math/powk_all.cpp

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• Last update: 2021-07-05 13:06:44+09:00

Depends on

• math/get_min_factor.cpp
• modint(固定MOD) (util/modint.cpp)

Code

#include "../util/modint.cpp"

#include "./get_min_factor.cpp"
vector<mint> powk_all(int n, ll k) {
    auto min_factor = get_min_factor(n);
    vector<mint> res(n+1);
    res[1] = 1;
    for (int i = 2; i <= n; ++i) {
        if(min_factor[i] == i) res[i] = mint(i).pow(k);
        else res[i] = res[i/min_factor[i]]*res[min_factor[i]];
    }
    return res;
}

#line 1 "util/modint.cpp"
template <uint M>
struct modint {
    uint val;
public:
    static modint raw(int v) { modint x; x.val = v; return x; }
    modint() : val(0) {}
    template <class T>
    modint(T v) { ll x = (ll)(v%(ll)(M)); if (x < 0) x += M; val = uint(x); }
    modint(bool v) { val = ((unsigned int)(v) % M); }
    modint& operator++() { val++; if (val == M) val = 0; return *this; }
    modint& operator--() { if (val == 0) val = M; val--; return *this; }
    modint operator++(int) { modint result = *this; ++*this; return result; }
    modint operator--(int) { modint result = *this; --*this; return result; }
    modint& operator+=(const modint& b) { val += b.val; if (val >= M) val -= M; return *this; }
    modint& operator-=(const modint& b) { val -= b.val; if (val >= M) val += M; return *this; }
    modint& operator*=(const modint& b) { ull z = val; z *= b.val; val = (uint)(z % M); return *this; }
    modint& operator/=(const modint& b) { return *this = *this * b.inv(); }
    modint operator+() const { return *this; }
    modint operator-() const { return modint() - *this; }
    modint pow(long long n) const { modint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; }
    modint inv() const { return pow(M-2); }
    friend modint operator+(const modint& a, const modint& b) { return modint(a) += b; }
    friend modint operator-(const modint& a, const modint& b) { return modint(a) -= b; }
    friend modint operator*(const modint& a, const modint& b) { return modint(a) *= b; }
    friend modint operator/(const modint& a, const modint& b) { return modint(a) /= b; }
    friend bool operator==(const modint& a, const modint& b) { return a.val == b.val; }
    friend bool operator!=(const modint& a, const modint& b) { return a.val != b.val; }
};
using mint = modint<MOD>;

/**
 * @brief modint(固定MOD)
 * @docs _md/modint.md
 */
#line 2 "math/powk_all.cpp"

#line 1 "math/get_min_factor.cpp"
vector<int> get_min_factor(int n) {
    if(n <= 1) return vector<int>{0, 1};
    vector<bool> prime(n+1, true);
    vector<int> min_factor(n+1, 0);
    min_factor[0] = 0, min_factor[1] = 1;
    prime[0] = false; prime[1] = false;
    for(ll i = 2; i <= n; i++){
        if(prime[i]) {
            min_factor[i] = i;
            for(ll j = i << 1; j <= n; j += i) {
                prime[j] = false;
                if(min_factor[j] == 0) min_factor[j] = i;
            }
        }
    }
    return min_factor;
}
#line 4 "math/powk_all.cpp"
vector<mint> powk_all(int n, ll k) {
    auto min_factor = get_min_factor(n);
    vector<mint> res(n+1);
    res[1] = 1;
    for (int i = 2; i <= n; ++i) {
        if(min_factor[i] == i) res[i] = mint(i).pow(k);
        else res[i] = res[i/min_factor[i]]*res[min_factor[i]];
    }
    return res;
}

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