結果

問題 No.1561 connect x connect
ユーザー ecottea
提出日時 2025-09-01 21:52:51
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
RE  
実行時間 -
コード長 51,713 bytes
コンパイル時間 11,136 ms
コンパイル使用メモリ 339,896 KB
実行使用メモリ 7,720 KB
最終ジャッジ日時 2025-09-01 21:53:04
合計ジャッジ時間 12,036 ms
ジャッジサーバーID
(参考情報)
judge2 / judge5
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
sample AC * 2 RE * 1
other AC * 14 RE * 21
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 #

#ifndef HIDDEN_IN_VS // 折りたたみ用

// 警告の抑制
#define _CRT_SECURE_NO_WARNINGS

// ライブラリの読み込み
#include <bits/stdc++.h>
using namespace std;

// 型名の短縮
using ll = long long; using ull = unsigned long long; // -2^63 ~ 2^63 = 9e18(int は -2^31 ~ 2^31 = 2e9)
using pii = pair<int, int>;	using pll = pair<ll, ll>;	using pil = pair<int, ll>;	using pli = pair<ll, int>;
using vi = vector<int>;		using vvi = vector<vi>;		using vvvi = vector<vvi>;	using vvvvi = vector<vvvi>;
using vl = vector<ll>;		using vvl = vector<vl>;		using vvvl = vector<vvl>;	using vvvvl = vector<vvvl>;
using vb = vector<bool>;	using vvb = vector<vb>;		using vvvb = vector<vvb>;
using vc = vector<char>;	using vvc = vector<vc>;		using vvvc = vector<vvc>;
using vd = vector<double>;	using vvd = vector<vd>;		using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;

// 定数の定義
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左)
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;

// 入出力高速化
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;

// 汎用マクロの定義
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x)))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x)))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順
#define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能)
#define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能)
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d ビット全探索(昇順)
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set の全要素(昇順)
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順)
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
#define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定

// 汎用関数の定義
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す)
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す)
template <class T> inline int getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // 非負mod

// 演算子オーバーロード
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }

#endif // 折りたたみ用


#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;

#ifdef _MSC_VER
#include "localACL.hpp"
#endif

//using mint = modint998244353;
using mint = static_modint<(int)1e9+7>;
//using mint = modint; // mint::set_mod(m);

using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif


#ifdef _MSC_VER // 手元環境(Visual Studio)
#include "local.hpp"
#else // 提出用(gcc)
int mute_dump = 0;
int frac_print = 0;
#if __has_include(<atcoder/all>)
namespace atcoder {
	inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
	inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
#endif
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(v)
#define dump_math(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE の代わりに MLE を出す
#endif


// 愚直
int H;
mint naive(const string& s) {
	int w = sz(s);
	if (w == 0) return 1;

	vi a(H * w);
	rep(j, w) {
		int val = s[j] - '0';
		rep(i, H) {
			int u = j * H + i;
			a[u] = getb(val, i);
		}
	}

	dsu d(H * w + 1);
	rep(i, H) rep(j, w - 1) {
		int u = j * H + i;
		int v = (j + 1) * H + i;
		if (a[u] && a[v]) d.merge(u, v);
	}
	rep(i, H - 1) rep(j, w) {
		int u = j * H + i;
		int v = j * H + (i + 1);
		if (a[u] && a[v]) d.merge(u, v);
	}
	rep(i, H) rep(j, w) {
		int u = j * H + i;
		if (!a[u]) d.merge(u, H * w);
	}

	return (int)(sz(d.groups()) <= 2);
}


//【行列】
/*
* Matrix<T>(int n, int m) : O(n m)
*	n×m 零行列で初期化する.
*
* Matrix<T>(int n) : O(n^2)
*	n×n 単位行列で初期化する.
*
* Matrix<T>(vvT a) : O(n m)
*	二次元配列 a[0..n)[0..m) の要素で初期化する.
*
* bool empty() : O(1)
*	行列が空かを返す.
*
* A + B : O(n m)
*	n×m 行列 A, B の和を返す.+= も使用可.
*
* A - B : O(n m)
*	n×m 行列 A, B の差を返す.-= も使用可.
*
* c * A / A * c : O(n m)
*	n×m 行列 A とスカラー c のスカラー積を返す.*= も使用可.
*
* A * x : O(n m)
*	n×m 行列 A と n 次元列ベクトル x の積を返す.
*
* x * A : O(n m)(やや遅い)
*	m 次元行ベクトル x と n×m 行列 A の積を返す.
*
* A * B : O(n m l)
*	n×m 行列 A と m×l 行列 B の積を返す.
*
* Mat pow(ll d) : O(n^3 log d)
*	自身を d 乗した行列を返す.
*/
template <class T>
struct Matrix {
	int n, m; // 行列のサイズ(n 行 m 列)
	vector<vector<T>> v; // 行列の成分

	// n×m 零行列で初期化する.
	Matrix(int n, int m) : n(n), m(m), v(n, vector<T>(m)) {}

	// n×n 単位行列で初期化する.
	Matrix(int n) : n(n), m(n), v(n, vector<T>(n)) { rep(i, n) v[i][i] = T(1); }

	// 二次元配列 a[0..n)[0..m) の要素で初期化する.
	Matrix(const vector<vector<T>>& a) : n(sz(a)), m(sz(a[0])), v(a) {}
	Matrix() : n(0), m(0) {}

	// 代入
	Matrix(const Matrix&) = default;
	Matrix& operator=(const Matrix&) = default;

	// アクセス
	inline vector<T> const& operator[](int i) const { return v[i]; }
	inline vector<T>& operator[](int i) {
		// verify : https://judge.yosupo.jp/problem/matrix_product

		// inline を付けて [] でアクセスするとなぜか v[] への直接アクセスより速くなった.
		return v[i];
	}

	// 入力
	friend istream& operator>>(istream& is, Matrix& a) {
		rep(i, a.n) rep(j, a.m) is >> a.v[i][j];
		return is;
	}

	// 行の追加
	void push_back(const vector<T>& a) {
		Assert(sz(a) == m);
		v.push_back(a);
		n++;
	}

	// 行の削除
	void pop_back() {
		Assert(n > 0);
		v.pop_back();
		n--;
	}

	// サイズ変更
	void resize(int n_) {
		v.resize(n_);
		n = n_;
	}

	void resize(int n_, int m_) {
		n = n_;
		m = m_;

		v.resize(n);
		rep(i, n) v[i].resize(m);
	}

	// 空か
	bool empty() const { return min(n, m) == 0; }

	// 比較
	bool operator==(const Matrix& b) const { return n == b.n && m == b.m && v == b.v; }
	bool operator!=(const Matrix& b) const { return !(*this == b); }

	// 加算,減算,スカラー倍
	Matrix& operator+=(const Matrix& b) {
		rep(i, n) rep(j, m) v[i][j] += b[i][j];
		return *this;
	}
	Matrix& operator-=(const Matrix& b) {
		rep(i, n) rep(j, m) v[i][j] -= b[i][j];
		return *this;
	}
	Matrix& operator*=(const T& c) {
		rep(i, n) rep(j, m) v[i][j] *= c;
		return *this;
	}
	Matrix operator+(const Matrix& b) const { return Matrix(*this) += b; }
	Matrix operator-(const Matrix& b) const { return Matrix(*this) -= b; }
	Matrix operator*(const T& c) const { return Matrix(*this) *= c; }
	friend Matrix operator*(const T& c, const Matrix<T>& a) { return a * c; }
	Matrix operator-() const { return Matrix(*this) *= T(-1); }

	// 行列ベクトル積 : O(m n)
	vector<T> operator*(const vector<T>& x) const {
		vector<T> y(n);
		rep(i, n) rep(j, m)	y[i] += v[i][j] * x[j];
		return y;
	}

	// ベクトル行列積 : O(m n)
	friend vector<T> operator*(const vector<T>& x, const Matrix& a) {
		vector<T> y(a.m);
		rep(i, a.n) rep(j, a.m) y[j] += x[i] * a[i][j];
		return y;
	}

	// 積:O(n^3)
	Matrix operator*(const Matrix& b) const {
		// verify : https://judge.yosupo.jp/problem/matrix_product

		Matrix res(n, b.m);
		rep(i, res.n) rep(k, m) rep(j, res.m) res[i][j] += v[i][k] * b[k][j];
		return res;
	}
	Matrix& operator*=(const Matrix& b) { *this = *this * b; return *this; }

	// 累乗:O(n^3 log d)
	Matrix pow(ll d) const {
		// verify : https://judge.yosupo.jp/problem/pow_of_matrix

		Matrix res(n), pow2 = *this;
		while (d > 0) {
			if (d & 1) res *= pow2;
			pow2 *= pow2;
			d >>= 1;
		}
		return res;
	}

