#1187109 (C++23) No.377 背景パターン

• 問題: No.377 背景パターン
• ユーザー: vjudge1
• 提出日時: 2026-09-17 00:28:30
• 言語: C++23 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 284 ms / 5,000 ms
• コード長: 8,166 bytes
• コンパイル時間: 5,217 ms
• コンパイル使用メモリ: 346,592 KB
• 実行使用メモリ: 6,400 KB
• 最終ジャッジ日時: 2026-09-17 00:28:39
• 合計ジャッジ時間: 6,219 ms
• ジャッジサーバーID （参考情報）: judge1_0 / judge2_0

ファイルパターン	結果
sample	AC * 5
other	AC * 14

ソースコード

#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pii pair<int, int>
#define bend(v) v.begin(),v.end()
#define vect vector 
#define prq priority_queue
#define umap unordered_map
#define eb emplace_back
#define pb push_back
#define pob pop_back
#define ef emplace_front
#define pf push_front
#define pof pop_front
#define el "\n"
#define deb cout<<"\nok\n";return 
#define nextl cout<<"\n"
#define lwb lower_bound 
#define upb upper_bound
#define rs resize
#define popcnt __builtin_popcountll
#define clz __builtin_clzll
#define ctz __builtin_ctzll
#define ull unsigned long long
#define ll long long 
#define dbl long double
#define int long long

#define FILE "ijustwannabepartofyourskibidi"
void IO(){
    if(fopen(FILE".in", "r")){
        freopen(FILE".in", "r", stdin);
        freopen(FILE".out", "w", stdout);
    }
    else if(fopen(FILE".inp", "r")){
        freopen(FILE".inp", "r", stdin);
        freopen(FILE".out", "w", stdout);
    }
}

const ll N = 3e5 + 10, MOD = 1e9+7, INF = 1000000000000000069;

mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());

ll rand(ll l, ll r){
    return uniform_int_distribution<ll>(l, r)(rng);
}
ll pm(ll a,const int b=MOD){return (a%=b) < 0 ? a + b : a;}
ll sq(ll x){return x*x;}
ll __lcm(ll a, ll b, const ll lim=LLONG_MAX){
    if(a == -1 || b == -1)return -1;
    ll g = __gcd(a,b);
    if(b/g > lim/a)return -1;
    return (a/g)*b;
}

int B(int a, int b=MOD-2){
    a %= MOD;
    b %= MOD-1;
    int res = 1;
    while(b){
        if(b&1) res = res * a % MOD;
        a = a * a % MOD;
        b >>= 1;
    }
    return res;
}

void sol(){
    int h, w, k;
    cin >> h >> w >> k;

    vect<pii> sus1, sus2;
    for(int i=1; i*i <= h; i++){
        if(h%i == 0){
            sus1.eb(i, h / i);
            if(i*i < h) sus1.eb(h/i, i);
        }
    }
    for(int i=1; i*i <= w; i++){
        if(w%i == 0){
            sus2.eb(i, w/i);
            if(i*i<w) sus2.eb(w/i, i);
        }
    }
    sort(bend(sus1), greater<pii>());
    sort(bend(sus2), greater<pii>());
    for(pii &i : sus1){
        for(pii &j : sus1){
            if(j.fi <= i.fi) continue;
            if(j.fi % i.fi == 0) i.se -= j.se;
        }
    }
    for(pii &i : sus2){
        for(pii &j : sus2){
            if(j.fi <= i.fi) continue;
            if(j.fi % i.fi == 0) i.se -= j.se;
        }
    }
    int ans = 0;
    for(pii &i : sus1){
        for(pii &j : sus2){
            // cout << i.fi << ' ' << j.fi << ' ' << j.se * i.se % MOD * B(k, w * h / __lcm(h/i.fi, w/j.fi)) % MOD << ' ' << __lcm(h/i.fi, w/j.fi) << ' ' << i.se << el;
            ans = (ans + j.se * i.se % MOD * B(k, w * h / __lcm(h/i.fi, w/j.fi)) % MOD) % MOD;
        }
    }

    cout << ans * B(w * h) % MOD << el;
}

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(NULL);cout.tie(NULL);
    IO();
    int t = 1;
    // cin >> t;
    while(t--) sol();
}
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