結果
| 問題 | No.1685 One by One |
| コンテスト | |
| ユーザー |
 ecottea
|
| 提出日時 | 2025-12-21 19:35:14 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 44 ms / 3,000 ms |
| コード長 | 61,385 bytes |
| 記録 | |
| コンパイル時間 | 9,181 ms |
| コンパイル使用メモリ | 365,388 KB |
| 実行使用メモリ | 7,852 KB |
| 最終ジャッジ日時 | 2025-12-21 19:35:28 |
| 合計ジャッジ時間 | 12,613 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 46 |
ソースコード
// QCFium 法
//#pragma GCC target("avx2") // yukicoder と codechef では消す
#pragma GCC optimize("O3") // たまにバグる
#pragma GCC optimize("unroll-loops")
#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); rep(i,9)cout<<MLE[i]; exit(0); } } // RE の代わりに MLE を出す
#endif
//【階乗など（法が大きな素数）】
/*
* Factorial_mint(int N) : O(n)
* N まで計算可能として初期化する．
*
* mint fact(int n) : O(1)
* n! を返す．
*
* mint fact_inv(int n) : O(1)
* 1/n! を返す（n が負なら 0 を返す）
*
* mint inv(int n) : O(1)
* 1/n を返す．
*
* mint perm(int n, int r) : O(1)
* 順列の数 nPr を返す．
*
* mint perm_inv(int n, int r) : O(1)
* 順列の数の逆数 1/nPr を返す．
*
* mint bin(int n, int r) : O(1)
* 二項係数 nCr を返す．
*
* mint bin_inv(int n, int r) : O(1)
* 二項係数の逆数 1/nCr を返す．
*
* mint mul(vi rs) : O(|rs|)
* 多項係数 nC[rs] を返す．（n = Σrs）
*
* mint hom(int n, int r) : O(1)
* 重複組合せの数 nHr = n+r-1Cr を返す（0H0 = 1 とする）
*
* mint neg_bin(int n, int r) : O(1)
* 負の二項係数 nCr = (-1)^r -n+r-1Cr を返す（n ≦ 0, r ≧ 0）
*
* mint pochhammer(int x, int n) : O(1)
* ポッホハマー記号 x^(n) を返す（n ≧ 0）
*
* mint pochhammer_inv(int x, int n) : O(1)
* ポッホハマー記号の逆数 1/x^(n) を返す（n ≧ 0）
*/
class Factorial_mint {
int n_max;
// 階乗と階乗の逆数の値を保持するテーブル
vm fac, fac_inv;
public:
// n! までの階乗とその逆数を前計算しておく．O(n)
Factorial_mint(int n) : n_max(n), fac(n + 1), fac_inv(n + 1) {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
fac[0] = 1;
repi(i, 1, n) fac[i] = fac[i - 1] * i;
fac_inv[n] = fac[n].inv();
repir(i, n - 1, 0) fac_inv[i] = fac_inv[i + 1] * (i + 1);
}
Factorial_mint() : n_max(0) {} // ダミー
// n! を返す．
mint fact(int n) const {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
Assert(0 <= n && n <= n_max);
return fac[n];
}
// 1/n! を返す（n が負なら 0 を返す）
mint fact_inv(int n) const {
// verify : https://atcoder.jp/contests/abc289/tasks/abc289_h
Assert(n <= n_max);
if (n < 0) return 0;
return fac_inv[n];
}
// 1/n を返す．
mint inv(int n) const {
// verify : https://atcoder.jp/contests/exawizards2019/tasks/exawizards2019_d
Assert(n > 0);
Assert(n <= n_max);
return fac[n - 1] * fac_inv[n];
}
// 順列の数 nPr を返す．
mint perm(int n, int r) const {
// verify : https://atcoder.jp/contests/abc172/tasks/abc172_e
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[n - r];
}
// 順列の数 nPr の逆数を返す．
mint perm_inv(int n, int r) const {
// verify : https://yukicoder.me/problems/no/3139
Assert(n <= n_max);
Assert(0 <= r); Assert(r <= n);
return fac_inv[n] * fac[n - r];
}
// 二項係数 nCr を返す．
mint bin(int n, int r) const {
// verify : https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[r] * fac_inv[n - r];
}
// 二項係数の逆数 1/nCr を返す．
mint bin_inv(int n, int r) const {
// verify : https://www.codechef.com/problems/RANDCOLORING
