結果
| 問題 | No.3505 Sum of Prod of Root |
| コンテスト | |
| ユーザー |
 Rubikun
|
| 提出日時 | 2026-04-17 21:12:18 |
| 言語 | C++17 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 305 ms / 2,000 ms |
| コード長 | 32,614 bytes |
| 記録 | |
| コンパイル時間 | 2,248 ms |
| コンパイル使用メモリ | 246,040 KB |
| 実行使用メモリ | 6,400 KB |
| 最終ジャッジ日時 | 2026-04-17 21:12:33 |
| 合計ジャッジ時間 | 4,445 ms |
|
ジャッジサーバーID （参考情報） |
judge3_1 / judge2_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 13 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define vi vector<int>
#define vl vector<ll>
#define vii vector<pair<int,int>>
#define vll vector<pair<ll,ll>>
#define vvi vector<vector<int>>
#define vvl vector<vector<ll>>
#define vvii vector<vector<pair<int,int>>>
#define vvll vector<vector<pair<ll,ll>>>
#define vst vector<string>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define mkunique(x) sort(all(x));(x).erase(unique(all(x)),(x).end())
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod=998244353,MAX=300005;
const ll INF=15LL<<58;
//modint+畳み込み+逆元テーブル
// from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9
// (based on AtCoder STL)
#include <algorithm>
#include <array>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#include <utility>
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;
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;
for (long long a : {2, 7, 61}) {
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);
} // 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
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
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());
}
static_modint(bool 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());
}
dynamic_modint(bool 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
#include <cassert>
#include <type_traits>
#include <vector>
namespace atcoder {
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) {
if (n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
long long diff =
c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5] = {
0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
} // namespace atcoder
using mint=atcoder::modint998244353;
vector<mint> inv,fac,finv;
void make(){
inv.resize(MAX);
fac.resize(MAX);
finv.resize(MAX);
fac[0]=fac[1]=1;
finv[0]=finv[1]=1;
inv[1]=1;
for(int i=2;i<MAX;i++){
inv[i]=-inv[mod%i]*(mod/i);
fac[i]=fac[i-1]*i;
finv[i]=finv[i-1]*inv[i];
}
}
mint comb(ll a,ll b){
if(a<b) return 0;
return fac[a]*finv[b]*finv[a-b];
}
mint perm(ll a,ll b){
if(a<b) return 0;
return fac[a]*finv[a-b];
}
int main(){
std::ifstream in("text.txt");
std::cin.rdbuf(in.rdbuf());
cin.tie(0);
ios::sync_with_stdio(false);
mint r2=mint(2).inv();
vector<mint> ume={563039326,369342839,57018046,483714709,922199560,793414763,738864680,775765369,130713524,463301220,631942102,208411044,801787053,790378971,931170244,814860648,903705984,752337161,281321481,419940687,18410204,372095227,98042605,603270638,214867440,11989264,862970568,177912413,108362786,34328138,161080834,817859489,702572756,463989271,76809916,784524273,100932300,843748480,735048675,87303214,869622709,723596860,437610167,125280016,277816977,388071528,683210306,656230193,376766136,199614294,949331897,992958200,606341395,269873800,635188742,36252798,84842243,183292986,200682441,347639222,9067829,468412178,15992275,129870228,735573319,70759026,63786113,613182996,913526057,723392426,608084907,209628863,742224416,900500458,953614143,279864114,715974760,807754509,915815098,67487393,50919027,37024629,27909326,110182592,488957974,638990412,402600836,733222421,197816803,242773264,143718428,500864354,708272213,737062848,560265652,89291186,560447299,593638793,264283761,599977003,891182050,303029818,532671776,569693534,491282655,329752920,889900429,955090791,435024844,957968631,194717159,121775514,607532329,109420941,244337977,612310250,671938621,166354474,789157313,53508748,183960940,454821693,840861390,346634569,486149277,656880179,664770350,623899811,679276758,411158479,927895683,692209939,127057269,40232406,384317493,755107439,514531706,430314053,328152489,879216417,985543100,890299692,295325802,793619821,849040255,918562249,574739602,509718453,766982383,763410039,54515607,727762181,475856011,753275006,632045624,282200106,920200063,309605675,759478325,521988794,93957573,64275002,338311264,326417806,711189860,757065159,834593543,442400637,983059502,627679507,674298360,488677043,788489609,222374861,111262956,176323748,507037334,729889457,30719976,160127759,175578096