結果

問題 No.644 G L C C D M
コンテスト
ユーザー paruki
提出日時 2018-02-02 23:20:09
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 42 ms / 2,000 ms
コード長 4,609 bytes
コンパイル時間 1,989 ms
コンパイル使用メモリ 174,028 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-12-31 08:13:56
合計ジャッジ時間 3,025 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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
other AC * 27
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 # 

#define _USE_MATH_DEFINES
#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 MT make_tuple
#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()
#define RT return
#define vv(a,b,c,d) vector<vector<a> >(b,vector<a>(c,d))
#define vvv(a,b,c,d,e) vector<vector<vector<a> > >(b,vv(a,c,d,e))
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;
using vll = vector<ll>;

long long gcd(long long a, long long b) {
    return b ? gcd(b, a%b) : a;
}

long long lcm(long long a, long long b) {
    return a*b / gcd(a, b);
}

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;
}

int bitcnt(unsigned int x) {
    x = (x & 0x55555555) + (x >> 1 & 0x55555555);
    x = (x & 0x33333333) + (x >> 2 & 0x33333333);
    x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
    x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
    x = (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
    return (int)x;
}

void test(int n) {
    vll a(n), b(n), c(n);
    iota(all(a), 1ll);
    do {
        copy(all(a), b.begin());

        rep(i, n - 1) {
            rep(j, n - 1 - i) {
                if (j & 1) {
                    c[j] = lcm(b[j], b[j + 1]);
                } else {
                    c[j] = gcd(b[j], b[j + 1]);
                }
            }
            swap(b, c);
        }
        if (b[0] != 1) {
            //cout << b[0] << endl;
            //rep(i, n)cout << a[i] << ' ' << (i != n - 1 ? ' ' : '\n');
        }
        assert(gcd(a[0], a[1]) == b[0]);
    } while (next_permutation(all(a)));
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);
    // test(12);

    int N, M;
    cin >> N >> M;
    vi cnt(N + 1);
    vi ps(100000);
    mint ans = 0;
    mint A = 1;
    for (int i = 1; i <= N - 2; ++i)A *= i;

    for (int i = 1; i <= N; ++i) {
        if (i%M != 0)continue;

        int pp = 1;
        int num = 0;
        int x = i / M;
        for (int j = 2; (long long)j*j <= x; ++j) {
            int flag = 0;
            while (x%j == 0) {
                flag = 1;
                x /= j;
            }
            if (flag) {
                pp *= j;
                ps[num++] = j;
            }

        }
        if (x > 1)ps[num++] = x;

        if (num == 0) {
            ans += A*cnt[1] * 2;
            cnt[1]++;
            continue;
        }

        int paired = 0;
        rep(S, 1 << num) {
            int val = 1;
            rep(j, num)if (S >> j & 1)val *= ps[j];
            if (bitcnt(S) & 1) {
                paired -= cnt[val];
            } else {
                paired += cnt[val];
            }
            cnt[val]++;
        }
        ans += A*paired * 2;
    }
    cout << ans << endl;
}
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