結果

問題 No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率
コンテスト
ユーザー fuppy_kyopro
提出日時 2021-06-11 22:24:21
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 79 ms / 2,000 ms
コード長 6,831 bytes
コンパイル時間 2,345 ms
コンパイル使用メモリ 205,068 KB
最終ジャッジ日時 2025-01-22 06:12:14
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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ファイルパターン 結果
other AC * 36
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ソースコード

diff # 

/*
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
//*/

#include <bits/stdc++.h>

// #include <atcoder/all>

using namespace std;
// using namespace atcoder;

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                        \
    cerr << #v << ":";                                      \
    for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \
        cerr << " " << v[iiiiiiii];                         \
    cerr << endl;
#define DEBUG_MAT(v)                            \
    cerr << #v << endl;                         \
    for (int i = 0; i < v.size(); i++) {        \
        for (int j = 0; j < v[i].size(); j++) { \
            cerr << v[i][j] << " ";             \
        }                                       \
        cerr << endl;                           \
    }
typedef long long ll;
#define int ll

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
    return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template <class S, class T>
ostream &operator<<(ostream &os, pair<S, T> p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}
#define X first
#define Y second
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rrep1(i, n) for (int i = (int)(n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
void YES(bool t = true) {
    cout << (t ? "YES" : "NO") << endl;
}
void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; }
void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; }
void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; }
void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; }
void no(bool t = true) { cout << (t ? "no" : "yes") << endl; }
template <class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
int popcount(ll t) { return __builtin_popcountll(t); }
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {0, 1, 0, -1}, dy = {-1, 0, 1, 0};
// vi dx2 = { 1,1,0,-1,-1,-1,0,1 }, dy2 = { 0,1,1,1,0,-1,-1,-1 };
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(25);
    }
} setup_io;
// const ll MOD = 1000000007;
const ll MOD = 998244353;
// #define mp make_pair
//#define endl '\n'

typedef vector<ll> vec;
typedef vector<vec> mat;

mat mul(mat &A, mat &B) {
    mat C(A.size(), vec(B[0].size()));
    for (int i = 0; i < A.size(); i++) {
        for (int k = 0; k < B.size(); k++) {
            for (int j = 0; j < B[0].size(); j++) {
                C[i][j] = C[i][j] + A[i][k] * B[k][j];
                C[i][j] %= MOD;
            }
        }
    }
    return C;
}

vec mul(mat &A, vec &B) {
    vec C(A.size());
    for (int i = 0; i < A.size(); i++) {
        for (int j = 0; j < B.size(); j++) {
            C[i] += A[i][j] * B[j];
            C[i] %= MOD;
        }
    }
    return C;
}

mat pow(mat A, ll n) {
    mat B(A.size(), vec(A.size()));
    for (int i = 0; i < A.size(); i++) {
        B[i][i] = 1;
    }
    while (n > 0) {
        if (n & 1) B = mul(B, A);
        A = mul(A, A);
        n >>= 1;
    }
    return B;
}

const int MAXN = 555555;

vl fact(MAXN);
vl rfact(MAXN);

ll mod_pow(ll x, ll p, ll M = MOD) {
    if (p < 0) {
        x = mod_pow(x, M - 2, M);
        p = -p;
    }
    ll a = 1;
    while (p) {
        if (p % 2)
            a = a * x % M;
        x = x * x % M;
        p /= 2;
    }
    return a;
}

ll mod_inverse(ll a, ll M = MOD) {
    return mod_pow(a, M - 2, M);
}

void set_fact(ll n, ll M = MOD) {
    fact[0] = 1;
    for (ll i = 1; i <= n; i++) {
        fact[i] = i * fact[i - 1] % M;
    }
    rfact[n] = mod_inverse(fact[n], M);
    for (ll i = n - 1; i >= 0; i--) {
        rfact[i] = (i + 1) * rfact[i + 1] % M;
    }
}

//http://drken1215.hatenablog.com/entry/2018/06/08/210000
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ll nCr(ll n, ll r, ll M = MOD) {
    if (r > n) return 0;
    assert(fact[2] == 2);
    ll ret = fact[n];
    if (rfact[r] == 0) {
        rfact[r] = mod_inverse(fact[r], M);
    }
    ret = (ret * rfact[r]) % M;
    if (rfact[n - r] == 0) {
        rfact[n - r] = mod_inverse(fact[n - r], M);
    }
    ret = (ret * rfact[n - r]) % M;
    return ret;
}

ll nHr(ll n, ll r) {
    return nCr(n + r - 1, r);
}

signed main() {
    ll ma, na, S;
    cin >> ma >> na >> S;
    ll pa = ma * mod_inverse(na) % MOD;
    ll mb, nb, T;
    cin >> mb >> nb >> T;
    ll pb = mb * mod_inverse(nb) % MOD;

    ll k;
    cin >> k;

    int n = S + T + 1;
    vl start(n);
    start[T] = 1;

    mat A(n, vec(n));

    rep(i, n) {
        if (i == 0 || i == n - 1) {
            A[i][i] = 1;
            continue;
        }

        int score = i - T;

        ll prob = 1;
        for (int j = 0; score <= S; j++) {
            if (score == S) {
                int ni = score + T;
                (A[ni][i] += prob) %= MOD;
                break;
            }

            ll prob2 = prob * (1 - pa) % MOD;
            ll score2 = score;
            for (int k = 0; score2 >= -T; k++) {
                if (score2 == -T) {
                    int ni = score2 + T;
                    (A[ni][i] += prob2) %= MOD;
                    break;
                }
                ll prob3 = prob2 * (1 - pb);
                int ni = score2 + T;
                (A[ni][i] += prob3) %= MOD;

                prob2 = prob2 * pb % MOD;
                score2--;
            }

            prob = prob * pa % MOD;
            score++;
        }
    }

    mat An = pow(A, k);

    vec goal = mul(An, start);

    cout << (goal.back() + MOD) % MOD << endl;
    cout << (goal[0] + MOD) % MOD << endl;
}
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