#ifdef _MSC_VER
	friend ostream& operator<<(ostream& os, const Matrix& a) {
		rep(i, a.n) {
			os << "[";
			rep(j, a.m) os << a[i][j] << " ]"[j == a.m - 1];
			if (i < a.n - 1) os << "\n";
		}
		return os;
	}
#endif
};


//【行簡約形(行交換なし)】O(n m min(n, m))
/*
* 行基本変形(行交換なし)で n×m 行列 A を行簡約形に変形し,ピボット位置のリストを返す.
*/
template <class T>
vector<pii> row_reduced_form(Matrix<T>& A) {
	int n = A.n, m = A.m;
	
	vector<pii> piv;
	piv.reserve(min(n, m));

	// 未確定の列を記録しておくリスト
	list<int> rjs;
	rep(j, m) rjs.push_back(j);

	rep(i, n) {
		// 第 i 行の係数を左から走査し非 0 を見つける.
		auto it = rjs.begin();
		for (; it != rjs.end(); it++) if (A[i][*it] != 0) break;

		// 第 i 行の全てが 0 なら無視する.
		if (it == rjs.end()) continue;

		// A[i][j] をピボットに選択する.
		int j = *it;
		rjs.erase(it);
		piv.emplace_back(i, j);

		// A[i][j] が 1 になるよう行全体を A[i][j] で割る.
		T Aij_inv = T(1) / A[i][j];
		repi(j2, j, m - 1) A[i][j2] *= Aij_inv;

		// 第 i 行以外の第 j 列の成分が全て 0 になるよう第 i 行を定数倍して減じる.
		rep(i2, n) if (A[i2][j] != 0 && i2 != i) {
			T mul = A[i2][j];
			repi(j2, j, m - 1) A[i2][j2] -= A[i][j2] * mul;
		}
	}

	return piv;
}


//【逆行列】O(n^3)
/*
* n 次正方行列 mat の逆行列を返す(存在しなければ空)
*/
template <class T>
Matrix<T> inverse_matrix(const Matrix<T>& mat) {
	// verify : https://judge.yosupo.jp/problem/inverse_matrix

	int n = mat.n;

	// 元の行列 mat と単位行列を繋げた拡大行列 v を作る.
	vector<vector<T>> v(n, vector<T>(2 * n));
	rep(i, n) rep(j, n) {
		v[i][j] = mat[i][j];
		if (i == j) v[i][n + j] = 1;
	}
	int m = 2 * n;

	// 注目位置を (i, j)(i 行目かつ j 列目)とする.
	int i = 0, j = 0;

	// 拡大行列に対して行基本変形を行い,左側を単位行列にすることを目指す.
	while (i < n && j < m) {
		// 同じ列の下方の行から非 0 成分を見つける.
		int i2 = i;
		while (i2 < n && v[i2][j] == T(0)) i2++;

		// 見つからなかったら全て 0 の列があったので mat は非正則
		if (i2 == n) return Matrix<T>();

		// 見つかったら i 行目とその行を入れ替える.
		if (i != i2) swap(v[i], v[i2]);

		// v[i][j] が 1 になるよう行全体を v[i][j] で割る.
		T vij_inv = T(1) / v[i][j];
		repi(j2, j, m - 1) v[i][j2] *= vij_inv;

		// v[i][j] と同じ列の成分が全て 0 になるよう i 行目を定数倍して減じる.
		rep(i2, n) {
			// i 行目だけは引かない.
			if (i2 == i) continue;

			T mul = v[i2][j];
			repi(j2, j, m - 1) v[i2][j2] -= v[i][j2] * mul;
		}

		// 注目位置を右下に移す.
		i++; j++;
	}

	// 拡大行列の右半分が mat の逆行列なのでコピーする.
	Matrix<T> mat_inv(n, n);
	rep(i, n) rep(j, n) mat_inv[i][j] = v[i][n + j];

	return mat_inv;
}


// 遷移行列の係数を計算し,埋め込み用のコードを出力する.
void embed_coefs(int COL, int len_max, int L_max, int loop_cnt,
	const vector<string>& ssT_ini = { "" }, const vector<string>& ssB_ini = { "" }) {
	mt19937_64 mt((int)time(NULL));
	uniform_int_distribution<int> rnd_len(1, len_max);
	uniform_int_distribution<int> rnd_col(0, COL - 1);
	uniform_int_distribution<int> rnd(7, 20);

	vector<string> ssT(ssT_ini), ssB(ssB_ini);

	rep(loop, loop_cnt) {
		if ((loop + 1) % 100 == 0) {
			dump("loop:", loop, "L:", sz(ssT));
			
			// 途中再開用
			sort(all(ssT));
			sort(all(ssB));
			string eb = "vvi ssT = {";
			repe(s, ssT) {
				eb += "{";
				repe(c, s) {
					eb += to_string((int)(c - '0'));
					eb += ",";
				}
				if (eb.back() == ',') eb.pop_back();
				eb += "},";
			}
			if (eb.back() == ',') eb.pop_back();
			eb += "};\n";

			eb += "vvi ssB = {";
			repe(s, ssB) {
				eb += "{";
				repe(c, s) {
					eb += to_string((int)(c - '0'));
					eb += ",";
				}
				if (eb.back() == ',') eb.pop_back();
				eb += "},";
			}
			if (eb.back() == ',') eb.pop_back();
			eb += "};\n";

			cerr << eb;
		}

		// 候補とする文字列をランダムに L_max 個追加する.
		rep(hoge, L_max) {
			int len = rnd_len(mt);
			string s;
			rep(fuga, len) s += '0' + rnd_col(mt);
			ssT.push_back(s);
		}
		rep(hoge, L_max) {
			int len = rnd_len(mt);
			string s;
			rep(fuga, len) s += '0' + rnd_col(mt);
			ssB.push_back(s);
		}		

		uniq(ssT);
		uniq(ssB);

		// (i,j) 成分が naive(ss[i] + ss[j]) であるような行列 mat を得る.
		int LT = sz(ssT), LB = sz(ssB);
		Matrix<mint> mat(LT, LB);
		rep(i, LT) rep(j, LB) mat[i][j] = naive(ssT[i] + ssB[j]);

		// mat に対して行基本変形を行いピボット位置のリスト piv を得る.
		auto piv = row_reduced_form(mat);
		
		// ランク上昇に寄与した文字列だけ残す.
		vector<string> nssT, nssB;
		for (auto [i, j] : piv) {
			nssT.push_back(ssT[i]);
			nssB.push_back(ssB[j]);
		}
		ssT = move(nssT);
		ssB = move(nssB);
	}

	// (i,j) 成分が naive(ss[i] + ss[j]) であるような行列 mat を得る.
	int LT = sz(ssT), LB = sz(ssB);
	Matrix<mint> mat(LT, LB);
	rep(i, LT) rep(j, LB) mat[i][j] = naive(ssT[i] + ssB[j]);

	// mat に対して行基本変形を行いピボット位置のリスト piv を得る.
	auto piv = row_reduced_form(mat);
	int DIM = sz(piv);
	
	// 選択した行 is と列 js を並べ直して 0 始まりにする.
	vi is(DIM), js(DIM);
	rep(r, DIM) tie(is[r], js[r]) = piv[r];
	repi(i, 1, DIM - 1) if (ssT[is[i]] == "") swap(is[i], is[0]);
	repi(j, 1, DIM - 1) if (ssB[js[j]] == "") swap(js[j], js[0]);
	assert(is[0] == 0);
	assert(js[0] == 0);

	// 基底の変換行列 P を得る.
	Matrix<mint> matP(DIM, DIM);
	rep(i, DIM) rep(j, DIM) matP[i][j] = naive(ssT[is[i]] + ssB[js[j]]);

	// P の逆行列 P_inv を得る.
	auto matP_inv = inverse_matrix(matP);

	// 各文字に対応する表現行列を得る.
	vector<Matrix<mint>> matAs(COL, Matrix<mint>(DIM, DIM));
	rep(k, COL) {
		char c = '0' + k;
		rep(i, DIM) rep(j, DIM) matAs[k][i][j] = naive(ssT[is[i]] + c + ssB[js[j]]);
		matAs[k] = matAs[k] * matP_inv;
	}

	// 右端を閉じるためのベクトルを得る.
	vm vecP(DIM);
	rep(i, DIM) vecP[i] = matP[i][0];

