#1010245 (C++17) No.2891 Mint

• 問題: No.2891 Mint
• ユーザー: tonegawa
• 提出日時: 2024-09-13 22:42:17
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 52 ms / 2,000 ms
• コード長: 6,588 bytes
• コンパイル時間: 864 ms
• コンパイル使用メモリ: 89,504 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-13 22:42:43
• 合計ジャッジ時間: 3,369 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	32 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	52 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	39 ms; 5,376 KB
testcase_18	AC	24 ms; 5,376 KB
testcase_19	AC	22 ms; 5,376 KB
testcase_20	AC	35 ms; 5,376 KB
testcase_21	AC	21 ms; 5,376 KB
testcase_22	AC	43 ms; 5,376 KB
testcase_23	AC	17 ms; 5,376 KB
testcase_24	AC	34 ms; 5,376 KB
testcase_25	AC	47 ms; 5,376 KB
testcase_26	AC	45 ms; 5,376 KB
testcase_27	AC	43 ms; 5,376 KB
testcase_28	AC	49 ms; 5,376 KB
testcase_29	AC	22 ms; 5,376 KB
testcase_30	AC	36 ms; 5,376 KB
testcase_31	AC	23 ms; 5,376 KB
testcase_32	AC	40 ms; 5,376 KB
testcase_33	AC	28 ms; 5,376 KB
testcase_34	AC	31 ms; 5,376 KB
testcase_35	AC	35 ms; 5,376 KB
testcase_36	AC	37 ms; 5,376 KB
testcase_37	AC	26 ms; 5,376 KB
testcase_38	AC	23 ms; 5,376 KB
testcase_39	AC	29 ms; 5,376 KB
testcase_40	AC	30 ms; 5,376 KB
testcase_41	AC	17 ms; 5,376 KB
testcase_42	AC	2 ms; 5,376 KB
testcase_43	AC	2 ms; 5,376 KB
testcase_44	AC	2 ms; 5,376 KB
testcase_45	AC	2 ms; 5,376 KB
testcase_46	AC	2 ms; 5,376 KB
testcase_47	AC	28 ms; 5,376 KB
testcase_48	AC	27 ms; 5,376 KB
testcase_49	AC	32 ms; 5,376 KB
testcase_50	AC	10 ms; 5,376 KB
testcase_51	AC	23 ms; 5,376 KB
testcase_52	AC	10 ms; 5,376 KB
testcase_53	AC	20 ms; 5,376 KB
testcase_54	AC	22 ms; 5,376 KB
testcase_55	AC	6 ms; 5,376 KB
testcase_56	AC	32 ms; 5,376 KB

ソースコード

#include <iostream>
#include <cmath>
#include <cassert>
#include <algorithm>
#include <tuple>
using namespace std;



#include <type_traits>








// @param m `1 <= m`
constexpr long long safe_mod(long long x, long long m){
  x %= m;
  if (x < 0) x += m;
  return x;
}

// x^n mod m
// @param n `0 <= n`
// @param m `1 <= m`
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 miller_rabin32_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 miller_rabin32 = miller_rabin32_constexpr(n);





// -10^18 <= _a, _b <= 10^18
long long gcd(long long _a, long long _b) {
    long long a = abs(_a), b = abs(_b);
    if (a == 0) return b;
    if (b == 0) return a;
    int shift = __builtin_ctzll(a | b);
    a >>= __builtin_ctzll(a);
    do{
        b >>= __builtin_ctzll(b);
        if(a > b) std::swap(a, b);
        b -= a;
    } while (b);
    return a << shift;
}

// 最大でa*b
// -10^18 <= a, b <= 10^18
// a, bは負でもいいが非負の値を返す
__int128_t lcm(long long a, long long b) {
    a = abs(a), b = abs(b);
    long long g = gcd(a, b);
    if (!g) return 0;
    return __int128_t(a) * b / g;
}

// {x, y, gcd(a, b)} s.t. ax + by = gcd(a, b)
// g >= 0
std::tuple<long long, long long, long long> extgcd(long long a, long long b) {
    long long x, y;
    for (long long u = y = 1, v = x = 0; a;) {
        long long q = b / a;
        std::swap(x -= q * u, u);
        std::swap(y -= q * v, v);
        std::swap(b -= q * a, a);
    }
    // x + k * (b / g), y - k * (a / g) も条件を満たす(kは任意の整数)
    return {x, y, b};
}

// @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<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;
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}



template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct modint32_static {
    using mint = modint32_static;
  public:
    static constexpr int mod() { return m; }
    
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
  
    modint32_static(): _v(0) {}
    
    template <class T>
    modint32_static(T v) { 
        long long x = v % (long long)umod();
        if (x < 0) x += umod();
        _v = x;
    }

    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 = 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 = miller_rabin32<m>;
};

template<int m>
std::ostream &operator<<(std::ostream &dest, const modint32_static<m> &a) {
    dest << a.val();
    return dest;
}

using modint998244353 = modint32_static<998244353>;
using modint1000000007 = modint32_static<1000000007>;


// x%1 + x%2 ... x%n
// @param 0 <= x, n
__int128_t mod_sum(__int128_t x, __int128_t n){
  assert(0 <= x && 0 <= n);
  if(x == 0) return 0;
  __int128_t ans = x * n;
  if(n > x) n = x;
  // floor(x / i)の値でグループ分け
  __int128_t sq = sqrtl(x);
  for(int i = 1; i <= sq; i++){
    __int128_t l = x / (i + 1) + 1, r = std::min(n + 1, x / i + 1);
    if(l < r){
      __int128_t sum_lr = (r * (r - 1) - l * (l - 1)) / 2;
      ans -= i * sum_lr;
    }
  }
  if(x / sq == sq) sq--;
  for(__int128_t i = std::min(n, sq); i >= 1; i--){
    ans -= i * (x / i);
  }
  return ans;
}


int main(){
  long long x, n;
  std::cin >> x >> n;
  __int128_t ans = mod_sum(n, x);
  ans %= 998244353;
  std::cout << (long long)ans << '\n';
}