結果

問題 No.2699 Simple Math (Returned)
ユーザー ゆにぽけゆにぽけ
提出日時 2024-03-29 21:31:43
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 214 ms / 2,000 ms
コード長 3,534 bytes
コンパイル時間 1,186 ms
コンパイル使用メモリ 130,468 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-09-30 15:39:18
合計ジャッジ時間 4,399 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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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 2 ms
5,248 KB
testcase_01 AC 136 ms
5,248 KB
testcase_02 AC 96 ms
5,248 KB
testcase_03 AC 43 ms
5,248 KB
testcase_04 AC 214 ms
5,248 KB
testcase_05 AC 131 ms
5,248 KB
testcase_06 AC 191 ms
5,248 KB
testcase_07 AC 153 ms
5,248 KB
testcase_08 AC 153 ms
5,248 KB
testcase_09 AC 153 ms
5,248 KB
testcase_10 AC 153 ms
5,248 KB
testcase_11 AC 151 ms
5,248 KB
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ソースコード

diff # 

#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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