	// スパース埋め込み用の文字列を出力する.
	vector<tuple<int, int, mint>> elems; vi offsets{ 0 };
	rep(c, COL) {
		rep(i, DIM) rep(j, DIM) {
			if (matAs[c][i][j] != 0) elems.emplace_back(i, j, matAs[c][i][j]);
		}
		offsets.push_back(sz(elems));
	}
	auto to_signed_string = [](mint x) {
		int v = x.val();
		int mod = mint::mod();
		if (2 * v > mod) v -= mod;
		return to_string(v);
	};
	string eb = "constexpr int DIM = ";
	eb += to_string(DIM);
	eb += ";\n";
	eb += "constexpr int COL = ";
	eb += to_string(COL);
	eb += ";\n";
	eb += "tuple<int, int, VTYPE> matAs[] = {";
	for (auto [i, j, v] : elems) {
		eb += "{";
		eb += to_string(i);
		eb += ",";
		eb += to_string(j);
		eb += ",";
		eb += to_signed_string(v);
		eb += "},";
	}
	eb.pop_back();
	eb += "};\n";
	eb += "int offset[COL + 1] = {";
	repi(c, 0, COL) eb += to_string(offsets[c]) + ",";
	eb.pop_back();
	eb += "};\n";
	eb += "VTYPE vecP[DIM] = {";
	rep(i, DIM) eb += to_signed_string(vecP[i]) + ",";
	eb.pop_back();
	eb += "};\n";
	cout << eb;

	exit(0);
}


template <class VTYPE>
vector<VTYPE> solve1(const string& s) {
	// --------------- embed_coefs() からの出力を貼る ----------------
	constexpr int DIM = 3;
	constexpr int COL = 2;
	tuple<int, int, VTYPE> matAs[] = { {0,0,1},{1,2,1},{2,2,1},{0,1,1},{1,1,1} };
	int offset[COL + 1] = { 0,3,5 };
	VTYPE vecP[DIM] = { 1,1,1 };
	// --------------------------------------------------------------

	int n = sz(s);
		
	array<VTYPE, DIM> dp;
	dp.fill(0);
	dp[0] = 1;

	vector<VTYPE> res(n + 1);
	res[0] = vecP[0];

	auto apply = [&](const array<VTYPE, DIM>& x, int col) {
		array<VTYPE, DIM> z;
		z.fill(0);

		repi(pt, offset[0], offset[COL] - 1) { // 重ね合わせ
			auto [i, j, v] = matAs[pt];
			z[j] += x[i] * v;
		}

		return z;
	};

	rep(p, n) {
		dp = apply(dp, s[p] - '0');
		dump(dp);
	
		rep(i, DIM) res[p + 1] += dp[i] * vecP[i];
	}

	return res;
}


template <class VTYPE>
vector<VTYPE> solve2(const string& s) {
	// --------------- embed_coefs() からの出力を貼る ----------------
	constexpr int DIM = 5;
	constexpr int COL = 4;
	tuple<int, int, VTYPE> matAs[] = { {0,0,1},{1,2,1},{2,2,1},{3,2,1},{4,2,1},{0,4,1},{3,4,1},{4,4,1},{0,1,1},{1,1,1},{3,1,1},{0,3,1},{1,3,1},{3,3,1},{4,3,1} };
	int offset[COL + 1] = { 0,5,8,11,15 };
	VTYPE vecP[DIM] = { 1,1,1,1,1 };
	// --------------------------------------------------------------

	int n = sz(s);

	array<VTYPE, DIM> dp;
	dp.fill(0);
	dp[0] = 1;

	vector<VTYPE> res(n + 1);
	res[0] = vecP[0];

	auto apply = [&](const array<VTYPE, DIM>& x, int col) {
		array<VTYPE, DIM> z;
		z.fill(0);

		repi(pt, offset[0], offset[COL] - 1) { // 重ね合わせ
			auto [i, j, v] = matAs[pt];
			z[j] += x[i] * v;
		}

		return z;
	};

	rep(p, n) {
		dp = apply(dp, s[p] - '0');
		
		rep(i, DIM) res[p + 1] += dp[i] * vecP[i];
	}

	return res;
}


template <class VTYPE>
vector<VTYPE> solve3(const string& s) {
	// --------------- embed_coefs() からの出力を貼る ----------------
	constexpr int DIM = 10;
	constexpr int COL = 8;
	tuple<int, int, VTYPE> matAs[] = { {0,0,1},{1,6,1},{2,6,1},{3,6,1},{4,6,1},{5,6,1},{6,6,1},{7,6,1},{9,6,1},{0,3,1},{2,3,1},{3,3,1},{4,3,1},{9,3,1},{0,1,1},{1,1,1},{2,1,1},{4,1,1},{7,1,1},{0,4,1},{1,4,1},{2,4,1},{3,4,1},{4,4,1},{7,4,1},{9,4,1},{0,5,1},{2,5,1},{5,5,1},{7,5,1},{9,5,1},{0,8,1},{2,9,1},{3,8,1},{4,8,1},{5,8,1},{7,8,1},{8,8,1},{9,9,1},{0,7,1},{1,7,1},{2,7,1},{4,7,1},{5,7,1},{7,7,1},{9,7,1},{0,2,1},{1,2,1},{2,2,1},{3,2,1},{4,2,1},{5,2,1},{7,2,1},{8,2,1},{9,2,1} };
	int offset[COL + 1] = { 0,9,14,19,26,31,39,46,55 };
	VTYPE vecP[DIM] = { 1,1,1,1,1,1,1,1,0,1 };
	// --------------------------------------------------------------

	int n = sz(s);

	array<VTYPE, DIM> dp;
	dp.fill(0);
	dp[0] = 1;

	vector<VTYPE> res(n + 1);
	res[0] = vecP[0];

	auto apply = [&](const array<VTYPE, DIM>& x, int col) {
		array<VTYPE, DIM> z;
		z.fill(0);

		repi(pt, offset[0], offset[COL] - 1) { // 重ね合わせ
			auto [i, j, v] = matAs[pt];
			z[j] += x[i] * v;
		}

		return z;
	};

	rep(p, n) {
		dp = apply(dp, s[p] - '0');

		rep(i, DIM) res[p + 1] += dp[i] * vecP[i];
	}

	return res;
}


template <class VTYPE>
vector<VTYPE> solve4(const string& s) {
	// --------------- embed_coefs() からの出力を貼る ----------------
	constexpr int DIM = 22;
	constexpr int COL = 16;
	tuple<int, int, VTYPE> matAs[] = { {0,0,1},{2,14,1},{3,14,1},{4,14,1},{5,14,1},{6,14,1},{7,14,1},{9,14,1},{10,14,1},{11,14,1},{13,14,1},{14,14,1},{16,14,1},{18,14,1},{19,14,1},{20,14,1},{21,14,1},{0,3,1},{3,3,1},{4,3,1},{7,3,1},{10,3,1},{11,3,1},{16,3,1},{18,3,1},{20,3,1},{0,13,1},{2,13,1},{4,13,1},{6,13,1},{7,13,1},{11,13,1},{13,13,1},{18,13,1},{21,13,1},{0,18,1},{2,18,1},{3,18,1},{4,18,1},{6,18,1},{7,18,1},{10,18,1},{11,18,1},{13,18,1},{16,18,1},{18,18,1},{20,18,1},{21,18,1},{0,5,1},{2,5,1},{5,5,1},{6,5,1},{7,5,1},{9,5,1},{10,5,1},{11,5,1},{16,5,1},{0,12,1},{1,12,1},{2,12,1},{3,12,1},{4,12,1},{5,12,1},{6,12,1},{7,10,1},{9,12,1},{10,10,1},{11,10,1},{12,12,1},{16,10,1},{18,12,1},{20,12,1},{0,6,1},{2,6,1},{4,6,1},{5,6,1},{6,6,1},{7,6,1},{9,6,1},{10,6,1},{11,6,1},{13,6,1},{16,6,1},{18,6,1},{21,6,1},{0,7,1},{1,7,1},{2,7,1},{3,7,1},{4,7,1},{5,7,1},{6,7,1},{7,7,1},{9,7,1},{10,7,1},{11,7,1},{12,7,1},{13,7,1},{16,7,1},{18,7,1},{20,7,1},{21,7,1},{0,19,1},{2,19,1},{4,19,1},{9,19,1},{11,19,1},{16,19,1},{19,19,1},{20,19,1},{21,19,1},{0,15,1},{1,15,1},{2,15,1},{3,15,1},{4,20,1},{7,15,1},{9,15,1},{10,15,1},{11,20,1},{15,15,1},{16,20,1},{17,15,1},{18,15,1},{19,15,1},{20,20,1},{21,15,1},{0,8,1},{2,21,1},{4,21,1},{6,8,1},{7,8,1},{8,8,1},{9,8,1},{11,21,1},{13,8,1},{16,8,1},{17,8,1},{18,8,1},{19,8,1},{20,8,1},{21,21,1},{0,17,1},{1,17,1},{2,4,1},{3,17,1},{4,4,1},{6,17,1},{7,17,1},{8,17,1},{9,17,1},{10,17,1},{11,4,1},{13,17,1},{15,17,1},{16,4,1},{17,17,1},{18,17,1},{19,17,1},{20,4,1},{21,4,1},{0,9,1},{2,9,1},{4,9,1},{5,9,1},{6,9,1},{7,9,1},{9,9,1},{10,9,1},{11,9,1},{16,9,1},{19,9,1},{20,9,1},{21,9,1},{0,1,1},{1,1,1},{2,1,1},{3,1,1},{4,16,1},{5,1,1},{6,1,1},{7,16,1},{9,1,1},{10,16,1},{11,16,1},{12,1,1},{15,1,1},{16,16,1},{17,1,1},{18,1,1},{19,1,1},{20,16,1},{21,1,1},{0,2,1},{2,2,1},{4,2,1},{5,2,1},{6,2,1},{7,2,1},{8,2,1},{9,2,1},{10,2,1},{11,2,1},{13,2,1},{16,2,1},{17,2,1},{18,2,1},{19,2,1},{20,2,1},{21,2,1},{0,11,1},{1,11,1},{2,11,1},{3,11,1},{4,11,1},{5,11,1},{6,11,1},{7,11,1},{8,11,1},{9,11,1},{10,11,1},{11,11,1},{12,11,1},{13,11,1},{15,11,1},{16,11,1},{17,11,1},{18,11,1},{19,11,1},{20,11,1},{21,11,1} };
	int offset[COL + 1] = { 0,17,26,35,48,57,72,85,102,111,127,142,161,174,193,210,231 };
	VTYPE vecP[DIM] = { 1,0,1,1,1,1,1,1,0,1,1,1,0,1,1,0,1,0,1,1,1,1 };
	// --------------------------------------------------------------

