結果

問題 No.886 Direct
ユーザー minato
提出日時 2021-01-11 16:48:28
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 245 ms / 4,000 ms
コード長 11,243 bytes
コンパイル時間 2,571 ms
コンパイル使用メモリ 207,348 KB
最終ジャッジ日時 2025-01-17 16:11:55
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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ファイルパターン 結果
sample AC * 4
other AC * 32
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ソースコード

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プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template<class T> using vec = vector<T>;
template<class T> using vvec = vector<vector<T>>;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rrep(i, n) for (int i = int(n) - 1; i >= 0; i--)
#define all(x) (x).begin(), (x).end()
constexpr char ln = '\n';
template<class Container> inline int SZ(Container& v) { return int(v.size()); }
template<class T> inline void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template<class T1, class T2> inline bool chmax(T1& a, T2 b) { if (a < b) {a = b; return true ;} return false ;}
template<class T1, class T2> inline bool chmin(T1& a, T2 b) { if (a > b) {a = b; return true ;} return false ;}
inline int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
inline int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
inline int popcount(ull x) { return __builtin_popcountll(x); }
inline int kthbit(ull x, int k) { return (x>>k) & 1; }
inline constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x-1) * 10; }
struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//O(NloglogN) で約数・倍数の畳み込み
// (1) divisor_zeta : 倍数方向に高速ゼータ変換(累積和)
// (2) divisor_moebius : 約数方向に高速メビウス変換(包除原理)　(1)の逆
// (3) multiple_zeta : 約数方向に高速ゼータ変換(累積和)
// (4) multiple_moebius : 倍数方向に高速メビウス変換(包除原理) (3)の逆
// メビウス関数は c[1] = 1 として(2) で求まる
struct PrimeZeta {
    int n_;
    vector<bool> sieve;
    PrimeZeta() {}
    PrimeZeta(int n) : n_(n), sieve(n+1, true) {
        sieve[0] = sieve[1] = false;
        for (int i = 2; i*i <= n; i++) {
            if (sieve[i]) {
                for (int j = i*i; j <= n; j += i) {
                    sieve[j] = false;
                }
            }
        }
    }
    // (1) divisor_zeta : 倍数方向に高速ゼータ変換(累積和)
    template<class T>
    void divisor_zeta(T &c) {
        int n = int(c.size());
        assert(n-1 <= n_);
        for (int i = 2; i < n; i++) {
            if (sieve[i]) {
                for (int j = 1; j*i < n; j++) {
                    c[j*i] += c[j];
                }
            }
        }
    }
    // (2) divisor_moebius : 約数方向に高速メビウス変換(包除原理)　(1)の逆
    template<class T>
    void divisor_moebius(T &c) {
        int n = int(c.size());
        assert(n-1 <= n_);
        for (int i = 2; i < n; i++) {
            if (sieve[i]) {
                for (int j = (n-1)/i; j >= 1; j--) {
                    c[j*i] -= c[j];
                }
            }
        }
    }
    // (3) multiple_zeta : 約数方向に高速ゼータ変換(累積和)
    template<class T>
    void multiple_zeta(T &c) {
        int n = int(c.size());
        assert(n-1 <= n_);
        for (int i = 2; i < n; i++) {
            if (sieve[i]) {
                for (int j = (n-1)/i; j >= 1; j--) {
                    c[j] += c[j*i];
                }
            }
        }
    }
    // (4) multiple_moebius : 倍数方向に高速メビウス変換(包除原理) (3)の逆
    template<class T>
    void multiple_moebius(T &c) {
        int n = int(c.size());
        assert(n-1 <= n_);
        for (int i = 2; i < n; i++) {
            if (sieve[i]) {
                for (int j = 1; j*i < n; j++) {
                    c[j] -= c[j*i];
                }
            }
        }
    }    
};
//////////////////////////////////////////////////////////////////////////////////////////////////////
template<int m> 
struct ModInt {
  public:
    static constexpr int mod() { return m; }
    static ModInt raw(int v) {
        ModInt x;
        x._v = v;
        return x;
    }
    ModInt() : _v(0) {}
    ModInt(long long v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    unsigned int val() const { return _v; }
    ModInt& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    ModInt& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    ModInt operator++(int) {
        ModInt result = *this;
        ++*this;
        return result;
    }
    ModInt operator--(int) {
        ModInt result = *this;
        --*this;
        return result;
    }
    ModInt& operator+=(const ModInt& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    ModInt& operator-=(const ModInt& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    ModInt& operator*=(const ModInt& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    ModInt& operator^=(long long n) {
        ModInt x = *this;
        *this = 1;
        if (n < 0) x = x.inv(), n = -n;
        while (n) {
            if (n & 1) *this *= x;
            x *= x;
            n >>= 1;
        }
        return *this;
    }
    ModInt& operator/=(const ModInt& rhs) { return *this = *this * rhs.inv(); }
    ModInt operator+() const { return *this; }
    ModInt operator-() const { return ModInt() - *this; }
    ModInt pow(long long n) const {
        ModInt r = *this;
        r ^= n;
        return r;
    }
    ModInt inv() const {
        int a = _v, b = umod(), y = 1, z = 0, t;
        for (; ; ) {
