結果

問題 No.1847 Good Sequence
コンテスト
ユーザー anmichi
提出日時 2022-02-20 00:42:39
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 842 ms / 3,000 ms
コード長 4,873 bytes
コンパイル時間 2,715 ms
コンパイル使用メモリ 213,336 KB
最終ジャッジ日時 2025-01-28 01:04:55
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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ファイルパターン 結果
other AC * 41
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, n) for (int i = 0; i < n; i++)
#define all(v) v.begin(), v.end()
template <class T, class U>
inline bool chmax(T& a, U b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template <class T, class U>
inline bool chmin(T& a, U b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
constexpr int INF = 1000000000;
constexpr ll llINF = 3000000000000000000;
constexpr int mod = 1000000007;
const ll half = (mod + 1) / 2;
constexpr double eps = 1e-10;

vector<int> prime_list(int n) {
    vector<int> v(n + 1), res;
    for (int i = n; i >= 2; i--) {
        for (int j = i; j <= n; j += i) v[j] = i;
    }
    for (int i = 2; i <= n; i++) {
        if (v[i] == i) res.push_back(i);
    }
    return res;
}
vector<int> next_divisor(int n) {
    vector<int> v(n + 1);
    for (int i = n; i >= 2; i--) {
        for (int j = i; j <= n; j += i) v[j] = i;
    }
    return v;
}
ll modpow(ll a, ll b, ll m = mod) {
    ll res = 1;
    while (b) {
        if (b & 1) {
            res *= a;
            res %= m;
        }
        a *= a;
        a %= m;
        b >>= 1;
    }
    return res;
}
vector<ll> inv, fact, factinv;
void init_fact(int n) {
    inv.resize(n + 1);
    fact.resize(n + 1);
    factinv.resize(n + 1);
    inv[0] = 0;
    inv[1] = 1;
    fact[0] = 1;
    factinv[0] = 1;
    for (ll i = 1; i <= n; i++) {
        if (i >= 2) inv[i] = mod - ((mod / i) * inv[mod % i] % mod);
        fact[i] = (fact[i - 1] * i) % mod;
        factinv[i] = factinv[i - 1] * inv[i] % mod;
    }
}
ll modinv(ll a, ll m = mod) {
    // gcd(a,m) must be 1
    ll b = m, u = 1, v = 0;
    while (b) {
        ll t = a / b;
        a -= t * b;
        swap(a, b);
        u -= t * v;
        swap(u, v);
    }
    u %= m;
    if (u < 0) u += m;
    return u;
}
ll comb(int a, int b) {
    if (a < b) return 0;
    if (a < 0) return 0;
    return fact[a] * factinv[a - b] % mod * factinv[b] % mod;
}
template <class T>
struct Matrix {
    int n;
    vector<vector<T>> m;
    Matrix(int x) : Matrix(vector<vector<T>>(x, vector<T>(x, 0))) {}
    Matrix(const vector<vector<T>>& a) {
        n = a.size();
        m = a;
    }
    vector<T>& operator[](int i) { return m[i]; }
    const vector<T>& operator[](int i) const { return m[i]; }
    static Matrix identity(int x) {
        Matrix res(x);
        for (int i = 0; i < x; i++) res[i][i] = 1;
        return res;
    }
    Matrix operator+(const Matrix& a) const {
        Matrix x = (*this);
        return x += a;
    }
    Matrix operator*(const Matrix& a) const {
        Matrix x = (*this);
        return x *= a;
    }
    Matrix& operator+=(const Matrix& a) {
        Matrix res(n);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                res[i][j] = (m[i][j] + a[i][j]) % mod;
            }
        }
        m = res.m;
        return *this;
    }
    Matrix& operator*=(const Matrix& a) {
        Matrix res(n);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                for (int k = 0; k < n; k++) {
                    res[i][j] += m[i][k] * a[k][j];
                    res[i][j] %= mod;
                }
            }
        }
        m = res.m;
        return *this;
    }
    Matrix pow(ll b) const {
        Matrix x = *this, res = identity(n);
        res[0][0] = 1;
        while (b) {
            if (b & 1) {
                res *= x;
            }
            x *= x;
            b >>= 1;
        }
        return res;
    }
};
void solve() {
    ll l;
    int n, m;
    cin >> l >> n >> m;
    vector<bool> flag(n + 1);
    rep(i, m) {
        int k;
        cin >> k;
        flag[k] = true;
    }
    vector<vector<ll>> v((n + 1) * (n + 1), vector<ll>((n + 1) * (n + 1)));
    vector<vector<ll>> initial((n + 1) * (n + 1), vector<ll>((n + 1) * (n + 1)));
    for (int i = 1; i <= n; i++) {
        for (int j = 0; j <= i; j++) {
            for (int k = 1; k <= n; k++) {
                if (flag[i] && i == j && i != k) continue;
                int f = (i == k ? (j == i || j == 0 ? 0 : j + 1) : 1);
                v[i * (n + 1) + j][k * (n + 1) + f] = 1;
            }
        }
    }
    for (int i = 1; i <= n; i++) {
        initial[i * (n + 1) + 1][i * (n + 1) + 1] = 1;
    }
    Matrix mat = Matrix(initial) * Matrix(v).pow(l - 1);
    ll ans = modpow(n, l);
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            for (int k = 0; k <= n; k++) {
                if (flag[j] && k == j) continue;
                ans += mod - mat[i * (n + 1) + 1][j * (n + 1) + k];
            }
        }
    }
    cout << ans % mod << endl;
}
int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    /*int t;
    cin >> t;
    while (t--)*/
    solve();
}
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