Assert(n <= n_max);
Assert(r >= 0);
Assert(n - r >= 0);
return fac_inv[n] * fac[r] * fac[n - r];
}
// 多項係数 nC[rs] を返す．
mint mul(const vi& rs) const {
// verify : https://yukicoder.me/problems/no/2141
if (rs.empty()) return 1;
if (*min_element(all(rs)) < 0) return 0;
int n = accumulate(all(rs), 0);
Assert(n <= n_max);
mint res = fac[n];
repe(r, rs) res *= fac_inv[r];
return res;
}
// 重複組合せの数 nHr = n+r-1Cr を返す（0H0 = 1 とする）
mint hom(int n, int r) {
// verify : https://mojacoder.app/users/riantkb/problems/toj_ex_2
if (n == 0) return (int)(r == 0);
if (r < 0 || n - 1 < 0) return 0;
Assert(n + r - 1 <= n_max);
return fac[n + r - 1] * fac_inv[r] * fac_inv[n - 1];
}
// 負の二項係数 nCr を返す（n ≦ 0, r ≧ 0）
mint neg_bin(int n, int r) {
// verify : https://atcoder.jp/contests/abc345/tasks/abc345_g
if (n == 0) return (int)(r == 0);
if (r < 0 || -n - 1 < 0) return 0;
Assert(-n + r - 1 <= n_max);
return (r & 1 ? -1 : 1) * fac[-n + r - 1] * fac_inv[r] * fac_inv[-n - 1];
}
// ポッホハマー記号 x^(n) を返す（n ≧ 0）
mint pochhammer(int x, int n) {
// verify : https://atcoder.jp/contests/agc070/tasks/agc070_c
int x2 = x + n - 1;
if (x <= 0 && 0 <= x2) return 0;
if (x > 0) {
Assert(x2 <= n_max);
return fac[x2] * fac_inv[x - 1];
}
else {
Assert(-x <= n_max);
return (n & 1 ? -1 : 1) * fac[-x] * fac_inv[-x2 - 1];
}
}
// ポッホハマー記号の逆数 1/x^(n) を返す（n ≧ 0）
mint pochhammer_inv(int x, int n) {
// verify : https://atcoder.jp/contests/agc070/tasks/agc070_c
int x2 = x + n - 1;
Assert(!(x <= 0 && 0 <= x2));
if (x > 0) {
Assert(x2 <= n_max);
return fac_inv[x2] * fac[x - 1];
}
else {
Assert(-x <= n_max);
return (n & 1 ? -1 : 1) * fac_inv[-x] * fac[-x2 - 1];
}
}
};
Factorial_mint fm((int)1e5 + 10);
// i=n, j=m に対する愚直解を返す．
mint naive_sub(int n, int M) {
mint res = 0;
if (n % 2 == 0) {
repi(m, 0, M) {
mint pres = res;
repi(t, 0, M - m) repi(s, 0, M - m - t) repi(i, 0, n / 2 - 1) repi(j, 0, n / 2 - 1) {
if ((s ^ t ^ m ^ M) & 1) continue;
if (t > 0 && i == 0) continue;
if (s > 0 && j == 0) continue;
int wgt = (m == 0 ? 1 : 2);
mint add = fm.bin(n - 1, i) * fm.bin(n - 1 - i, j);
if (i > 0) add *= fm.bin(t - 1, i - 1);
if (j > 0) add *= fm.bin(s - 1, j - 1);
//dump("m,t,s,i,j:", m, t, s, i, j, ":", add);
add *= wgt;
res += add;
}
//dump(m, ":", res - pres);
}
}
else {
// m : median
repi(m, 0, M) {
mint pres = res;
if (m == 0) {
// パリティ一致
repi(t, 0, M - m) repi(s, 0, M - m - t) {
if ((s ^ t ^ m ^ M) & 1) continue;
repi(i, 0, n / 2) repi(j, 0, n / 2) {
if (t > 0 && i == 0) continue;
if (s > 0 && j == 0) continue;
int wgt = 1;
mint add = fm.bin(n - 1, i) * fm.bin(n - 1 - i, j);
if (i > 0) add *= fm.bin(t - 1, i - 1);
if (j > 0) add *= fm.bin(s - 1, j - 1);
if (add == 0) continue;
add *= wgt;
//dump("0,m,t,s,i,j:", m, t, s, i, j, ":", add);
res += add;
}
}
// パリティ不一致
// x : neg cnt, y : pos cnt
repi(x, 0, n / 2) repi(y, 0, n / 2) {
// All 1 から
if (x <= y) {
int M_rem = M - 1 - 2 * x - (n - 1 - x - y);
// s : ad neg sum, t : ad pos sum
repi(s, 0, M_rem) repi(t, 0, M_rem - s) {
if ((1 ^ (2 * x) ^ (n - 1 - x - y) ^ s ^ t ^ M) & 1) continue;
