結果

問題 No.194 フィボナッチ数列の理解(1)
コンテスト
ユーザー paruki
提出日時 2016-08-26 10:37:46
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 13 ms / 5,000 ms
コード長 4,839 bytes
コンパイル時間 2,219 ms
コンパイル使用メモリ 179,424 KB
実行使用メモリ 7,284 KB
最終ジャッジ日時 2024-11-08 04:01:42
合計ジャッジ時間 3,408 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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 * 3
other AC * 37
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 # 

#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 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()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<ll> vll;

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;
}

template<class Val>
class Matrix{
public:
    int n, m;
    Matrix(){ }
    Matrix(int n_, int m_):n(n_), m(m_), A(n, vector<Val>(m)){ }
#define ITER(a,b) for(int i=0;i<a;++i)for(int j=0;j<b;++j)
    Matrix operator +(Matrix &B){
        assert(n == B.n && m == B.m);
        Matrix C(n, m);
        ITER(n,m) C(i, j) = A[i][j] + B(i, j);
        return C;
    }
    Matrix operator -(Matrix &B){
        assert(n == B.n && m == B.m);
        Matrix C(n, m);
        ITER(n, m) C(i, j) = A[i][j] - B(i, j);
        return C;
    }
    Matrix* operator +=(Matrix &B){
        assert(n == B.n && m == B.m);
        ITER(n, m) A[i][j] += B(i, j);
        return this;
    }
    Matrix* operator -=(Matrix &B){
        assert(n == B.n && m == B.m);
        ITER(n, m) A[i][j] -= B(i, j);
        return this;
    }
    Matrix operator *(Matrix &B){
        assert(m == B.n);
        Matrix C(n, B.m);
        ITER(C.n, B.m)
            for(int k = 0; k < m; ++k)
                C(i, j) += A[i][k] * B(k, j);
        return C;
    }
    Matrix* operator *=(Matrix &B){
        return &(*this = *this*B);
    }
    Matrix* operator ^=(long long k){
        return &(*this = *this^k);
    }
#undef ITER
    Matrix operator ^(long long k){
        assert(n == m);
        Matrix C(n, n), D = *this;
        for(int i = 0; i < n; ++i)C(i, i) = 1;
        while(k > 0){
            if(k & 1) C *= D;
            D *= D;
            k >>= 1;
        }
        return C;
    }
    Val& operator()(int i, int j){
        return A[i][j];
    }
    vector<Val>& operator[](int i){
        return A[i];
    }
    vector<Val> mulVec(const vector<Val> & u){
        assert((int)u.size() == m);
        Matrix v(m, 1);
        for(int i = 0; i < m; ++i)v[i][0] = u[i];
        v = (*this)*v;
        vector<Val> w(n);
        for(int i = 0; i < n; ++i)w[i] = v[i][0];
        return w;
    }
private:
    vector<vector<Val>> A;
};
typedef Matrix<mint> mat;

int main(){
    const int R = (int)1e6;
    int N;
    ll K;
    vi A;
    vector<mint> F, v;
    mint x, y;
    mat B;

    cin >> N >> K;
    A.resize(N);
    rep(i, N)scanf("%d", &A[i]);

    if(K <= R){
        F.resize(K);
        rep(i, N)x += F[i] = A[i];
        F[N] = x;
        FOR(i, N+1, K){
            x = x * 2 - F[i - N - 1];
            F[i] = x;
        }
        y = accumulate(all(F), mint());
    } else{
        B = mat(N + 1, N + 1);
        rep(i, N + 1)B[0][i] = 1;
        FOR(i, 1, N + 1)B[1][i] = 1;
        FOR(i, 2, N + 1)B[i][i - 1] = 1;
        B ^= (K - N);
        v.resize(N + 1);
        rep(i, N) x += v[N - i] = A[i];
        v[0] = x;
        v = B.mulVec(v);
        x = v[1], y = v[0];
    }

    cout << x << ' ' << y << endl;
}
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