#758875 (C++17) No.1933 ABC String

• 問題: No.1933 ABC String
• ユーザー: heno239
• 提出日時: 2022-05-06 23:07:23
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 438 ms / 2,000 ms
• コード長: 8,904 bytes
• コンパイル時間: 2,790 ms
• コンパイル使用メモリ: 176,404 KB
• 最終ジャッジ日時: 2025-01-29 04:07:11
• ジャッジサーバーID （参考情報）: judge5 / judge5

ファイルパターン	結果
sample	AC * 3
other	AC * 36

ソースコード

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-8;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 100005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;

const string drul = "DRUL";
//DRUL
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------
//x ball y box
modint calc(int x, int y) {
	if (x == 0 && y == 0)return 1;
	return comb(x + y-1, y-1);
}


int get_premitive_root() {
	int primitive_root = 0;
	if (!primitive_root) {
		primitive_root = [&]() {
			set<int> fac;
			int v = mod - 1;
			for (ll i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
			if (v > 1) fac.insert(v);
			for (int g = 1; g < mod; g++) {
				bool ok = true;
				for (auto i : fac) if (mod_pow(g, (mod - 1) / i) == 1) { ok = false; break; }
				if (ok) return g;
			}
			return -1;
		}();
	}
	return primitive_root;
}
const int proot = get_premitive_root();

typedef vector <modint> poly;
void dft(poly& f, bool inverse = false) {
	int n = f.size(); if (n == 1)return;

	static poly w{ 1 }, iw{ 1 };
	for (int m = w.size(); m < n / 2; m *= 2) {
		modint dw = mod_pow(proot, (mod - 1) / (4 * m)), dwinv = (modint)1 / dw;
		w.resize(m * 2); iw.resize(m * 2);
		for (int i = 0; i < m; i++)w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
	}
	if (!inverse) {
		for (int m = n; m >>= 1;) {
			for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
				for (int i = s; i < s + m; i++) {
					modint x = f[i], y = f[i + m] * w[k];
					f[i] = x + y, f[i + m] = x - y;
				}
			}
		}
	}
	else {
		for (int m = 1; m < n; m *= 2) {
			for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
				for (int i = s; i < s + m; i++) {
					modint x = f[i], y = f[i + m];
					f[i] = x + y, f[i + m] = (x - y) * iw[k];
				}
			}
		}
		modint n_inv = (modint)1 / (modint)n;
		for (modint& v : f)v *= n_inv;
	}
}
poly multiply(poly g, poly h) {
	int n = 1;
	int pi = 0, qi = 0;
	rep(i, g.size())if (g[i])pi = i;
	rep(i, h.size())if (h[i])qi = i;
	int sz = pi + qi + 2;
	while (n < sz)n *= 2;
	g.resize(n); h.resize(n);
	dft(g); dft(h);
	rep(i, n) {
		g[i] *= h[i];
	}
	dft(g, true);
	return g;
}

//i<=j
poly ordered_multiply(poly p, poly q, bool eq) {
	poly res;
	function<void(int, int)> dfs = [&](int l, int r) {
		if (l + 1 == r)return;
		int m = (l + r) / 2;
		dfs(l, m);
		dfs(m, r);
		poly pl, pr;
		Rep(j, l, m)if (j < p.size())pl.push_back(p[j]);
		Rep(j, m, r)pr.push_back(q[j]);
		poly pp = multiply(pl, pr);
		rep(j, pp.size())addv(res, l + m + j, pp[j]);
	};
	dfs(0, q.size());
	if (eq) {
		rep(j, q.size())if (j < p.size())addv(res, 2 * j, p[j] * q[j]);
	}
	return res;
}
void solve() {
	string s; cin >> s;
	sort(all(s));
	vector<int> cnt(3); rep(i, 3)cin >> cnt[i];
	modint al = fact[cnt[0] + cnt[1] + cnt[2]];
	rep(i, 3)al *= factinv[cnt[i]];
	vector<int> num(3);
	rep(i, s.size())num[s[i] - 'a']++;
	if (num[0] == 0 && num[1] == 0) {
		swap(num[0], num[2]);
		swap(cnt[0], cnt[2]);
	}
	modint ans = 0;
	rep(i, num[1]) {
		int A = num[0];
		int B = i + 1;
		int a = cnt[0] - num[0];
		int b = cnt[1] - i;
		int c = cnt[2];
		modint val = 1;
		val *= calc(b, A);
		val *= calc(a, B);
		val *= calc(c,A + B + a + b);
		ans += val;
	}
	//ここは畳み込みできる
	/*rep(i, num[2]) {
		int A = num[0];
		int B = num[1];
		int a = cnt[0] - num[0];
		int b = cnt[1] - num[1];
		int C = i + 1;
		int c = cnt[2] - i;
		rep(x, a + 1)rep(y, b + 1) {
			modint val = 1;
			val *= fact[x + y + C - 1] * factinv[x] * factinv[y] * factinv[C - 1];
			val *= comb(a - x + B - 1, a - x);
			val *= comb(b - y + A - 1, b - y);
			val *= comb(c + A + B + a + b - (x + y) - 1, c);
			ans += val;
		}
	}*/
	//cout << "? " << ans << "\n";
	int r = cnt[2] + 1;
	if (num[2] > 0) {
		int A = num[0];
		int B = num[1];
		int a = cnt[0] - num[0];
		int b = cnt[1] - num[1];
		poly px(a + 1);
		rep(x, a + 1)px[x] = factinv[x] * calc(a - x, B);
		poly py(b + 1);
		rep(y, b + 1)py[y] = factinv[y] * calc(b - y, A);
		poly pxy = multiply(px, py);
		rep(i, pxy.size()) {
			if (A + B + a + b - i - 1 >= 0) {
				pxy[i] *= factinv[A + B + a + b - i - 1];
			}
		}
		int len = pxy.size();
		poly pxyc(a + b + num[2]+1);
		rep1(i, pxyc.size() - 1) {
			if (A + B + a + b + r - 1 - i >= 0) {
				pxyc[i] = fact[i - 1] * fact[A + B + a + b + r - 1 - i];
			}
		}
		//coutarray(px);
		//coutarray(py);
		//coutarray(pxy);
		//coutarray(pxyc);
		reverse(all(pxy));
		poly pc = multiply(pxyc, pxy);
		//coutarray(pc);
		rep(i, pc.size()) {
			int C = i - (len - 1);
			if (1 <= C && C <= num[2]) {
				int c = r - C;
				modint val = pc[i];
				val *= factinv[C - 1];
				val *= factinv[c];
				ans += val;

			}
		}
	}
	//cout << "? " << ans << "\n";
	ans = al - ans;
	cout << ans << "\n";
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout << fixed << setprecision(10);
	init_f();
	//init();
	//while(true)
	//expr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}