	int n = sz(s);

	array<VTYPE, DIM> dp;
	dp.fill(0);
	dp[0] = 1;

	vector<VTYPE> res(n + 1);
	res[0] = vecP[0];

	auto apply = [&](const array<VTYPE, DIM>& x, int col) {
		array<VTYPE, DIM> z;
		z.fill(0);

		repi(pt, offset[0], offset[COL] - 1) { // 重ね合わせ
			auto [i, j, v] = matAs[pt];
			z[j] += x[i] * v;
		}

		return z;
	};

	rep(p, n) {
		dp = apply(dp, s[p] - '0');

		rep(i, DIM) res[p + 1] += dp[i] * vecP[i];
	}

	return res;
}


template <class VTYPE>
vector<VTYPE> solve5(const string& s) {
	// --------------- embed_coefs() からの出力を貼る ----------------
	constexpr int DIM = 52;
	constexpr int COL = 32;
	tuple<int, int, VTYPE> matAs[] = { {0,0,1},{2,12,1},{3,12,1},{4,12,1},{5,12,1},{9,12,1},{11,12,1},{12,12,1},{13,12,1},{19,12,1},{20,12,1},{21,12,1},{22,12,1},{23,12,1},{24,12,1},{25,12,1},{27,12,1},{31,12,1},{32,12,1},{34,12,1},{35,12,1},{36,12,1},{39,12,1},{40,12,1},{42,12,1},{43,12,1},{44,12,1},{45,12,1},{46,12,1},{47,12,1},{48,12,1},{50,12,1},{51,12,1},{0,11,1},{2,11,1},{11,11,1},{19,11,1},{22,11,1},{23,11,1},{32,11,1},{34,11,1},{35,11,1},{36,11,1},{39,11,1},{40,11,1},{43,11,1},{46,11,1},{48,11,1},{50,11,1},{51,11,1},{0,20,1},{4,20,1},{19,20,1},{20,20,1},{21,20,1},{22,20,1},{23,20,1},{25,20,1},{27,20,1},{32,20,1},{34,20,1},{36,20,1},{40,20,1},{44,20,1},{45,20,1},{46,20,1},{47,20,1},{0,22,1},{2,22,1},{4,22,1},{11,22,1},{19,22,1},{20,22,1},{21,22,1},{22,22,1},{23,22,1},{25,22,1},{27,22,1},{32,22,1},{34,22,1},{35,22,1},{36,22,1},{39,22,1},{40,22,1},{43,22,1},{44,22,1},{45,22,1},{46,22,1},{47,22,1},{48,22,1},{50,22,1},{51,22,1},{0,13,1},{2,13,1},{4,13,1},{5,13,1},{9,13,1},{13,13,1},{19,13,1},{21,13,1},{24,13,1},{25,13,1},{27,13,1},{32,13,1},{34,13,1},{35,13,1},{36,13,1},{43,13,1},{48,13,1},{0,30,1},{2,35,1},{4,30,1},{5,30,1},{9,30,1},{10,30,1},{11,30,1},{13,30,1},{16,30,1},{19,35,1},{21,30,1},{22,30,1},{23,30,1},{24,30,1},{25,30,1},{26,30,1},{27,30,1},{30,30,1},{32,35,1},{34,35,1},{35,35,1},{36,35,1},{39,30,1},{40,30,1},{43,35,1},{46,30,1},{48,35,1},{49,30,1},{50,30,1},{51,30,1},{0,25,1},{2,25,1},{4,25,1},{5,25,1},{9,25,1},{13,25,1},{19,25,1},{20,25,1},{21,25,1},{22,25,1},{23,25,1},{24,25,1},{25,25,1},{27,25,1},{32,25,1},{34,25,1},{35,25,1},{36,25,1},{40,25,1},{43,25,1},{44,25,1},{45,25,1},{46,25,1},{47,25,1},{48,25,1},{0,34,1},{2,34,1},{4,34,1},{5,34,1},{9,34,1},{10,34,1},{11,34,1},{13,34,1},{16,34,1},{19,34,1},{20,34,1},{21,34,1},{22,34,1},{23,34,1},{24,34,1},{25,34,1},{26,34,1},{27,34,1},{30,34,1},{32,34,1},{34,34,1},{35,34,1},{36,34,1},{39,34,1},{40,34,1},{43,34,1},{44,34,1},{45,34,1},{46,34,1},{47,34,1},{48,34,1},{49,34,1},{50,34,1},{51,34,1},{0,3,1},{2,3,1},{3,3,1},{4,3,1},{5,3,1},{9,3,1},{19,3,1},{21,3,1},{23,3,1},{31,3,1},{36,3,1},{39,3,1},{40,3,1},{43,3,1},{44,3,1},{47,3,1},{50,3,1},{0,29,1},{2,39,1},{3,29,1},{4,29,1},{5,29,1},{8,29,1},{9,29,1},{11,29,1},{14,29,1},{16,29,1},{18,29,1},{19,39,1},{21,29,1},{22,29,1},{23,39,1},{26,29,1},{29,29,1},{31,29,1},{32,29,1},{34,29,1},{35,29,1},{36,39,1},{39,39,1},{40,39,1},{43,39,1},{44,29,1},{46,29,1},{47,29,1},{48,29,1},{50,39,1},{51,29,1},{0,33,1},{2,33,1},{3,33,1},{4,44,1},{5,33,1},{8,33,1},{9,33,1},{14,33,1},{19,44,1},{20,33,1},{21,44,1},{22,33,1},{23,44,1},{25,33,1},{27,33,1},{28,33,1},{31,33,1},{32,33,1},{33,33,1},{34,33,1},{36,44,1},{39,33,1},{40,44,1},{43,33,1},{44,44,1},{45,33,1},{46,33,1},{47,44,1},{50,33,1},{0,14,1},{2,40,1},{3,14,1},{4,40,1},{5,14,1},{8,14,1},{9,14,1},{11,14,1},{14,14,1},{16,14,1},{18,14,1},{19,40,1},{20,14,1},{21,40,1},{22,14,1},{23,40,1},{25,14,1},{26,14,1},{27,14,1},{28,14,1},{29,14,1},{31,14,1},{32,14,1},{33,14,1},{34,14,1},{35,14,1},{36,40,1},{39,40,1},{40,40,1},{43,40,1},{44,40,1},{45,14,1},{46,14,1},{47,40,1},{48,14,1},{50,40,1},{51,14,1},{0,5,1},{2,5,1},{3,5,1},{4,5,1},{5,5,1},{9,5,1},{13,5,1},{19,5,1},{21,5,1},{23,5,1},{24,5,1},{25,5,1},{27,5,1},{31,5,1},{32,5,1},{34,5,1},{35,5,1},{36,5,1},{39,5,1},{40,5,1},{43,5,1},{44,5,1},{47,5,1},{48,5,1},{50,5,1},{0,26,1},{2,43,1},{3,26,1},{4,26,1},{5,26,1},{8,26,1},{9,26,1},{10,26,1},{11,26,1},{13,26,1},{14,26,1},{16,26,1},{18,26,1},{19,43,1},{21,26,1},{22,26,1},{23,43,1},{24,26,1},{25,26,1},{26,26,1},{27,26,1},{29,26,1},{30,26,1},{31,26,1},{32,43,1},{34,43,1},{35,43,1},{36,43,1},{39,43,1},{40,43,1},{43,43,1},{44,26,1},{46,26,1},{47,26,1},{48,43,1},{49,26,1},{50,43,1},{51,26,1},{0,4,1},{2,4,1},{3,4,1},{4,4,1},{5,4,1},{8,4,1},{9,4,1},{13,4,1},{14,4,1},{19,4,1},{20,4,1},{21,4,1},{22,4,1},{23,4,1},{24,4,1},{25,4,1},{27,4,1},{28,4,1},{31,4,1},{32,4,1},{33,4,1},{34,4,1},{35,4,1},{36,4,1},{39,4,1},{40,4,1},{43,4,1},{44,4,1},{45,4,1},{46,4,1},{47,4,1},{48,4,1},{50,4,1},{0,36,1},{2,36,1},{3,36,1},{4,36,1},{5,36,1},{8,36,1},{9,36,1},{10,36,1},{11,36,1},{13,36,1},{14,36,1},{16,36,1},{18,36,1},{19,36,1},{20,36,1},{21,36,1},{22,36,1},{23,36,1},{24,36,1},{25,36,1},{26,36,1},{27,36,1},{28,36,1},{29,36,1},{30,36,1},{31,36,1},{32,36,1},{33,36,1},{34,36,1},{35,36,1},{36,36,1},{39,36,1},{40,36,1},{43,36,1},{44,36,1},{45,36,1},{46,36,1},{47,36,1},{48,36,1},{49,36,1},{50,36,1},{51,36,1},{0,42,1},{2,42,1},{9,42,1},{19,42,1},{21,42,1},{23,42,1},{24,42,1},{27,42,1},{31,42,1},{32,42,1},{42,42,1},{45,42,1},{46,42,1},{47,42,1},{48,42,1},{50,42,1},{51,42,1},{0,38,1},{1,38,1},{2,51,1},{8,38,1},{9,38,1},{10,38,1},{11,38,1},{15,38,1},{16,38,1},{18,38,1},{19,51,1},{21,38,1},{22,38,1},{23,51,1},{24,38,1},{27,38,1},{31,38,1},{32,51,1},{34,38,1},{35,38,1},{36,38,1},{37,38,1},{38,38,1},{39,38,1},{40,38,1},{42,38,1},{43,38,1},{45,38,1},{46,51,1},{47,38,1},{48,51,1},{50,51,1},{51,51,1},{0,41,1},{1,41,1},{2,41,1},{4,41,1},{7,41,1},{8,41,1},{9,41,1},{15,41