int wgt = 1;
mint add = fm.bin(n - 1, x) * fm.bin(n - 1 - x, y);
if (x > 0 || s > 0) add *= fm.bin(x + s - 1, s);
if (y > 0 || t > 0) add *= fm.bin(y + t - 1, t);
add *= wgt;
if (add == 0) continue;
//dump("1,m,x,y,s,t:", m, x, y, s, t, ":", add);
res += add;
}
}
// All -1 から
else {
int M_rem = M - 1 - 2 * y - (n - 1 - x - y);
// s : ad neg sum, t : ad pos sum
repi(s, 0, M_rem) repi(t, 0, M_rem - s) {
if ((1 ^ (2 * y) ^ (n - 1 - x - y) ^ s ^ t ^ M) & 1) continue;
int wgt = 1;
mint add = fm.bin(n - 1, x) * fm.bin(n - 1 - x, y);
if (x > 0 || s > 0) add *= fm.bin(x + s - 1, s);
if (y > 0 || t > 0) add *= fm.bin(y + t - 1, t);
add *= wgt;
if (add == 0) continue;
//dump("1,m,x,y,s,t:", m, x, y, s, t, ":", add);
res += add;
}
}
}
}
else {
// パリティ一致
repi(t, 0, M - m) repi(s, 0, M - m - t) repi(i, 0, n / 2 - 1) repi(j, 0, n / 2) {
if ((s ^ t ^ m ^ M) & 1) continue;
if (t > 0 && i == 0) continue;
if (s > 0 && j == 0) continue;
int wgt = 2;
mint add = fm.bin(n - 1, i) * fm.bin(n - 1 - i, j);
if (i > 0) add *= fm.bin(t - 1, i - 1);
if (j > 0) add *= fm.bin(s - 1, j - 1);
add *= wgt;
//dump("0,m,t,s,i,j:", m, t, s, i, j, ":", add);
res += add;
}
// パリティ不一致
// x : neg cnt, y : pos cnt
repi(x, 0, n / 2 - 1) repi(y, 0, n / 2) {
// All m+1 から
if ((m - 1) + 2 * y + (n - 1 - x - y) >= (m + 1) + 2 * x + (n - 1 - x - y)) {
int M_rem = M - (m + 1) - 2 * x - (n - 1 - x - y);
// s : ad neg sum, t : ad pos sum
repi(s, 0, M_rem) repi(t, 0, M_rem - s) {
if (((m + 1) ^ (2 * x) ^ (n - 1 - x - y) ^ s ^ t ^ M) & 1) continue;
int wgt = 2;
mint add = fm.bin(n - 1, x) * fm.bin(n - 1 - x, y);
if (x > 0 || s > 0) add *= fm.bin(x + s - 1, s);
if (y > 0 || t > 0) add *= fm.bin(y + t - 1, t);
add *= wgt;
if (add == 0) continue;
//dump("1,m,x,y,s,t:", m, x, y, s, t, ":", add);
res += add;
}
}
// All m-1 から
else {
int M_rem = M - (m - 1) - 2 * y - (n - 1 - x - y);
// s : ad neg sum, t : ad pos sum
repi(s, 0, M_rem) repi(t, 0, M_rem - s) {
if (((m + 1) ^ (2 * y) ^ (n - 1 - x - y) ^ s ^ t ^ M) & 1) continue;
int wgt = 2;
mint add = fm.bin(n - 1, x) * fm.bin(n - 1 - x, y);
if (x > 0 || s > 0) add *= fm.bin(x + s - 1, s);
if (y > 0 || t > 0) add *= fm.bin(y + t - 1, t);
add *= wgt;
if (add == 0) continue;
//dump("1,m,x,y,s,t:", m, x, y, s, t, ":", add);
res += add;
}
}
}
}
//dump(m, ":", res - pres);
}
}
return res;
}
// (i,j)∈[0..n)×[0..m) に対する愚直解を返す．
vvm naive() {
int n = 40;
vvm tbl(n);
rep(i, n) {
tbl[i].resize(n);
rep(j, n) {
dump("i, j:", i, j);
tbl[i][j] = naive_sub(i, j);
}
}
#ifdef _MSC_VER
// 埋め込み用
string eb;
eb += "vvm tbl = {\n";
rep(i, sz(tbl)) {
eb += "{";
rep(j, sz(tbl[i])) eb += to_string(tbl[i][j].val()) + ",";
eb.pop_back();
eb += "},\n";
}
eb.pop_back(); eb.pop_back();
eb += "};\n\n";
cout << eb;
#endif
return tbl;
}
//【行列】
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) {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 {
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 {
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
