auto i:reversed(range(__VA_ARGS__)))
// #define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
// #define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
// #define irep(i) for(lint i=0;;++i)
// inline vector<long long> range(long long n){if(n<=0)return vector<long long>();vector<long long>v(n);iota(v.begin(),v.end(),0LL);return v;}
// inline vector<long long> range(long long a,long long b){if(b<=a)return vector<long long>();vector<long long>v(b-a);iota(v.begin(),v.end(),a);return v;}
// inline vector<long long> range(long long a,long long b,long long c){if((b-a+c-1)/c<=0)return vector<long long>();vector<long long>v((b-a+c-1)/c);for(int i=0;i<(int)v.size();++i)v[i]=i?v[i-1]+c:a;return v;}
// template<typename T>inline T reversed(T v){reverse(v.begin(),v.end());return v;}
#define all(n) begin(n),end(n)
template<typename T,typename E>bool chmin(T& s,const E& t){bool res=s>t;s=min<T>(s,t);return res;}
template<typename T,typename E>bool chmax(T& s,const E& t){bool res=s<t;s=max<T>(s,t);return res;}
const string ds="DRUL";
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
#if __cplusplus>=201703L
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
#endif
#define extrep(v,...) for(auto v:__MAKE_MAT__({__VA_ARGS__}))
#define bit(n,a) ((n>>a)&1)
vector<vector<long long>> __MAKE_MAT__(vector<long long> v){if(v.empty())return vector<vector<long long>>(1,vector<long long>());long long n=v.back();v.pop_back();vector<vector<long long>> ret;vector<vector<long long>> tmp=__MAKE_MAT__(v);for(auto e:tmp)for(long long i=0;i<n;++i){ret.push_back(e);ret.back().push_back(i);}return ret;}
using graph=vector<vector<int>>;
template<typename T>using graph_w=vector<vector<pair<int,T>>>;
template<typename T,typename E>ostream& operator<<(ostream& out,pair<T,E>v){out<<"("<<v.first<<","<<v.second<<")";return out;}
#if __cplusplus>=201703L
constexpr inline long long powll(long long a,long long b){long long res=1;while(b--)res*=a;return res;}
#endif
template<typename T,typename E>pair<T,E>& operator+=(pair<T,E>&s,const pair<T,E>&t){s.first+=t.first;s.second+=t.second;return s;}
template<typename T,typename E>pair<T,E>& operator-=(pair<T,E>&s,const pair<T,E>&t){s.first-=t.first;s.second-=t.second;return s;}
template<typename T,typename E>pair<T,E> operator+(const pair<T,E>&s,const pair<T,E>&t){auto res=s;return res+=t;}
template<typename T,typename E>pair<T,E> operator-(const pair<T,E>&s,const pair<T,E>&t){auto res=s;return res-=t;}
#define BEGIN_STACK_EXTEND(size) void * stack_extend_memory_ = malloc(size);void * stack_extend_origin_memory_;char * stack_extend_dummy_memory_ = (char*)alloca((1+(int)(((long long)stack_extend_memory_)&127))*16);*stack_extend_dummy_memory_ = 0;asm volatile("mov %%rsp, %%rbx\nmov %%rax, %%rsp":"=b"(stack_extend_origin_memory_):"a"((char*)stack_extend_memory_+(size)-1024));
#define END_STACK_EXTEND asm volatile("mov %%rax, %%rsp"::"a"(stack_extend_origin_memory_));free(stack_extend_memory_);
#line 6 "cpplib/math/prime_list.hpp"
/**
* @brief 素数列挙
*/
std::bitset<10'000'001> p;
std::vector<long long> prime_list(int n) {
p.set();
p[0]=0;
for(int i=2;i*i<=n;++i){
if(!p[i])continue;
for(int j=2*i;j<=n;j+=i)p[j]=0;
}
std::vector<long long>list;
for(int i=2;i<=n;++i)if(p[i])list.push_back(i);
return list;
}
#line 2 "cpplib/math/ACL_modint998244353.hpp"
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
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;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long 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);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