,1},{19,45,1},{20,41,1},{21,45,1},{22,41,1},{23,45,1},{24,41,1},{25,41,1},{27,45,1},{28,41,1},{31,41,1},{32,45,1},{34,41,1},{36,41,1},{40,41,1},{41,41,1},{42,41,1},{44,41,1},{45,45,1},{46,45,1},{47,45,1},{48,41,1},{50,41,1},{51,41,1},{0,15,1},{1,15,1},{2,46,1},{4,15,1},{7,15,1},{8,15,1},{9,15,1},{10,15,1},{11,15,1},{15,15,1},{16,15,1},{18,15,1},{19,46,1},{20,15,1},{21,46,1},{22,15,1},{23,46,1},{24,15,1},{25,15,1},{27,46,1},{28,15,1},{31,15,1},{32,46,1},{34,15,1},{35,15,1},{36,15,1},{37,15,1},{38,15,1},{39,15,1},{40,15,1},{41,15,1},{42,15,1},{43,15,1},{44,15,1},{45,46,1},{46,46,1},{47,46,1},{48,46,1},{50,46,1},{51,46,1},{0,6,1},{1,6,1},{2,24,1},{4,6,1},{5,6,1},{6,6,1},{7,6,1},{9,24,1},{13,6,1},{19,24,1},{21,24,1},{23,6,1},{24,24,1},{25,6,1},{27,24,1},{31,6,1},{32,24,1},{34,6,1},{35,6,1},{36,6,1},{37,6,1},{42,6,1},{43,6,1},{45,6,1},{46,6,1},{47,6,1},{48,24,1},{49,6,1},{50,6,1},{51,6,1},{0,17,1},{1,37,1},{2,48,1},{4,17,1},{5,17,1},{6,17,1},{7,17,1},{8,17,1},{9,10,1},{10,10,1},{11,17,1},{13,17,1},{15,17,1},{16,10,1},{17,17,1},{18,17,1},{19,48,1},{21,10,1},{22,17,1},{23,49,1},{24,10,1},{25,17,1},{26,17,1},{27,10,1},{30,17,1},{31,17,1},{32,48,1},{34,37,1},{35,37,1},{36,37,1},{37,37,1},{38,17,1},{39,17,1},{40,17,1},{42,17,1},{43,37,1},{45,17,1},{46,49,1},{47,17,1},{48,48,1},{49,49,1},{50,49,1},{51,49,1},{0,7,1},{1,7,1},{2,27,1},{4,7,1},{5,7,1},{6,7,1},{7,7,1},{8,7,1},{9,27,1},{13,7,1},{15,7,1},{19,27,1},{20,7,1},{21,27,1},{22,7,1},{23,27,1},{24,27,1},{25,7,1},{27,27,1},{28,7,1},{31,7,1},{32,27,1},{34,7,1},{35,7,1},{36,7,1},{37,7,1},{40,7,1},{41,7,1},{42,7,1},{43,7,1},{44,7,1},{45,27,1},{46,27,1},{47,27,1},{48,27,1},{49,7,1},{50,7,1},{51,7,1},{0,1,1},{1,1,1},{2,32,1},{4,1,1},{5,1,1},{6,1,1},{7,1,1},{8,1,1},{9,32,1},{10,32,1},{11,1,1},{13,1,1},{15,1,1},{16,32,1},{17,1,1},{18,1,1},{19,32,1},{20,1,1},{21,32,1},{22,1,1},{23,32,1},{24,32,1},{25,1,1},{26,1,1},{27,32,1},{28,1,1},{30,1,1},{31,1,1},{32,32,1},{34,1,1},{35,1,1},{36,1,1},{37,1,1},{38,1,1},{39,1,1},{40,1,1},{41,1,1},{42,1,1},{43,1,1},{44,1,1},{45,32,1},{46,32,1},{47,32,1},{48,32,1},{49,32,1},{50,32,1},{51,32,1},{0,31,1},{2,31,1},{3,31,1},{4,31,1},{5,31,1},{9,31,1},{19,31,1},{21,31,1},{23,31,1},{24,31,1},{27,31,1},{31,31,1},{32,31,1},{36,31,1},{39,31,1},{40,31,1},{42,31,1},{43,31,1},{44,31,1},{45,31,1},{46,31,1},{47,31,1},{48,31,1},{50,31,1},{51,31,1},{0,18,1},{1,18,1},{2,50,1},{3,18,1},{4,18,1},{5,18,1},{8,18,1},{9,18,1},{10,18,1},{11,18,1},{14,18,1},{15,18,1},{16,18,1},{18,18,1},{19,50,1},{21,18,1},{22,18,1},{23,50,1},{24,18,1},{26,18,1},{27,18,1},{29,18,1},{31,18,1},{32,50,1},{34,18,1},{35,18,1},{36,50,1},{37,18,1},{38,18,1},{39,50,1},{40,50,1},{42,18,1},{43,50,1},{44,18,1},{45,18,1},{46,50,1},{47,18,1},{48,50,1},{50,50,1},{51,50,1},{0,28,1},{1,28,1},{2,28,1},{3,28,1},{4,47,1},{5,28,1},{7,28,1},{8,28,1},{9,28,1},{14,28,1},{15,28,1},{19,47,1},{20,28,1},{21,47,1},{22,28,1},{23,47,1},{24,28,1},{25,28,1},{27,47,1},{28,28,1},{31,28,1},{32,47,1},{33,28,1},{34,28,1},{36,47,1},{39,28,1},{40,47,1},{41,28,1},{42,28,1},{43,28,1},{44,47,1},{45,47,1},{46,47,1},{47,47,1},{48,28,1},{50,28,1},{51,28,1},{0,8,1},{1,8,1},{2,23,1},{3,8,1},{4,23,1},{5,8,1},{7,8,1},{8,8,1},{9,8,1},{10,8,1},{11,8,1},{14,8,1},{15,8,1},{16,8,1},{18,8,1},{19,23,1},{20,8,1},{21,23,1},{22,8,1},{23,23,1},{24,8,1},{25,8,1},{26,8,1},{27,23,1},{28,8,1},{29,8,1},{31,8,1},{32,23,1},{33,8,1},{34,8,1},{35,8,1},{36,23,1},{37,8,1},{38,8,1},{39,23,1},{40,23,1},{41,8,1},{42,8,1},{43,23,1},{44,23,1},{45,23,1},{46,23,1},{47,23,1},{48,23,1},{50,23,1},{51,23,1},{0,9,1},{1,9,1},{2,9,1},{3,9,1},{4,9,1},{5,9,1},{6,9,1},{7,9,1},{9,9,1},{13,9,1},{19,9,1},{21,9,1},{23,9,1},{24,9,1},{25,9,1},{27,9,1},{31,9,1},{32,9,1},{34,9,1},{35,9,1},{36,9,1},{37,9,1},{39,9,1},{40,9,1},{42,9,1},{43,9,1},{44,9,1},{45,9,1},{46,9,1},{47,9,1},{48,9,1},{49,9,1},{50,9,1},{51,9,1},{0,16,1},{1,2,1},{2,2,1},{3,16,1},{4,16,1},{5,16,1},{6,16,1},{7,16,1},{8,16,1},{9,16,1},{10,16,1},{11,16,1},{13,16,1},{14,16,1},{15,16,1},{16,16,1},{17,16,1},{18,16,1},{19,2,1},{21,16,1},{22,16,1},{23,2,1},{24,16,1},{25,16,1},{26,16,1},{27,16,1},{29,16,1},{30,16,1},{31,16,1},{32,2,1},{34,2,1},{35,2,1},{36,2,1},{37,2,1},{38,16,1},{39,2,1},{40,2,1},{42,16,1},{43,2,1},{44,16,1},{45,16,1},{46,2,1},{47,16,1},{48,2,1},{49,2,1},{50,2,1},{51,2,1},{0,21,1},{1,21,1},{2,21,1},{3,21,1},{4,21,1},{5,21,1},{6,21,1},{7,21,1},{8,21,1},{9,21,1},{13,21,1},{14,21,1},{15,21,1},{19,21,1},{20,21,1},{21,21,1},{22,21,1},{23,21,1},{24,21,1},{25,21,1},{27,21,1},{28,21,1},{31,21,1},{32,21,1},{33,21,1},{34,21,1},{35,21,1},{36,21,1},{37,21,1},{39,21,1},{40,21,1},{41,21,1},{42,21,1},{43,21,1},{44,21,1},{45,21,1},{46,21,1},{47,21,1},{48,21,1},{49,21,1},{50,21,1},{51,21,1},{0,19,1},{1,19,1},{2,19,1},{3,19,1},{4,19,1},{5,19,1},{6,19,1},{7,19,1},{8,19,1},{9,19,1},{10,19,1},{11,19,1},{13,19,1},{14,19,1},{15,19,1},{16,19,1},{17,19,1},{18,19,1},{19,19,1},{20,19,1},{21,19,1},{22,19,1},{23,19,1},{24,19,1},{25,19,1},{26,19,1},{27,19,1},{28,19,1},{29,19,1},{30,19,1},{31,19,1},{32,19,1},{33,19,1},{34,19,1},{35,19,1},{36,19,1},{37,19,1},{38,19,1},{39,19,1},{40,19,1},{41,19,1},{42,19,1},{43,19,1},{44,19,1},{45,19,1},{46,19,1},{47,19,1},{48,19,1},{49,19,1},{50,19,1},{51,19,1} };
	int offset[COL + 1] = { 0,33,50,67,92,109,139,164,198,215,246,275,312,337,375,408,450,467,500,531,571,601,644,682,729,754,794,831,877,911,958,1000,1051 };
	VTYPE vecP[DIM] = { 1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,0,1,0,0,0,1,1,0,1,1,1,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1 };
	// --------------------------------------------------------------