};
//【線形方程式】O(n m min(n, m))
template <class T>
vector<T> gauss_jordan_elimination(const Matrix<T>& A, const vector<T>& b, vector<vector<T>>* xs = nullptr) {
int n = A.n, m = A.m;
// v : 拡大係数行列 (A | b)
vector<vector<T>> v(n, vector<T>(m + 1));
rep(i, n) rep(j, m) v[i][j] = A[i][j];
rep(i, n) v[i][m] = b[i];
// pivots[i] : 第 i 行のピボットが第何列にあるか
vi pivots;
// 注目位置を v[i][j] とする．
int i = 0, j = 0;
while (i < n && j <= m) {
// 注目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注目位置を右に移す．
if (i2 == n) { j++; continue; }
// 見つかったら第 i 行とその行を入れ替える．
if (i != i2) swap(v[i], v[i2]);
// v[i][j] をピボットに選択する．
pivots.push_back(j);
// v[i][j] が 1 になるよう第 i 行全体を v[i][j] で割る．
T vij_inv = T(1) / v[i][j];
repi(j2, j, m) v[i][j2] *= vij_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 (v[i2][j] == T(0) || i2 == i) continue;
T mul = v[i2][j];
repi(j2, j, m) v[i2][j2] -= v[i][j2] * mul;
}
// 注目位置を右下に移す．
i++; j++;
}
// 最後に見つかったピボットの位置が第 m 列ならば解なし．
if (!pivots.empty() && pivots.back() == m) return vector<T>();
// A x = b の特殊解 x0 の構成（任意定数は全て 0 にする）
vector<T> x0(m);
int rnk = sz(pivots);
rep(i, rnk) x0[pivots[i]] = v[i][m];
// 同次形 A x = 0 の一般解 {x} の基底の構成（任意定数を 1-hot にする）
if (xs != nullptr) {
xs->clear();
int i = 0;
rep(j, m) {
if (i < rnk && j == pivots[i]) {
i++;
continue;
}
vector<T> x(m);
x[j] = T(1);
rep(i2, i) x[pivots[i2]] = -v[i2][j];
xs->emplace_back(move(x));
}
}
return x0;
}
// https://qiita.com/satoshin_astonish/items/a628ec64f29e77501d07
namespace satoshin {
/* 内積 */
double dot(const vl& x, const vd& y) {
double z = 0.0;
const int n = sz(x);
for (int i = 0; i < n; ++i) z += x[i] * y[i];
return z;
}
double dot(const vd& x, const vd& y) {
double z = 0.0;
const int n = sz(x);
for (int i = 0; i < n; ++i) z += x[i] * y[i];
return z;
}
double dot(const vl& x, const vl& y) {
double z = 0.0;
const int n = sz(x);
for (int i = 0; i < n; ++i) z += x[i] * y[i];
return z;
}
/* Gram-Schmidtの直交化 */
tuple<vd, vvd> Gram_Schmidt_squared(const vvl& b) {
const int n = sz(b), m = sz(b[0]); int i, j, k;
vd B(n);
vvd GSOb(n, vd(m)), mu(n, vd(n));
for (i = 0; i < n; ++i) {
mu[i][i] = 1.0;
for (j = 0; j < m; ++j) GSOb[i][j] = (double)b[i][j];
for (j = 0; j < i; ++j) {
mu[i][j] = dot(b[i], GSOb[j]) / dot(GSOb[j], GSOb[j]);
for (k = 0; k < m; ++k) GSOb[i][k] -= mu[i][j] * GSOb[j][k];
}
B[i] = dot(GSOb[i], GSOb[i]);
}
return std::forward_as_tuple(B, mu);
}
/* 部分サイズ基底簡約 */
void SizeReduce(vvl& b, vvd& mu, const int i, const int j) {
ll q;
const int m = sz(b[0]);
if (mu[i][j] > 0.5 || mu[i][j] < -0.5) {
q = (ll)round(mu[i][j]);
for (int k = 0; k < m; ++k) b[i][k] -= q * b[j][k];
for (int k = 0; k <= j; ++k) mu[i][k] -= mu[j][k] * q;
}
}
/* LLL基底簡約 */
void LLLReduce(vvl& b, const float d = 0.99) {
const int n = sz(b), m = sz(b[0]); int j, i, h;
double t, nu, BB, C;
auto [B, mu] = Gram_Schmidt_squared(b);
ll tmp;
for (int k = 1; k < n;) {
h = k - 1;
for (j = h; j > -1; --j) SizeReduce(b, mu, k, j);
//Checks if the lattice basis matrix b satisfies Lovasz condition.
