提出 #6177286

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ソースコード 拡げる

#include <bits/stdc++.h>
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) begin(x), end(x)
using namespace std;
template <class T, class U> inline void chmax(T & a, U const & b) { a = max<T>(a, b); }
template <class T, class U> inline void chmin(T & a, U const & b) { a = min<T>(a, b); }
template <typename X, typename T> auto make_vectors(X x, T a) { return vector<T>(x, a); }
template <typename X, typename Y, typename Z, typename... Zs> auto make_vectors(X x, Y y, Z z, Zs... zs) { auto cont = make_vectors(y, z, zs...); return vector<decltype(cont)>(x, cont); }

template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    inline mint<MOD> operator + (mint<MOD> other) const { int32_t c = this->value + other.value; return mint<MOD>(c >= MOD ? c - MOD : c); }
    inline mint<MOD> operator - (mint<MOD> other) const { int32_t c = this->value - other.value; return mint<MOD>(c <    0 ? c + MOD : c); }
    inline mint<MOD> operator * (mint<MOD> other) const { int32_t c = (int64_t)this->value * other.value % MOD; return mint<MOD>(c < 0 ? c + MOD : c); }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (int64_t)this->value * other.value % MOD; if (this->value < 0) this->value += MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0); }
    mint<MOD> pow(uint64_t k) const {
        mint<MOD> x = *this, y = 1;
        for (; k; k >>= 1) {
            if (k & 1) y *= x;
            x *= x;
        }
        return y;
    }
    mint<MOD> inv() const {
        assert (value != 0);
        int64_t a = value, b = MOD;
        int64_t x = 0, y = 1;
        for (int64_t u = 1, v = 0; a; ) {
            int64_t q = b / a;
            x -= q * u; std::swap(x, u);
            y -= q * v; std::swap(y, v);
            b -= q * a; std::swap(b, a);
        }
        assert (value * x + MOD * y == b);
        assert (b == 1);
        return x;
    }
    inline mint<MOD> operator /  (mint<MOD> other) const { return *this *  other.inv(); }
    inline mint<MOD> operator /= (mint<MOD> other)       { return *this *= other.inv(); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
};
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }


constexpr int MOD = 1e9 + 7;
mint<MOD> solve(int n, int k) {
    int sqrt_n = floor(sqrt(n));
    int len = 2 * sqrt_n + 1;
    vector<mint<MOD> > cnt(len);
    REP3 (j, 1, len) {
        if (j <= sqrt_n) {
            cnt[j] = 1;
        } else {
            int l = max(sqrt_n, n / (len - j + 1));
            int r = max(sqrt_n, n / (len - j));  // (l, r]
            cnt[j] = r - l;
        }
    }
    auto dp = make_vectors(k, len, mint<MOD>());
    dp[0] = cnt;
    REP (i, k - 1) {
        vector<mint<MOD> > acc(len + 1);
        partial_sum(ALL(dp[i]), acc.begin() + 1);
        REP3 (j, sqrt_n + 1, len) {
            int l = max(sqrt_n, n / (len - j + 1));
            int r = max(sqrt_n, n / (len - j));  // (l, r]
            dp[i + 1][j] = cnt[j] * acc[n / r + 1];
            dp[i + 1][n / r] = cnt[n / r] * acc[j + 1];
        }
    }
    return accumulate(ALL(dp[k - 1]), mint<MOD>());
}

int main() {
    int n, k; cin >> n >> k;
    cout << solve(n, k) << endl;
    return 0;
}

提出情報

ジャッジ結果