結果

問題 No.2699 Simple Math (Returned)
ユーザー ゆにぽけ
提出日時 2024-03-29 21:31:43
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 249 ms / 2,000 ms
コード長 3,534 bytes
コンパイル時間 1,312 ms
コンパイル使用メモリ 125,356 KB
最終ジャッジ日時 2025-02-20 14:48:04
ジャッジサーバーID
（参考情報） 		judge5 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 11
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <iostream>
#include <vector>
#include <algorithm>
#include <array>
#include <iterator>
#include <string>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <cassert>
#include <cmath>
#include <ctime>
#include <iomanip>
#include <numeric>
#include <stack>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <bitset>
#include <random>
#include <utility>
#include <functional>
using namespace std;
template<int m> struct modint
{
    private:
    unsigned int value;
    static constexpr int mod() {return m;}
    public:
    constexpr modint(const long long x = 0) noexcept
    {
        long long y = x;
        if(y < 0 || y >= mod())
        {
            y %= mod();
            if(y < 0) y += mod();
        }
        value = (unsigned int)y;
    }
    static constexpr int get_mod() noexcept {return m;}
    static constexpr int primitive_root() noexcept
    {
        assert(m == 998244353);
        return 3;
    }
    constexpr unsigned int val() noexcept {return value;}
    constexpr modint &operator+=(const modint &other) noexcept
    {
        value += other.value;
        if(value >= mod()) value -= mod();
        return *this;
    }
    constexpr modint &operator-=(const modint &other) noexcept
    {
        unsigned int x = value;
        if(x < other.value) x += mod();
        x -= other.value;
        value = x;
        return *this;
    }
    constexpr modint &operator*=(const modint &other) noexcept
    {
        unsigned long long x = value;
        x *= other.value;
        value = (unsigned int) (x % mod());
        return *this;
    }
    constexpr modint &operator/=(const modint &other) noexcept
    {
        return *this *= other.inverse();
    }
    constexpr modint inverse() const noexcept
    {
        assert(value);
        long long a = value,b = mod(),x = 1,y = 0;
        while(b)
        {
            long long q = a/b;
            a -= q*b; swap(a,b);
            x -= q*y; swap(x,y);
        }
        return modint(x);
    }
    constexpr modint power(long long N) const noexcept
    {
        assert(N >= 0);
        modint p = *this,ret = 1;
        while(N)
        {
            if(N & 1) ret *= p;
            p *= p;
            N >>= 1;
        }
        return ret;
    }
    constexpr modint operator+() {return *this;}
    constexpr modint operator-() {return modint() - *this;}
    constexpr modint &operator++(int) noexcept {return *this += 1;}
    constexpr modint &operator--(int) noexcept {return *this -= 1;}
    friend modint operator+(const modint& lhs, const modint& rhs) {return modint(lhs) += rhs;}
    friend modint operator-(const modint& lhs, const modint& rhs) {return modint(lhs) -= rhs;}
    friend modint operator*(const modint& lhs, const modint& rhs) {return modint(lhs) *= rhs;}
    friend modint operator/(const modint& lhs, const modint& rhs) {return modint(lhs) /= rhs;}
    friend ostream &operator<<(ostream &os,const modint &x) {return os << x.value;}
};
using mint = modint<998244353>;
/* using mint = modint<1000000007>; */
//10 ^ N - 1 = q * (10 ^ M + 1) + r;
void Main()
{
    //x keta x + M keta = N
    //x = N - M
    int N,M;
    cin >> N >> M;
    if(N <= M)
    {
        cout << mint(10).power(N) - 1 << "\n";
    }
    else
    {
        int K = N - M;
        const mint T = mint(10).power(M);
        mint L = (T - 1) * T;
        //K / (2M) := Q
        //K % (2M) := R
        //L + L * 10^2M + L * 10 ^ 4M + ... + L * 10^2M(Q - 1) = L * (1 - 10 ^ 2MQ) / (1 - 10 ^ 2M)
        int Q = K / (2 * M),R = K % (2 * M);
        mint q = L * (1 - T.power(2 * Q)) / (1 - T * T);
        if(R <= M)
        {
            q *= mint(10).power(R);
            q += mint(10).power(R) - 1;
        }
        else
        {
            q *= T;
            q += T - 1;
            q *= mint(10).power(R - M);
        }
        mint ans = (mint(10).power(N) - 1) - q * (T + 1);
        cout << ans << "\n";
    }
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int tt = 1;
    cin >> tt;
    while(tt--) Main();
}
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