if (k > 0 && B[k] < (d - mu[k][h] * mu[k][h]) * B[h]) {
for (i = 0; i < m; ++i) { tmp = b[h][i]; b[h][i] = b[k][i]; b[k][i] = tmp; }
nu = mu[k][h]; BB = B[k] + nu * nu * B[h]; C = 1.0 / BB;
mu[k][h] = nu * B[h] * C; B[k] *= B[h] * C; B[h] = BB;
for (i = 0; i <= k - 2; ++i) {
t = mu[h][i]; mu[h][i] = mu[k][i]; mu[k][i] = t;
}
for (i = k + 1; i < n; ++i) {
t = mu[i][k]; mu[i][k] = mu[i][h] - nu * t;
mu[i][h] = t + mu[k][h] * mu[i][k];
}
--k;
}
else ++k;
}
}
}
vl LLLReduce(const vvm& lat_) {
int h = sz(lat_);
int w = sz(lat_[0]);
vvl lat(h + w, vl(w));
rep(i, h) rep(j, w) lat[i][j] = lat_[i][j].val();
rep(i, w) lat[h + i][i] = mint::mod();
h = sz(lat);
satoshin::LLLReduce(lat);
// L1 ノルムをチェックする．
ll sum = 0;
rep(j, w) sum += abs(lat[0][j]);
dump("L1:", sum);
// L1 ノルムが大きいものは捨てる．
repi(i, 1, h - 1) {
ll sum2 = 0;
rep(j, w) sum2 += abs(lat[i][j]);
if (sum2 > sum * 10.) {
lat.resize(i);
h = i;
break;
}
}
dump("lat:"); frac_print = 1; dumpel(lat); frac_print = 0;
return lat[0];
}
// 変数係数線形漸化式の係数を計算し，埋め込み用のコードを出力する．
vvm embed_coefs_1D(const vm& seq, int TRM_ini = 1, int DEG_ini = 1, bool LLL = false) {
int n = sz(seq);
// TRM 項間の，係数多項式の次数 DEG 未満の変数係数線形漸化式
// Σt∈[0..TRM) Σd∈[0..DEG) coefs[t][d] (i-TRM+1+t)^d seq[i-t] = 0
// を探す．
int TRM = TRM_ini, DEG = DEG_ini;
while (1) {
//dump("TRM:", TRM, "DEG:", DEG);
int h = n - TRM + 1;
int w = TRM * DEG;
// 行列方程式 A x = 0 を解いて一般解の基底 xs を求める．
Matrix<mint> A(h, w);
repi(i, TRM - 1, n - 1) {
rep(t, TRM) rep(d, DEG) {
A[i - TRM + 1][t * DEG + d] = mint(i - TRM + 1 + t).pow(d) * seq[i - t];
}
}
vvm xs;
gauss_jordan_elimination(A, vm(h), &xs);
// 自明解 x = 0 しか存在しない場合は失敗．
if (xs.empty()) {
if (DEG == 1) {
DEG = TRM + DEG;
TRM = 1;
}
else {
TRM++;
DEG--;
}
continue;
}
dump("TRM:", TRM, "DEG:", DEG);
dump("#eq:", h, "#var:", w);
dump("xs:"); frac_print = 1; dumpel(xs); frac_print = 0;
// 変数係数線形漸化式の係数
vvm coefs(TRM, vm(DEG));
if (LLL) {
// A x = 0 の解空間の基底に LLL を適用する．
// 性能はいまいちなのでガチでやるなら Mathematica を使う．
auto lat0 = LLLReduce(xs);
rep(t, TRM) rep(d, DEG) coefs[t][d] = lat0[t * DEG + d];
}
else {
rep(t, TRM) rep(d, DEG) coefs[t][d] = xs.back()[t * DEG + d];
}
return coefs;
}
return vvm();
}
// 変数係数線形漸化式の係数を計算し，埋め込み用のコードを出力する．
pair<vvvm, vvvm> embed_coefs_2D(const vvm& tbl, int DEG1_ini = 1, int TRM2_ini = 1, int DEG2_ini = 1, bool LLL = false) {
int n1 = sz(tbl);
// TRM 項間の，係数多項式の次数 DEG 未満の変数係数線形漸化式
// Σt1∈[0..TRM1) Σd1∈[0..DEG1) Σt2∈[0..TRM2) Σd2∈[0..DEG2)
// c[t1][d1][t2][d2] (i1-TRM1+1+t1)^d1 (i2-TRM2+1+t2)^d2 tbl[i1-t1][i2-t2] = 0
// を探す．
int TRM1 = 1, DEG1 = DEG1_ini;
int TRM2 = TRM2_ini, DEG2 = DEG2_ini;
int P_MAX = max({ TRM1, DEG1, TRM2, DEG2 });
while (1) {
dump("TRM1:", TRM1, "DEG1:", DEG1, "TRM2:", TRM2, "DEG2:", DEG2);
int w = TRM1 * DEG1 * TRM2 * DEG2;
// 行列方程式 A x = 0 を解いて一般解の基底 xs を求める．
Matrix<mint> A(0, w);
repi(i1, TRM1 - 1, n1 - 1) {
int n2 = sz(tbl[i1]);
repi(i2, TRM2 - 1, n2 - 1) {
vm a(w); bool valid = true;
rep(t1, TRM1) rep(d1, DEG1) rep(t2, TRM2) rep(d2, DEG2) {
if (i2 - t2 >= sz(tbl[i1 - t1])) {
valid = false;
break;
}
int idx = ((t1 * DEG1 + d1) * TRM2 + t2) * DEG2 + d2;