	int n = sz(s);

	array<VTYPE, DIM> dp;
	dp.fill(0);
	dp[0] = 1;

	vector<VTYPE> res(n + 1);
	res[0] = vecP[0];

	auto apply = [&](const array<VTYPE, DIM>& x, int col) {
		array<VTYPE, DIM> z;
		z.fill(0);

		repi(pt, offset[0], offset[COL] - 1) { // 重ね合わせ
			auto [i, j, v] = matAs[pt];
			z[j] += x[i] * v;
		}

		return z;
	};

	rep(p, n) {
		dp = apply(dp, s[p] - '0');

		rep(i, DIM) res[p + 1] += dp[i] * vecP[i];
	}

	return res;
}


//【線形漸化式の発見】O(n^2)
/*
* 与えられた数列 a[0..n) に対し,以下の等式を満たす c[0..m) で m を最小とするものを返す:
*		a[i] = Σj∈[0..m) c[j] a[i-1-j]  (∀i∈[m..n))
*
* 制約 : mint::mod は大きい素数
*/
vm berlekamp_massey(const vm& a) {
	// 参考 : https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm
	// verify : https://judge.yosupo.jp/problem/find_linear_recurrence

	vm S(a), C{ 1 }, B{ 1 };
	int N = sz(a), m = 1; mint b = 1;

	rep(n, N) {
		mint d = 0;
		rep(i, sz(C)) d += C[i] * S[n - i];

		if (d == 0) {
			m++;
		}
		else if (2 * (sz(C) - 1) <= n) {
			vm T(C);

			mint coef = d * b.inv();
			C.resize(max(sz(C), sz(B) + m));
			rep(j, sz(B)) C[j + m] -= coef * B[j];

			B = T;
			b = d;
			m = 1;
		}
		else {
			mint coef = d * b.inv();
			C.resize(max(sz(C), sz(B) + m));
			rep(j, sz(B)) C[j + m] -= coef * B[j];

			m++;
		}
	}

	C.erase(C.begin());
	rep(i, sz(C)) C[i] *= -1;

	return C;
}


//【畳込み(素朴)】O(n m)
/*
* a[0..n) と b[0..m) を畳み込んだ数列 c[0..n+m-1) を返す.
* すなわち c[k] = Σ_(i+j=k) a[i] b[j] である.
*/
template <class T>
vector<T> naive_convolution(const vector<T>& a, const vector<T>& b) {
	// verify : https://atcoder.jp/contests/abc214/tasks/abc214_g

	int n = sz(a), m = sz(b);
	if (n == 0 || m == 0) return vector<T>();

	// c[k] = Σ_(i+j=k) a[i] b[j]
	vector<T> c(n + m - 1);
	if (n < m) {
		rep(i, n) rep(j, m) c[i + j] += a[i] * b[j];
	}
	else {
		rep(j, m) rep(i, n) c[i + j] += a[i] * b[j];
	}

	return c;
}

//【形式的冪級数】
/*
* MFPS() : O(1)
*	零多項式 f = 0 で初期化する.
*
* MFPS(mint c0) : O(1)
*	定数多項式 f = c0 で初期化する.
*
* MFPS(mint c0, int n) : O(n)
*	n 次未満の項をもつ定数多項式 f = c0 で初期化する.
*
* MFPS(vm c) : O(n)
*	f(z) = c[0] + c[1] z + ... + c[n - 1] z^(n-1) で初期化する.
*
* set_conv(vm(*CONV)(const vm&, const vm&)) : O(1)
*	畳込み用の関数を CONV に設定する.
*
* c + f, f + c : O(1)	f + g : O(n)
* f - c : O(1)			c - f, f - g, -f : O(n)
* c * f, f * c : O(n)	f * g : O(n log n)		f * g_sp : O(n |g|)
* f / c : O(n)			f / g : O(n log n)		f / g_sp : O(n |g|)
*	形式的冪級数としての和,差,積,商の結果を返す.
*	g_sp はスパース多項式であり,{次数, 係数} の次数昇順の組の vector で表す.
*	制約 : 商では g(0) != 0
*
* MFPS f.inv(int d) : O(n log n)
*	1 / f mod z^d を返す.
*	制約 : f(0) != 0
*
* MFPS f.quotient(MFPS g) : O(n log n)
* MFPS f.reminder(MFPS g) : O(n log n)
* pair<MFPS, MFPS> f.quotient_remainder(MFPS g) : O(n log n)
*	多項式としての f を g で割った商,余り,商と余りの組を返す.
*	制約 : g の最高次の係数は 0 でない
*
* int f.deg(), int f.size() : O(1)
*	多項式 f の次数[項数]を返す.
*
* MFPS::monomial(int d, mint c = 1) : O(d)
*	単項式 c z^d を返す.
*
* mint f.assign(mint c) : O(n)
*	多項式 f の不定元 z に c を代入した値を返す.
*
* f.resize(int d) : O(1)
*	mod z^d をとる.
*
* f.resize() : O(n)
*	不要な高次の項を削る.
*
* f >> d, f << d : O(n)
*	係数列を d だけ右[左]シフトした多項式を返す.
*  (右シフトは z^d の乗算,左シフトは z^d で割った商と等価)
*
* f.push_back(c) : O(1)
*	最高次の係数として c を追加する.
*/
struct MFPS {
	using SMFPS = vector<pim>;

	int n; // 係数の個数(次数 + 1)
	vm c; // 係数列
	inline static vm(*CONV)(const vm&, const vm&) = convolution; // 畳込み用の関数