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; (long long)(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);
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long 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;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
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;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<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,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
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
} // namespace atcoder
namespace atcoder {
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 mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
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 -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
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(long long 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 {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
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;
}
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) {
long long x = (long long)(v % (long long)(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(long long 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;
}
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 modint998244353 = static_modint<998244353>;
using modint1000000007 = 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
} // namespace atcoder
using mint=atcoder::modint998244353;
#line 4 "cpplib/math/ACL_modint_base.hpp"
std::ostream& operator<<(std::ostream& lhs, const mint& rhs) noexcept {
lhs << rhs.val();
return lhs;
}
std::istream& operator>>(std::istream& lhs,mint& rhs) noexcept {
long long x;
lhs >> x;
rhs=x;
return lhs;
}
int MOD_NOW=-1;
int sz=0;
std::vector<mint>fact_table,fact_inv_table;
void update(int x){
if(MOD_NOW!=mint::mod()||sz==0){
fact_table.assign(1,1);
fact_inv_table.assign(1,1);
sz=1;
MOD_NOW=mint::mod();
}
while(sz<=x){
fact_table.resize(sz*2);
fact_inv_table.resize(sz*2);
for(int i=sz;i<sz*2;++i){
fact_table[i]=fact_table[i-1]*i;
}
fact_inv_table[sz*2-1]=fact_table[sz*2-1].inv();
for(int i=sz*2-2;i>=sz;--i){
fact_inv_table[i]=fact_inv_table[i+1]*(i+1);
}
sz*=2;
}
}
inline mint fact(int x){
assert(x>=0);
update(x);
return fact_table[x];
}
inline mint fact_inv(int x){
assert(x>=0);
update(x);
return fact_inv_table[x];
}
inline mint comb(int x,int y){
if(x<0||x<y||y<0)return 0;
return fact(x)*fact_inv(y)*fact_inv(x-y);
}
inline mint perm(int x,int y){
return fact(x)*fact_inv(y);
}
inline mint multi_comb(int x,int y){
return comb(x+y-1,y);
}
#line 4 "main.cpp"
template<typename T>
struct Dirichlet{
using P=Dirichlet<T>;
static long long N,K,L;
std::vector<T>a,A;
Dirichlet():a(K+1),A(L+1){}
P& operator+=(const P& x){
for(int i=1;i<=K;++i)a[i]+=x.a[i];
for(int i=1;i<=L;++i)A[i]+=x.A[i];
}
P& operator-=(const P& x){
for(int i=1;i<=K;++i)a[i]-=x.a[i];
for(int i=1;i<=L;++i)A[i]-=x.A[i];
}
P& operator*=(const P& x){
P res;
for(int i=1;i<=K;++i){
for(int j=1;i*j<=K;++j){
res.a[i*j]+=a[i]*x.a[j];
}
}
std::vector<T>sum_a=a,sum_b=x.a;
for(int i=1;i<=K;++i){
sum_a[i]+=sum_a[i-1];
sum_b[i]+=sum_b[i-1];
}
auto getA=[&](long long n){return (n<=K?sum_a[n]:A[N/n]);};
auto getB=[&](long long n){return (n<=K?sum_b[n]:x.A[N/n]);};
for(int i=1;i<=L;++i){
const long long n=N/i,m=std::floor(std::sqrt(n));
for(int j=1;j<=m;++j){
res.A[i]+=a[j]*getB(n/j);
res.A[i]+=x.a[j]*(getA(n/j)-getA(m));
}
}
return (*this)=res;
}
P& operator/=(const P& x){
assert(x.a[1]!=T());
//(*this)=x*res;
P res(*this);
for(int i=1;i<=K;++i){
for(int j=2;i*j<=K;++j){
res.a[i*j]-=res.a[i]*x.a[j];
}