mint pow_i = mint(i1 - TRM1 + 1 + t1).pow(d1) * mint(i2 - TRM2 + 1 + t2).pow(d2);
a[idx] = pow_i * tbl[i1 - t1][i2 - t2];
}
if (valid) A.push_back(a);
}
}
int h = A.n;
vvm xs;
gauss_jordan_elimination(A, vm(h), &xs);
// 自明解 x = 0 しか存在しない場合は失敗．
if (xs.empty()) {
while (1) {
DEG2++;
if (DEG2 > P_MAX) { DEG2 = 1; TRM2++; };
if (TRM2 > P_MAX) { TRM2 = 1; DEG1++; };
if (DEG1 > P_MAX) { DEG1 = 1; TRM1++; };
if (TRM1 > 1) { TRM1 = 1; P_MAX++; };
if (max({ TRM1, DEG1, TRM2, DEG2 }) == P_MAX) break;
}
continue;
}
dump("TRM1:", TRM1, "DEG1:", DEG1, "TRM2:", TRM2, "DEG2:", DEG2);
dump("#eq:", h, "#var:", w);
dump("xs:"); frac_print = 1; dumpel(xs); frac_print = 0;
// 変数係数線形漸化式の係数
vvvm coefs(DEG1, vvm(TRM2, vm(DEG2)));
if (LLL) {
// A x = 0 の解空間の基底に LLL を適用する．
// 性能はいまいちなのでガチでやるなら Mathematica を使う．
auto lat0 = LLLReduce(xs);
rep(d1, DEG1) rep(t2, TRM2) rep(d2, DEG2) {
int idx = (d1 * TRM2 + t2) * DEG2 + d2;
coefs[d1][t2][d2] = lat0[idx];
}
}
else {
rep(d1, DEG1) rep(t2, TRM2) rep(d2, DEG2) {
int idx = (d1 * TRM2 + t2) * DEG2 + d2;
coefs[d1][t2][d2] = xs.back()[idx];
}
}
// i1 方向への初項の延長
dump("------- embed_coefs_1D -------");
vvvm coefs1(TRM2 - 1);
rep(i2, TRM2 - 1) {
dump("--- i2:", i2, "---");
vm seq; int offset = 0;
rep(i1, sz(tbl)) {
if (sz(tbl[i1]) <= i2) {
if (offset == i1) {
offset = i1 + 1;
continue;
}
else {
break;
}
}
seq.emplace_back(tbl[i1][i2]);
}
coefs1[i2] = embed_coefs_1D(seq, 1, 1, LLL);
}
#ifdef _MSC_VER
// 埋め込み用の文字列を出力する．
auto to_signed_string = [](mint x) {
int v = x.val();
int mod = mint::mod();
if (v > mod / 2) v -= mod;
return to_string(v);
};
string eb;
eb += "\n";
eb += "constexpr int TRM1 = ";
eb += to_string(TRM1);
eb += ";\n";
eb += "constexpr int DEG1 = ";
eb += to_string(DEG1);
eb += ";\n";
eb += "constexpr int TRM2 = ";
eb += to_string(TRM2);
eb += ";\n";
eb += "constexpr int DEG2 = ";
eb += to_string(DEG2);
eb += ";\n\n";
eb += "vvm coefs1[TRM2 - 1] = {\n";
rep(i2, TRM2 - 1) {
eb += "{";
rep(t, sz(coefs1[i2])) {
eb += "{";
rep(d, sz(coefs1[i2][t])) {
eb += to_signed_string(coefs1[i2][t][d]) + ",";
}
eb.pop_back();
eb += "},";
}
eb.pop_back();
eb += "},\n";
}
eb.pop_back(); eb.pop_back();
eb += "};\n\n";
eb += "mint coefs[DEG1][TRM2][DEG2] = {\n";
rep(d1, DEG1) {
eb += "{";
rep(t2, TRM2) {
eb += "{";
rep(d2, DEG2) {
eb += to_signed_string(coefs[d1][t2][d2]) + ",";
}
eb.pop_back();
eb += "},";
}
eb.pop_back();
eb += "},\n";
}
eb.pop_back(); eb.pop_back();
eb += "};\n";
cout << eb;
#endif
return { coefs1, coefs };
}
return pair<vvvm, vvvm>();
}
// 数列 seq を延長して seq[0..N] にする．
void solve_1D(vm& seq, int N, vvm coefs) {
int TRM = sz(coefs);
int DEG = sz(coefs[0]);
int n = sz(seq);
seq.resize(N + 1);
// TRM 項間の，係数多項式の次数 DEG 未満の変数係数線形漸化式
// Σt∈[0..TRM) Σd∈[0..DEG) coefs[t][f] (i-TRM+1+t)^d a[i-t] = 0
// を用いて数列 a を延長する．
repi(i, n, N) {
mint dnm = 0;
mint pow_i = 1;
rep(d, DEG) {
dnm += coefs[0][d] * pow_i;
pow_i *= i - TRM + 1;
}
mint num = 0;
repi(t, 1, TRM - 1) {
mint pow_i = 1;
rep(d, DEG) {
num += coefs[t][d] * pow_i * seq[i - t];
pow_i *= i - TRM + 1 + t;
}
}
// dnm * a[i] + num = 0 を解く．分母 0 に注意！
if (dnm == 0) {
dump("DIVISION BY ZERO at i =", i);