	// コンストラクタ(0,定数,係数列で初期化)
	MFPS() : n(0) {}
	MFPS(mint c0) : n(1), c({ c0 }) {}
	MFPS(int c0) : n(1), c({ mint(c0) }) {}
	MFPS(mint c0, int d) : n(d), c(n) { if (n > 0) c[0] = c0; }
	MFPS(int c0, int d) : n(d), c(n) { if (n > 0) c[0] = c0; }
	MFPS(const vm& c_) : n(sz(c_)), c(c_) {}
	MFPS(const vi& c_) : n(sz(c_)), c(n) { rep(i, n) c[i] = c_[i]; }

	// 代入
	MFPS(const MFPS& f) = default;
	MFPS& operator=(const MFPS& f) = default;
	MFPS& operator=(const mint& c0) { n = 1; c = { c0 }; return *this; }

	void push_back(mint cn) { c.emplace_back(cn); ++n; }
	void pop_back() { c.pop_back(); --n; }
	[[nodiscard]] mint back() { return c.back(); }

	// 比較
	[[nodiscard]] bool operator==(const MFPS& g) const { return c == g.c; }
	[[nodiscard]] bool operator!=(const MFPS& g) const { return c != g.c; }

	// アクセス
	inline mint const& operator[](int i) const { return c[i]; }
	inline mint& operator[](int i) { return c[i]; }

	// 次数
	[[nodiscard]] int deg() const { return n - 1; }
	[[nodiscard]] int size() const { return n; }

	static void set_conv(vm(*CONV_)(const vm&, const vm&)) {
		// verify : https://atcoder.jp/contests/tdpc/tasks/tdpc_fibonacci

		CONV = CONV_;
	}

	// 加算
	MFPS& operator+=(const MFPS& g) {
		if (n >= g.n) rep(i, g.n) c[i] += g.c[i];
		else {
			rep(i, n) c[i] += g.c[i];
			repi(i, n, g.n - 1)	c.push_back(g.c[i]);
			n = g.n;
		}
		return *this;
	}
	[[nodiscard]] MFPS operator+(const MFPS& g) const { return MFPS(*this) += g; }

	// 定数加算
	MFPS& operator+=(const mint& sc) {
		if (n == 0) { n = 1; c = { sc }; }
		else { c[0] += sc; }
		return *this;
	}
	[[nodiscard]] MFPS operator+(const mint& sc) const { return MFPS(*this) += sc; }
	[[nodiscard]] friend MFPS operator+(const mint& sc, const MFPS& f) { return f + sc; }
	MFPS& operator+=(const int& sc) { *this += mint(sc); return *this; }
	[[nodiscard]] MFPS operator+(const int& sc) const { return MFPS(*this) += sc; }
	[[nodiscard]] friend MFPS operator+(const int& sc, const MFPS& f) { return f + sc; }

	// 減算
	MFPS& operator-=(const MFPS& g) {
		if (n >= g.n) rep(i, g.n) c[i] -= g.c[i];
		else {
			rep(i, n) c[i] -= g.c[i];
			repi(i, n, g.n - 1) c.push_back(-g.c[i]);
			n = g.n;
		}
		return *this;
	}
	[[nodiscard]] MFPS operator-(const MFPS& g) const { return MFPS(*this) -= g; }

	// 定数減算
	MFPS& operator-=(const mint& sc) { *this += -sc; return *this; }
	[[nodiscard]] MFPS operator-(const mint& sc) const { return MFPS(*this) -= sc; }
	[[nodiscard]] friend MFPS operator-(const mint& sc, const MFPS& f) { return -(f - sc); }
	MFPS& operator-=(const int& sc) { *this += -sc; return *this; }
	[[nodiscard]] MFPS operator-(const int& sc) const { return MFPS(*this) -= sc; }
	[[nodiscard]] friend MFPS operator-(const int& sc, const MFPS& f) { return -(f - sc); }

	// 加法逆元
	[[nodiscard]] MFPS operator-() const { return MFPS(*this) *= -1; }

	// 定数倍
	MFPS& operator*=(const mint& sc) { rep(i, n) c[i] *= sc; return *this; }
	[[nodiscard]] MFPS operator*(const mint& sc) const { return MFPS(*this) *= sc; }
	[[nodiscard]] friend MFPS operator*(const mint& sc, const MFPS& f) { return f * sc; }
	MFPS& operator*=(const int& sc) { *this *= mint(sc); return *this; }
	[[nodiscard]] MFPS operator*(const int& sc) const { return MFPS(*this) *= sc; }
	[[nodiscard]] friend MFPS operator*(const int& sc, const MFPS& f) { return f * sc; }

	// 右からの定数除算
	MFPS& operator/=(const mint& sc) { *this *= sc.inv(); return *this; }
	[[nodiscard]] MFPS operator/(const mint& sc) const { return MFPS(*this) /= sc; }
	MFPS& operator/=(const int& sc) { *this /= mint(sc); return *this; }
	[[nodiscard]] MFPS operator/(const int& sc) const { return MFPS(*this) /= sc; }

	// 積
	MFPS& operator*=(const MFPS& g) { c = CONV(c, g.c); n = sz(c); return *this; }
	[[nodiscard]] MFPS operator*(const MFPS& g) const { return MFPS(*this) *= g; }

	// 除算
	[[nodiscard]] MFPS inv(int d) const {
		// 参考:https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
		// verify : https://judge.yosupo.jp/problem/inv_of_formal_power_series

		//【方法】
		// 1 / f mod z^d を求めることは,
		//		f g = 1 (mod z^d)
		// なる g を求めることである.
		// この d の部分を 1, 2, 4, ..., 2^i と倍々にして求めていく.
		//
		// d = 1 のときについては
		//		g = 1 / f[0] (mod z^1)
		// である.
		//
		// 次に,
		//		g = h (mod z^k)
		// が求まっているとして
		//		g mod z^(2 k)
		// を求める.最初の式を変形していくことで
		//		g - h = 0 (mod z^k)
		//		⇒ (g - h)^2 = 0 (mod z^(2 k))
		//		⇔ g^2 - 2 g h + h^2 = 0 (mod z^(2 k))
		//		⇒ f g^2 - 2 f g h + f h^2 = 0 (mod z^(2 k))
		//		⇔ g - 2 h + f h^2 = 0 (mod z^(2 k))  (f g = 1 (mod z^d) より)
		//		⇔ g = (2 - f h) h (mod z^(2 k))
		// を得る.
		//
		// この手順を d ≦ 2^i となる i まで繰り返し,d 次以上の項を削除すればよい.

		Assert(!c.empty());
		Assert(c[0] != 0);

		MFPS g(c[0].inv());
		for (int k = 1; k < d; k <<= 1) {
			int len = max(min(2 * k, d), 1);
			MFPS tmp(0, len);
			rep(i, min(len, n)) tmp[i] = -c[i];	// -f
			tmp *= g;							// -f h
			tmp.resize(len);
			tmp[0] += 2;						// 2 - f h
			g *= tmp;							// (2 - f h) h
			g.resize(len);
		}

		return g;
	}
	MFPS& operator/=(const MFPS& g) { return *this *= g.inv(max(n, g.n)); }
	[[nodiscard]] MFPS operator/(const MFPS& g) const { return MFPS(*this) /= g; }

	// 余り付き除算
	[[nodiscard]] MFPS quotient(const MFPS& g) const {
		// 参考 : https://nyaannyaan.github.io/library/fps/formal-power-series.hpp
		// verify : https://judge.yosupo.jp/problem/division_of_polynomials

		//【方法】
		// f(x) = g(x) q(x) + r(x) となる q(x) を求める.
		// f の次数は n-1, g の次数は m-1 とする.(n ≧ m)
		// 従って q の次数は n-m,r の次数は m-2 となる.
		// 
		// f^R で f の係数列を逆順にした多項式を表す.すなわち
		//		f^R(x) := f(1/x) x^(n-1)
		// である.他の多項式も同様とする.
		//
		// 最初の式で x → 1/x と置き換えると,
		//		f(1/x) = g(1/x) q(1/x) + r(1/x)
		//		⇔ f(1/x) x^(n-1) = g(1/x) q(1/x) x^(n-1) + r(1/x) x^(n-1)
		//		⇔ f(1/x) x^(n-1) = g(1/x) x^(m-1) q(1/x) x^(n-m) + r(1/x) x^(m-2) x^(n-m+1)
		//		⇔ f^R(x) = g^R(x) q^R(x) + r^R(x) x^(n-m+1)
		//		⇒ f^R(x) = g^R(x) q^R(x) (mod x^(n-m+1))
		// 	    ⇒ q^R(x) = f^R(x) / g^R(x)  (mod x^(n-m+1))
		// を得る.
		// 	   
		// これで q を mod x^(n-m+1) で正しく求めることができることになるが,
		// q の次数は n-m であったから,q 自身を正しく求めることができた.