,480398779,299964187,210413382,206782832,714713085,935375939,826061196,239998878,14674770,998021279,291752105,593080919,933319544,336541518,317678915,135626962,893039426,362653062,506526066,296542749,47162576,31549761,668242852,767454332,740353835,175786066,830773658,401182175,924179574,202989059,667133288,188471932,224665133,218945799,787614550,67633533,867732128,131802423,897888372,188791464,365117719,265622435,433099386,469997021,194343570,997962966,967383480,96085127,436178330,945973959,117920930,330995204,220986754,851040047,831128432,67973490,35389897,350873338,27247914,979547667,487363320,735281918,299062720,69308670,819960937,341488557,637972507,392637257,561590858,377034712,653389678,7031957,553311944,846582108,435129360,228397086,897913664,283119663,327997212,333250239,72808925,450486861,362352706,890259581,707999338,692299846,862428826,101030829,18549253,36314162,412595273,249007599,303244921,543073439,586977593,866886864,46171500,465412914,453238517,40302332,995827618,7747316,588267653,323313973,312168455,912347107,492093104,335501659,126764754,987110566,90940702,717460631,111499184,111551285,514385598,236998546,112499046,879745967,64922719,935502582,920751254,546003727,462626245,896105548,547814065,681423461,352903116,610937895,788198148,219130125,438984782,480177305,374292988,489148244,839711234,399551921,375492432,684193331,205941319,804700200,706809705,212070233,12432814,556384664,153425005,311864697,584105281,273063701,179113738,763018459,863142631,248120268,632890827,621536969,740524550,435136522,283728665,675466302,416795738,380039647,630304766,94984825,527991135,508785241,231687142,222766502,578280226,177047673,61150820,180459193,797142070,292906722,270186359,211980238,150052477,905873905,968795548,704835477,257561555,943634294,966570375,823717233,687369178,227345439,675531091,563138351,792413109,644241497,743604441,276075809,455785370,432449697,854411557,473329671,565648573,373629320,135677279,132899909,99932800,917439035,101025071,346730477,912228597,540999009,957144559,209218119,475386621,103309107,966870703,618835116,559738897,19225595,493550889,825094025,977941349,61247506,253381439,674356905,569210217,288184764,273039591,868213402,991425622,612324762,94952214,631878225,963506121,761568456,65390895,183084590,767778805,974912473,881048631,462119315,407338097,964209797,589767895,218277756,292806320,205122038,54072496,250854118,270320331,622755650,209162451,91618433,167156350,847092451,751530189,828026690,353927945,724042652,718402817,884256540,159227640,714641671,418216539,899676084,238087605,69610456,173505204,200188627,493548919,710019767,405145424,777107695,771124645,900576822,848886024,359326179,949879501,685384036,730897024,270174981,458894291,758593053,860925383,905048481,244521373,352520207,194107600,730296271,898632004,778839544,550102824,480497142,527480477,360915764,28061909,668039952,587582460,289440243,635160339,523345363,4430814,69152518,183233477,125635832,159157508,372037980,480369926,743502563,449671777,703779722,755473699,892190711,892560765,801980455,289655071,381431778,754345762,233269083,313955543,874007247,982133606,647317720,63420981,264478843,175041949,695920505,366345780,387360056,384813380,233879407,876226860,42013049,80669925,839514022,267435013,96422750,144701921,679138825,839257285,332173017,645755628,276314363,878196595,98168884,23897573,876637680,965675953,135255350,375716254,939696619,825560244,161744316,570079040,403492623,481942468,67072866,432848773,214234812,376068194,658864568,162722591,452733898,399609339,535157345,889204280,510266393,831152456,802300820,870558443,918877260,671693071,465204202,921212125,493512336,722756218,218158695,578685951,983075894,497561392,553662167,785510453,253040808,309725980,318735307,52007753,405340280,244105093,422698584,296916991,418535223,628902966,991149309,969978045,450002502,373036476,372747252,49274384,247077831,225595867,329377763,688645051,345998757,156202419,467065940,74173706,945957595,448042904,830798477,661817267,754604295,705165062,888921770,19504355,484078419,923971814,224989020,901730616,638273892,639610823,199015468,543861710,10939252,573077008,186596094,815141880,634260074,113933007,17065481,169572607,730488849,560861444,102190810,318239774,752756539,234646761,979303563,39965629,670009713,421206412,220847114,720789909,394372397,809450016,715034437,554271632,687332196,522948402,777618878,346894019,437147991,325216527,536145643,314834298,582923864,550310019,905024972,680211