Assert(dnm != 0);
}
seq[i] = -num / dnm;
}
}
vm z1 = { 0,2,27,284,2875,29112,297381,3066968,31898043,334088600,519333016,249880213,834895512,469745464,809678609,770302353,566062593,812058088,218212551,901440335,898199270,477774349,202661371,832970536,129226607,576996613,333676942,968684808,533096993,418662272,824300530,407648070,678363484,168129458,968388076,778604702,175906262,829390085,57583480,213326768,930656681,307994764,935585620,771902300,8214665,833552892,122899009,573662991,669762934,972508139 };
vm z2 = { 0,3,125,4347,144909,4760723,155545403,73073960,453001994,654862203,398876864,734463270,99659308,350082331,368127076,512791401,172515187,536365159,23469814,422249787,897783296,925184653,451666059,40572789,261775399,391664909,51972785,168327643,267817362,399495046,669366828,87767199,706613561,182540867,497742294,121931186,848955643,370375160,251510108,813098062,732304856,631196824,415428866,39316986,787094430,570259453,217945948,757243535,115011554,624361953 };
vm z3 = { 1,37,1131,33839,1027351,31735023,994338281,499036480,347092189,113948318,94544338,459963291,722046640,680408420,278149373,766038487,767074750,15284168,648438851,411834579,97747849,525790458,604858863,928788161,862923360,318030456,85440844,458208762,421535214,657423093,494949332,614828104,936289590,654590010,488973278,580913505,463433462,867949104,142618563,37841376,911822175,74085347,977850501,663052862,147845703,403638052,7778208,130117969,519049705,70834228,244527609,446243312,504346758,769995090,238466792,271068688,537138945,10379216,399738200,149921575,939503343,805758052,761583479,163912346,226588623,477248432,629727423,583595395,453821036,192607247,606633602,65478998,486274477,575968390,438573835,820769756,773207644,699613925,619052690,431516800,678049184 };
vm z4 = { 0,4,216,8408,298000,10167312,340670344,309535267,658085485,375827748,777839176,700175710,833266097,251752820,181571011,705241694,800980978,804410785,321236177,504171421,445867961,797803082,596264674,201407725,250403725,334365699,528172526,424157265,882778614,797551814,51380549,250966804,771899423,869589875,914097640,151164201,975696993,510028536,936972831,411915492,149646687,91071251,690825013,312876604,996619554,986806458,273353319,737929544,651927808,784018238 };
vm z5 = { 1,61,2221,71835,2262853,71282113,260193819,184622865,180947277,87825311,326027200,613797793,164758037,615439574,442163315,229071225,465033260,257130666,116188968,557520062,634977872,225213252,395132840,237994599,234603550,592324848,680156774,295381283,507167402,287080123,628929735,137144626,998616437,366583659,291542172,116863379,751482250,124378544,65468746,78937307,809559596,643483877,705303563,955938620,471201519,645272719,362486264,195115922,133834650,437886360,201227060,794882043,514665990,779438531,497751730,348437447,753329635,898574238,409880249,520807735,978416754,599241196,384753442,44728630,172022941,376582233,567671085,796012458,925930828,970304109,113780354,53670715,670137826,449084847,371038249,614784672,833539984,311718578,730337578,456619540 };
// 2 次元数列 tbl を元に seq = tbl[N][0..M] を計算する．