res.a[i]/=x.a[1];
}
std::vector<T>sum_a=x.a,sum_b=res.a;
for(int i=1;i<=K;++i){
sum_a[i]+=sum_a[i-1];
sum_b[i]+=sum_b[i-1];
}
auto getA=[&](long long n){return (n<=K?sum_a[n]:x.A[N/n]);};
auto getB=[&](long long n){return (n<=K?sum_b[n]:res.A[N/n]);};
for(int i=L;i>=1;--i){
const long long n=N/i,m=std::floor(std::sqrt(n));
for(int j=1;j<=m;++j){
if(j!=1)res.A[i]-=x.a[j]*getB(n/j);
res.A[i]-=res.a[j]*(getA(n/j)-getA(m));
}
res.A[i]/=x.a[1];
}
return (*this)=res;
}
P operator*=(const T&x){
for(int i=1;i<=K;++i){
a[i]*=x;
}
for(int i=1;i<=L;++i){
A[i]*=x;
}
return *this;
}
P operator+(const P&x)const{return P(*this)+=x;}
P operator-(const P&x)const{return P(*this)-=x;}
P operator*(const P&x)const{return P(*this)*=x;}
P operator/(const P&x)const{return P(*this)/=x;}
P inv()const{return ident()/=(*this);}
T get(){return A[1];}
P pow(long long x){
P res=ident();
P tmp(*this);
while(x){
if(x%2)res*=tmp;
tmp*=tmp;
x/=2;
}
return res;
}
void clear(){a.clear();A.clear();}
template<typename F,typename G>
static P make(F f,G g){
P res;
for(int i=1;i<=K;++i)res.a[i]=f(i);
for(int i=1;i<=L;++i)res.A[i]=g(N/i);
return res;
}
static P ident(){
P res;
res.a[1]=1;
res.A.assign(L+1,1);
return res;
}
//ζ(s-k)
static P zeta_shift(int k){
P res;
std::vector<T>tmp(k+2),fact(k+2,1),fact_inv(k+2,1);
for(int i=1;i<=k+1;++i)tmp[i]=tmp[i-1]+T(i).pow(k);
for(int i=1;i<=k+1;++i)fact[i]=fact[i-1]*i;
fact_inv[k+1]=T(1)/fact[k+1];
for(int i=k;i>=0;--i)fact_inv[i]=fact_inv[i+1]*T(i+1);
for(int i=1;i<=K;++i)res.a[i]=T(i).pow(k);
auto get=[&](long long n){
if(n<=k+1)return tmp[n];
T tmp2=1,res=0;
for(int i=0;i<=k+1;++i)tmp2*=T(n-i);
if(tmp2==T()){
for(int i=0;i<=k+1;++i){
T tmp3=1;
if(T(n-i)==T()){
for(int j=0;j<=k+1;++j){
if(i!=j)tmp3*=T(n-i);
}
}
res+=tmp[i]*fact_inv[i]*fact_inv[k+1-i]*tmp3*((k+1-i)%2?T(-1):T(1));
}
}else{
for(int i=0;i<=k+1;++i){
res+=tmp[i]*fact_inv[i]*fact_inv[k+1-i]*tmp2/T(n-i)*((k+1-i)%2?T(-1):T(1));
}
}
return res;
};
for(int i=1;i<=L;++i){
res.A[i]=get(N/i);
}
return res;
}
//ζ(s)
static P zeta(){
P res;
res.a.assign(K+1,1);
res.a[0]=0;
for(int i=1;i<=L;++i)res.A[i]=N/i;
return res;
}
//μ(s)=1/ζ(s)
static P mebius(){return zeta().inv();}
//σ_k(s)=ζ(s)ζ(s-k)
static P divisor(int k){
return zeta()*zeta_shift(k);
}
//φ(s)=ζ(s-1)/ζ(s)
static P euler(){
return zeta_shift(1)/zeta();
}
static void resize(long long n){
N=n;
K=std::ceil(std::cbrt(n)*std::cbrt(n));
L=std::ceil(std::cbrt(n));
}
static long long size(){return N;}
};
template<typename T>long long Dirichlet<T>::N=0;
template<typename T>long long Dirichlet<T>::K=0;
template<typename T>long long Dirichlet<T>::L=0;
int main(){
lint n,m;
cin>>n>>m;
// vector<mint> v(m+1,1);
// rep(i,2,m+1){
// rep(j,i,m+1,i){
// v[j]++;
// }
// }
// mint ans=0;
// rep(i,1,m+1){
// ans+=v[i].pow(n);
// }
// cout<<ans<<endl;
vec x;
{
lint l=1,r;
while(l<=m){
r=m/(m/l)+1;
x.emplace_back(m/l);
l=r;
}
}
vector<lint>dp=x;
lint sqm=sqrt(m);
auto p=prime_list(sqm);
const lint r=x.size();
rep(i,p.size()){
for(lint j=0;x[j]>=p[i]*p[i];j++){
const lint xk=x[j]/p[i];
const lint k=xk<=m/xk?r-xk:m/xk-1;
assert(xk==x[k]);
dp[j]+=(i+1-dp[k]);
}
}
rep(i,r)dp[i]--;
mint ans=0;
array<mint,50>po;
rep(i,1,50){
po[i]=mint(i).pow(n);
}
auto f=[&](lint x){
const lint k=x<=m/x?r-x:m/x-1;
return dp[k];
};
auto dfs=[&](auto dfs,lint i,lint c,lint v,lint lim,mint cur)->void{
ans+=cur*po[c+2];
if(lim>=p[i]*p[i]){
dfs(dfs,i,c+1,p[i]*v,lim/p[i],cur);
}
cur*=po[c+1];
ans+=cur*po[2]*(f(lim)-f(p[i]));
for(lint j=i+1;j<(int)p.size()&&p[j]*p[j]<=lim;++j){
dfs(dfs,j,1,p[j],lim/p[j],cur);
}
};
rep(i,p.size())dfs(dfs,i,1,p[i],m/p[i],1);
ans+=dp[0]*po[2]+1;
cout<<ans<<endl;
}