612,557423082,521894919,879812298,976209137,539501713,789684752,802683554,213687176,967162610,161511112,169447521,327259781,655146848,363745571,852395183,228258996,958739133,189019557,359510235,862556216,483005217,231539750,676945330,116949719,395417300,316885051,395192297,592670701,610508794,242442600,571038157,333308361,213030640,443499695,475837122,494219720,836491004,229809578,548468130,642758100,938572692,722994520,417385900,609929192,282778638,497379261,743352032,477559759,550492549,689545084,759576777,921992179,583551780,721249249,696148930,106920758,427085844,587301421,28477168,824924559,212858432,531733749,60407643,474386780,413874861,940755315,502823177,840332027,201445712,606494224,25964441,678626651,813862638,771677862,710275054,678521536,947129298,292233544,811695809,277003728,342608441,62388640,718173768,669348312,317792820,78320291,139540398,698213945,899444457,176196315,86834909,934246154,580070721,627489025,609080033,690840696,411587256,315123676,564148931,364024921,979536696,941109799,660442016,908090870,268961675,540456205,202115980,891755259,447185208,175127778,36748514,341301176,213900212,301069325,852795621,120249756,77323390,923331717,355277731,459696507,295501566,499716930,116693997,875236333,757136461,897545734,975306291,635663807,26420205,863210697,599848782,607198493,50073741,28389291,646699796,591982926,200383749,873365108,746655406,865801455,549808315,357905975,245947560,27396384,487664605,245550619,13313226,238319745,834269172,218863351,459678457,68923352,4708232,718081982,540766091,770689814,888762535,790754054,653620128,938206163,18889041,759629710,695426234,372622616,774538191,493617228,887287203,18479979,208839949,528857590,899918656,842909050,906311619,175948672,585985504,610262479,246767488,604219414,737479680,184096063,125172635,604631686,249178756,484935518,65404451,535657252,551024946,756401619,602617367,34361876,358139089,637279800,132392257,278815583,235897676,84283608,403410265,312097164,459364106,38250844,74484166,230874636,768391610,10481614,256977047,676486123,468566099,24901802,702241822,665637257,907909145,599961785,714809231,596778550,51847005,352400114,155791213,539434338,854626507,554792568,718058106,361814829,473326885,554219109,987084535,433203418,844491010,908597350,101389303,153064915,962834731,483680900,689498370,932627079,265521107,635210193,800977648,699773801,562523503,59332097,568696865,756609252,858461962,655470409,528876138,79321940,571331213,437058605,885899904,537886657,258896532,915230539,645548212,677896443,108351150,373239689,206969284,967157064,569627742,794133346,881877308,962636596,648974367,483353415,659788280,973349943,813099037,781014631,717047776,181094707,482367333,48224991,330445186,252117294,879222970,372926084,438607637,326276889,211208738,867184235,733289120,242573402,276484652,93970560,443315691,54080748,263633573,31446328,324650772,34744864,749883257,162179778,747119543,676733121,711879438,861665152,559814038,835883524,961962739,432921688,502408208,210050763,438118445,590237938,838606038,21240580,531841258,575228096,17624483,671417778,708411648,54789855,31561960,542735386,821098804,330241367,995481744,104429484,887837039,299511425,549252455,40606311,165975198,461224965,71239698,64258801,767039177,433940071,382301349,810819793,115595260,513395407,408553401,125050602,526518289,154068323,353970756,553977942,34204353,584234100,285861301,515054903,211456362,338097216,854978058,888319744,994168625,416199582,252533505,642069540,905487192,137840351,108982888,12676422,549794498,541385864,734358880,443800275,755480427,681850849,811819883,946593277,881222058,47487641,960004486,57512637,633585111,530771023};
ll N;cin>>N;
ll okn=0;
mint ans=0;
for(ll i=1000000;;i+=1000000){
if((i+1)*(i+1)-1<=N){
okn=i;
ans=ume[i/1000000-1];
}else{
break;
}
}
vl S(62,1),T(62,1);
for(ll n=okn+1;;n++){
ll L=n*n,R=min((n+1)*(n+1)-1,N);
if(L>R) break;
S[2]=n;
mint sum=0;
while(1){
pll mi=mp(INF,INF);
for(ll k=3;k<=60;k++){
if(T[k]<=R){
chmin(mi,mp(T[k]-1,k));
}
}
//cout<<n<<" "<<mi.fi<<" "<<mi.se<<" "<<sum.val()<<endl;
if(mi.fi==INF){
mint X=1;
for(ll k=3;k<=60;k++) X*=(S[k]-1);
X*=(L+R);
X*=(R-L+1);
X*=r2;
X*=n;
sum+=X;
break;
}else{
if(L<=mi.fi){
mint X=1;
for(ll k=3;k<=60;k++) X*=(S[k]-1);
X*=(L+mi.fi);
X*=(mi.fi-L+1);
X*=r2;
X*=n;
sum+=X;
}
chmax(L,mi.fi+1);
//L=mi.fi+1;
{
ll k=mi.se;
S[k]++;
T[k]=1;
for(ll t=0;t<k;t++){
T[k]*=S[k];
if(T[k]>1000000000000000000LL){
T[k]=INF;
break;
}
}
}
}
}
ans+=sum;
}
cout<<ans.val()<<endl;
}