結果

問題 No.681 Fractal Gravity Glue
コンテスト
ユーザー paruki
提出日時 2018-04-28 16:11:48
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 4,229 bytes
コンパイル時間 1,700 ms
コンパイル使用メモリ 176,136 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-06-27 23:22:16
合計ジャッジ時間 2,451 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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
other AC * 20
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ソースコード

diff # 

#define _USE_MATH_DEFINES
#include "bits/stdc++.h"
using namespace std;
#define FOR(i,j,k) for(int (i)=(j);(i)<(int)(k);++(i))
#define rep(i,j) FOR(i,0,j)
#define each(x,y) for(auto &(x):(y))
#define mp make_pair
#define MT make_tuple
#define all(x) (x).begin(),(x).end()
#define debug(x) cout<<#x<<": "<<(x)<<endl
#define smax(x,y) (x)=max((x),(y))
#define smin(x,y) (x)=min((x),(y))
#define MEM(x,y) memset((x),(y),sizeof (x))
#define sz(x) (int)(x).size()
#define RT return
#define vv(a,b,c,d) vector<vector<a> >(b,vector<a>(c,d))
#define vvv(a,b,c,d,e) vector<vector<vector<a> > >(b,vv(a,c,d,e))
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;
using vll = vector<ll>;

const int MOD = (int)1e9 + 7;

vector<vector<int> > mulMatMod(const vector<vector<int> > &A, const vector<vector<int> > &B) {
    auto n = A.size(), m = A[0].size(), p = B[0].size();
    vector<vector<int> > res(n, vector<int>(p));
    for (int i = 0; i < n; ++i)for (int j = 0; j < p; ++j) for (int k = 0; k < m; ++k)
        res[i][j] = (int)((res[i][j] + (long long)A[i][k] * B[k][j]) % MOD);
    return res;
}

vector<vector<int> > powMatMod(vector<vector<int> > A, long long k) {
    auto n = A.size();
    vector<vector<int> > res(n, vector<int>(n));
    for (int i = 0; i < n; ++i)res[i][i] = 1;
    while (k) {
        if (k % 2)res = mulMatMod(res, A);
        k /= 2;
        A = mulMatMod(A, A);
    }
    return res;
}

template<int MOD>
class ModInt {
public:
    ModInt() :value(0) {}
    ModInt(long long val) :value((int)(val<0 ? MOD + val%MOD : val%MOD)) { }

    ModInt& operator+=(ModInt that) {
        value = value + that.value;
        if (value >= MOD)value -= MOD;
        return *this;
    }
    ModInt& operator-=(ModInt that) {
        value -= that.value;
        if (value<0)value += MOD;
        return *this;
    }
    ModInt& operator*=(ModInt that) {
        value = (int)((long long)value * that.value % MOD);
        return *this;
    }
    ModInt &operator/=(ModInt that) {
        return *this *= that.inverse();
    }
    ModInt operator+(ModInt that) const {
        return ModInt(*this) += that;
    }
    ModInt operator-(ModInt that) const {
        return ModInt(*this) -= that;
    }
    ModInt operator*(ModInt that) const {
        return ModInt(*this) *= that;
    }
    ModInt operator/(ModInt that) const {
        return ModInt(*this) /= that;
    }
    ModInt pow(long long k) const {
        if (value == 0)return 0;
        ModInt n = *this, res = 1;
        while (k) {
            if (k & 1)res *= n;
            n *= n;
            k >>= 1;
        }
        return res;
    }
    ModInt inverse() const {
        long long a = value, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b;
            swap(a, b);
            u -= t * v;
            swap(u, v);
        }
        return ModInt(u);
    }
    int toi() const { return value; }

private:
    int value;
};
typedef ModInt<1000000007> mint;
ostream& operator<<(ostream& os, const mint& x) {
    os << x.toi();
    return os;
}

mint g(int b, int d) {
    vector<vi> A(3, vi(3));
    A[0][0] = d + 1;
    A[0][1] = d;
    A[1][1] = A[1][2] = A[2][2] = 1;
    A = powMatMod(A, b);
    RT mint(A[0][1]) + mint(A[0][2]);
}

ll powll(ll x, ll k) {
    ll re = 1;
    while (k > 0) {
        if (k & 1)re *= x;
        k >>= 1;
        x *= x;
    }
    RT re;
}

ll num(int b, int d) {
    if (pow(d + 1.0, b) - 1 > (int)2e9)RT(int)1e9 + 1;
    RT powll(d+1ll, b) - 1;
}

mint f(int b, int d, int n) {
    if (n <= 0)RT 0;

    int lb = 1, ub = b + 1;
    while (ub - lb > 1) {
        int mid = (lb + ub) / 2;
        if (n <= num(mid - 1, d))ub = mid;
        else lb = mid;
    }
    b = lb;

    ll m = num(b - 1, d);

    mint gg = g(b - 1, d);
    n -= (int)m;
    mint re = (gg + b)*(n / (m + 1)) + gg;
    n %= (m + 1);
    if (n > 0) {
        re += b;
        n--;
    }
    if (n > 0)re += f(b - 1, d, n);
    RT re;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);

    int N, B, D;
    while (cin >> N >> B >> D) {
        mint re = g(B, D);
        re -= f(B, D, N);
        cout << re << endl;
    }
}
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