            t = a / b; a -= t * b;
            if (a == 0) {
                assert(b == 1 || b == -1);
                return ModInt(b * z);
            }
            y -= t * z;
            t = b / a; b -= t * a;
            if (b == 0) {
                assert(a == 1 || a == -1);
                return ModInt(a * y);
            }
            z -= t * y;
        }
    }
    friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) += rhs; }
    friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) -= rhs; }
    friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) *= rhs; }
    friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) /= rhs; }
    friend ModInt operator^(const ModInt& lhs, long long rhs) { return ModInt(lhs) ^= rhs; }
    friend bool operator==(const ModInt& lhs, const ModInt& rhs) { return lhs._v == rhs._v; }
    friend bool operator!=(const ModInt& lhs, const ModInt& rhs) { return lhs._v != rhs._v; }
    friend ModInt operator+(long long lhs, const ModInt& rhs) { return (ModInt(lhs) += rhs); }
    friend ModInt operator-(long long lhs, const ModInt& rhs) { return (ModInt(lhs) -= rhs); }
    friend ModInt operator*(long long lhs, const ModInt& rhs) { return (ModInt(lhs) *= rhs); }
    friend ostream& operator<<(ostream& os, const ModInt& M) { return os << M._v; }
    friend istream& operator>>(istream& is, ModInt& M) {
        long long x; is >> x;
        M = ModInt(x);
        return is;
    }
  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
};
constexpr int MOD = 1000000007;
//constexpr int MOD = 998244353;
using mint = ModInt<MOD>;
struct ModCombination {
  private:
    int max_n;
    vector<mint> fac_,facinv_;
  public:
    ModCombination() {}
    ModCombination(int n) : max_n(n), fac_(n+1), facinv_(n+1) {
        assert(1 <= n);
        fac_[0] = 1;
        for (int i = 1; i <= n; i++) fac_[i] = fac_[i-1]*i;
        facinv_[n] = fac_[n].inv();
        for (int i = n; i >= 1; i--) facinv_[i-1] = facinv_[i]*i;
    }
    mint fac(int k) const { 
        assert(0 <= k and k <= max_n);
        return fac_[k]; 
    }
    mint facinv(int k) const {
        assert(0 <= k and k <= max_n); 
        return facinv_[k]; 
    }
    mint invs(int k) const { 
        assert(1 <= k and k <= max_n);
        return facinv_[k]*fac_[k-1]; 
    }
    mint P(int n, int k) const {
        if (k < 0 or k > n) return mint(0);
        assert(n <= max_n);
        return fac_[n]*facinv_[n-k];
    }
    mint C(int n, int k) const {
        if (k < 0 or k > n) return mint(0);
        assert(n <= max_n);
        return fac_[n]*facinv_[n-k]*facinv_[k];
    }
    mint H(int n, int k) const {
        if (n == 0 and k == 0) return mint(1);
        return C(n+k-1,k);
    }
    mint catalan(int n) const {
        if (n == 0) return mint(1);
        return C(n*2,n) - C(n*2,n-1);
    }
};
//O(NloglogN)
struct PrimeFactorTable {
    int n;
    vector<int> table;
    PrimeFactorTable() {}
    PrimeFactorTable(int n_) : n(n_), table(n_+1) {
        iota(table.begin(),table.end(),0);
        for (int i = 2; i*i <= n; i++) {
            if (table[i] == i) {
                for (int j = i*i; j <= n; j += i) {
                    if (table[j] == j) table[j] = i;
                }
            }
        }
    }
    int operator[](int x) const { return table[x]; }
    vector<pair<int, int>> prime_factor(int x) {
        assert(1 <= x and x <= n);
        vector<pair<int, int>> ret;
        while (x != 1) {
            if (ret.empty() or ret.back().first != table[x]) {
                ret.emplace_back(table[x],1);
            } else {
                ret.back().second++;
            }
            x /= table[x];
        }
        return ret;
    }
};
void yukico886() {
    int H,W; cin >> H >> W;
    const int MAX = 3e6;
    PrimeZeta zet(MAX);
    vec<mint> cnt(MAX+1);
    for (int i = 1; i < H; i++) {
        cnt[i] = H-i;
    }
    zet.multiple_zeta(cnt);
    vec<mint> e(MAX+1);
    e[1] = 1;
    zet.divisor_moebius(e);
    rep(i,MAX+1) {
        cnt[i] *= e[i];
    }
    zet.divisor_zeta(cnt);
    mint ans = 0;
    for (int i = 1; i < W; i++) {
        ans += cnt[i]*(W-i);
    }
    ans *= 2;
    ans += mint(H)*(W-1) + mint(W)*(H-1);
    cout << ans << ln;
}
void CF325E() {
    const int MAX = 1e7;
    PrimeFactorTable PFT(MAX);
    PrimeZeta PZ(MAX);
    int N; cin >> N;
    vec<int> A(N),divs(MAX+1);
    rep(i,N) {
        cin >> A[i];
        divs[A[i]]++;
    }
 
    vec<mint> beki(N+1,1);
    rep(i,N) beki[i+1] = beki[i]*2;
    PZ.multiple_zeta(divs);
 
    vec<mint> S(MAX+1);
    rep(i,MAX+1) S[i] = beki[divs[i]] - 1;
    PZ.multiple_moebius(S);
    S[1] = 0;
    
    PZ.multiple_zeta(S);
 
    mint ans = 0;
    rep(i,N) {
        auto primes = PFT.prime_factor(A[i]);
        int K = primes.size();
        mint tmp = 0;
        rep(mask,1<<K) {
            int val = 1;
            rep(k,K) {
                if (kthbit(mask,k)) val *= primes[k].first;
            }
            if (popcount(mask)&1) tmp -= S[val];
            else tmp += S[val];
        }
        ans += tmp;
    }
 
    cout << ans << ln;
}
int main() {
    yukico886();
    //CF325E();
}
/*
  verified on 2021/01/11
  https://yukicoder.me/problems/no/886
*/
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