		if (n < g.n) return MFPS();
		return ((this->rev() / g.rev()).resize(n - g.n + 1)).rev();
	}
	[[nodiscard]] MFPS reminder(const MFPS& g) const {
		// verify : https://judge.yosupo.jp/problem/division_of_polynomials

		return (*this - this->quotient(g) * g).resize();
	}
	[[nodiscard]] pair<MFPS, MFPS> quotient_remainder(const MFPS& g) const {
		// verify : https://judge.yosupo.jp/problem/division_of_polynomials

		pair<MFPS, MFPS> res;
		res.first = this->quotient(g);
		res.second = (*this - res.first * g).resize();
		return res;
	}

	// スパース積
	MFPS& operator*=(const SMFPS& g) {
		// g の定数項だけ例外処理
		auto it0 = g.begin();
		mint g0 = 0;
		if (it0->first == 0) {
			g0 = it0->second;
			it0++;
		}

		// 後ろからインライン配る DP
		repir(i, n - 1, 0) {
			// 上位項に係数倍して配っていく.
			for (auto it = it0; it != g.end(); it++) {
				auto [j, gj] = *it;

				if (i + j >= n) break;

				c[i + j] += c[i] * gj;
			}

			// 定数項は最後に配るか消去しないといけない.
			c[i] *= g0;
		}

		return *this;
	}
	[[nodiscard]] MFPS operator*(const SMFPS& g) const { return MFPS(*this) *= g; }

	// スパース商
	MFPS& operator/=(const SMFPS& g) {
		// g の定数項だけ例外処理
		auto it0 = g.begin();
		Assert(it0->first == 0 && it0->second != 0);
		mint g0_inv = it0->second.inv();
		it0++;

		// 前からインライン配る DP(後ろに累積効果あり)
		rep(i, n) {

			// 定数項は最初に配らないといけない.
			c[i] *= g0_inv;

			// 上位項に係数倍して配っていく.
			for (auto it = it0; it != g.end(); it++) {
				auto [j, gj] = *it;

				if (i + j >= n) break;

				c[i + j] -= c[i] * gj;
			}
		}

		return *this;
	}
	[[nodiscard]] MFPS operator/(const SMFPS& g) const { return MFPS(*this) /= g; }

	// 係数反転
	[[nodiscard]] MFPS rev() const { MFPS h = *this; reverse(all(h.c)); return h; }

	// 単項式
	[[nodiscard]] static MFPS monomial(int d, mint coef = 1) {
		MFPS mono(0, d + 1);
		mono[d] = coef;
		return mono;
	}

	// 不要な高次項の除去
	MFPS& resize() {
		// 最高次の係数が非 0 になるまで削る.
		while (n > 0 && c[n - 1] == 0) {
			c.pop_back();
			n--;
		}
		return *this;
	}

	// x^d 以上の項を除去する.
	MFPS& resize(int d) {
		n = d;
		c.resize(d);
		return *this;
	}

	// 不定元への代入
	[[nodiscard]] mint assign(const mint& x) const {
		mint val = 0;
		repir(i, n - 1, 0) val = val * x + c[i];
		return val;
	}

	// 係数のシフト
	MFPS& operator>>=(int d) {
		n += d;
		c.insert(c.begin(), d, 0);
		return *this;
	}
	MFPS& operator<<=(int d) {
		n -= d;
		if (n <= 0) { c.clear(); n = 0; }
		else c.erase(c.begin(), c.begin() + d);
		return *this;
	}
	[[nodiscard]] MFPS operator>>(int d) const { return MFPS(*this) >>= d; }
	[[nodiscard]] MFPS operator<<(int d) const { return MFPS(*this) <<= d; }

#ifdef _MSC_VER
	friend ostream& operator<<(ostream& os, const MFPS& f) {
		if (f.n == 0) os << 0;
		else {
			rep(i, f.n) {
				os << f[i] << "z^" << i;
				if (i < f.n - 1) os << " + ";
			}
		}
		return os;
	}
#endif
};


//【展開係数】O(n log n log N)
/*
* [z^N] f(z)/g(z) を返す.
*
* 制約 : deg f < deg g, g[0] ≠ 0
*/
mint bostan_mori(MFPS f, MFPS g, ll N) {
	// 参考 : http://q.c.titech.ac.jp/docs/progs/polynomial_division.html
	// verify : https://judge.yosupo.jp/problem/kth_term_of_linearly_recurrent_sequence

	//【方法】
	// 分母分子に g(-z) を掛けることにより
	//		f(z) / g(z) = f(z) g(-z) / g(z) g(-z)
	// を得る.ここで g(z) g(-z) は偶多項式なので
	//		g(z) g(-z) = e(z^2)
	// と表すことができる.
	// 
	// 分子について
	//		f(z) g(-z) = E(z^2) + z O(z^2)
	// というように偶多項式部分と奇多項式部分に分けると,N が偶数のときは
	//		[z^N] f(z) g(-z) / g(z) g(-z)
	//		= [z^N] E(z^2) / e(z^2)
	//		= [z^(N/2)] E(z) / e(z)
	// となり,N が奇数のときは
	//		[z^N] f(z) g(-z) / g(z) g(-z)
	//		= [z^N] z O(z^2) / e(z^2)
	//		= [z^((N-1)/2)] O(z) / e(z)
	// となる.
	//
	// これを繰り返せば N を半分ずつに減らしていくことができる.

	Assert(g.n >= 1 && g[0] != 0);

	// f(z) = 0 のときは 0 を返す.
	if (f.n == 0) return 0;

	while (N > 0) {
		// f2(z) = f(z) g(-z), g2(z) = g(z) g(-z) を求める.
		MFPS f2, g2 = g;
		rep(i, g2.n) if (i & 1) g2[i] *= -1;
		f2 = f * g2;
		g2 *= g;

		// f3(z) = E(z) or O(z), g3(z) = e(z) を求める.
		f.c.clear(); g.c.clear();
		if (N & 1) rep(i, min<ll>(f2.n / 2, N / 2 + 1)) f.c.push_back(f2[2 * i + 1]);
		else rep(i, min<ll>((f2.n + 1) / 2, N / 2 + 1)) f.c.push_back(f2[2 * i]);
		f.n = sz(f.c);
		rep(i, min<ll>((g2.n + 1) / 2, N / 2 + 1)) g.c.push_back(g2[2 * i]);
		g.n = sz(g.c);

		// N を半分にして次のステップに進む.
		N /= 2;
	}

	// N = 0 になったら定数項を返す.
	return f[0] / g[0];
}


//【線形漸化式】O(n log n log N)
/*
* 初項 a[0..n) と漸化式 a[i] = Σj∈[0..n) c[j] a[i-1-j] で定義される
* 数列 a について,a[N] の値を返す.
*
* 利用:【展開係数】
*/
mint linearly_recurrent_sequence(const vm& a, const vm& c, ll N) {
	// verify : https://judge.yosupo.jp/problem/kth_term_of_linearly_recurrent_sequence

	int n = sz(c);
	if (n == 0) return 0;

	MFPS A(a), C(c);
	MFPS Dnm = 1 - (C >> 1);
	MFPS Num = (Dnm * A).resize(n);
	return bostan_mori(Num, Dnm, N);
}


int main() {
//	input_from_file("input.txt");
//	output_to_file("output.txt");

	//【方法】
	// 愚直を書いて集めたデータをもとに遷移行列を復元する.

	//【使い方】
	// 1. mint naive(文字列) を実装する.
	// 2. embed_coefs(文字の種類数); を実行する.
	// 3. 出力を solve() 内に貼る.
	// 4. auto dp = solve<答えの型>(文字列) で勝手に DP してくれる.
	
	MFPS::set_conv(naive_convolution);

	H = 6;
	vector<string> ssT_ini{ "" }, ssB_ini{ "" };

	// 途中から再開
	//repe(a, ssT) {
	//	string s;
	//	repe(x, a) s += '0' + x;
	//	ssT_ini.push_back(s);
	//}
	//repe(a, ssB) {
	//	string s;
	//	repe(x, a) s += '0' + x;
	//	ssB_ini.push_back(s);
	//}

	//dump("naive:", naive("00"));
	//dump("naive:", naive("01"));
	//dump("naive:", naive("10"));
	//dump("naive:", naive("11"));
	
	//embed_coefs(1 << H, 7, 300, 1000, ssT_ini, ssB_ini);
	
	int n; ll m;
	cin >> n >> m;

	string s;
	rep(i, 300) s += '?';

	vm seq;
	if (n == 1) seq = solve1<mint>(s);
	else if (n == 2) seq = solve2<mint>(s);
	else if (n == 3) seq = solve3<mint>(s);
	else if (n == 4) seq = solve4<mint>(s);
	else if (n == 5) seq = solve5<mint>(s);
	else exit(-1); // ムリ
	dump(seq);

	auto coef = berlekamp_massey(seq);
	dump(coef);

	EXIT(linearly_recurrent_sequence(seq, coef, m) - 1);
}
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