vm solve_2D(const vvm& tbl, int N, int M, vvvm coefs1, vvvm coefs) {
int TRM1 = 1;
int DEG1 = sz(coefs);
int TRM2 = sz(coefs[0]);
int DEG2 = sz(coefs[0][0]);
vm res(TRM2 - 1);
// i1 方向に tbl[..][0], ..., tbl[..][TRM2-2] を延長する．
dump("------- solve_1D -------");
rep(i2, TRM2 - 1) {
dump("--- i2:", i2, "---");
vm seq; int offset = 0;
rep(i1, sz(tbl)) {
if (sz(tbl[i1]) <= i2) {
if (offset == i1) {
offset = i1 + 1;
continue;
}
else {
break;
}
}
seq.emplace_back(tbl[i1][i2]);
}
if (N - offset < 0) continue;
solve_1D(seq, N - offset, coefs1[i2]);
//dump("seq:", seq);
res[i2] = seq[N - offset];
}
vm pow_i1s(DEG1);
pow_i1s[0] = 1;
repi(d1, 1, DEG1 - 1) pow_i1s[d1] = pow_i1s[d1 - 1] * (N - TRM1 + 1);
// i2 方向に tbl[N][..] を延長する．
res.resize(M + 1);
repi(i2, TRM2 - 1, M) {
// 0 除算回避
if (i2 * 2 == N) { res[i2] = z1[i2]; continue; }
if (i2 == N && N % 2 == 0) { res[i2] = z2[i2 / 2]; continue; }
if (i2 == N && N % 2 == 1) { res[i2] = z3[i2 / 2]; continue; }
if (i2 == N + 1 && N % 2 == 0) { res[i2] = z4[i2 / 2]; continue; }
if (i2 == N + 1 && N % 2 == 1) { res[i2] = z5[(i2 - 1) / 2]; continue; }
mint dnm = 0;
mint pow_i2 = 1;
rep(d2, DEG2) {
rep(d1, DEG1) {
dnm += coefs[d1][0][d2] * pow_i1s[d1] * pow_i2;
}
pow_i2 *= i2 - TRM2 + 1;
}
mint num = 0;
repi(t2, 1, TRM2 - 1) {
mint pow_i2 = 1;
rep(d2, DEG2) {
rep(d1, DEG1) {
num += coefs[d1][t2][d2] * pow_i1s[d1] * pow_i2 * res[i2 - t2];
}
pow_i2 *= i2 - TRM2 + 1 + t2;
}
}
// dnm * tbl[N][i2] + num = 0 を解く．分母 0 に注意！
if (dnm == 0) {
dump("DIVISION BY ZERO at i1 =", N, "i2 =", i2);
Assert(dnm != 0);
}
res[i2] = -num / dnm;
}
return res;
}
// 2 次元数列 tbl を元に seq = tbl[N][0..M] を計算する．
vm solve_2D(const vvm& tbl, int N, int M) {
// --------------- embed_coefs() からの出力を貼る ----------------
constexpr int TRM1 = 1;
constexpr int DEG1 = 9;
constexpr int TRM2 = 9;
constexpr int DEG2 = 9;
vvm coefs1[TRM2 - 1] = {
{{0,-1},{-1,1}},
{{0,2,-1},{0,-3,1}},
{{333333329,266666674,400000005,-1},{-399999950,-333333375,-266666662,0},{399999970,66666701,-133333345,1}},
{{66577001,-311598402,-314214026,213260290,345975137},{349369338,-33184907,-374006956,137489659,-345975138},{118729377,356575277,-273853618,-4774813,1}},
{{17092941,7736056,401769268,309399017,-468646266},{-338263852,348337235,-379989771,301431812,-438045381},{81622559,287160231,-446595573,389169178,-93308361},{-400647397,454116353,-244583862,0,1}},
{{0,-38171886,269510995,9050615,210934850,345295689},{-60970913,325237279,406055001,318612110,-38457292,2493551},{248218958,-217288234,-337873575,463616249,-172477558,-347789241},{-207044180,-375478380,164133633,278265504,0,1}},
{{-350973086,327787223,382003216,47129214,-65494643},{-491093622,496059889,170183137,-25989695,88143047},{-76130611,27409397,-271950843,48964970,331128826},{74775146,-449606165,-432622621,481676299,-353777231},{-356928157,-499289515,-232085006,-173642761,1}},
{{-376520682,386350120,-380023509,-218237421,192922230,-205939579},{-289972421,361455589,-74968629,-212208352,-120474050,340223008},{-419014931,289448539,236393134,224996636,-261591340,412340631},{334639407,-67482033,173389415,-17204091,239207349,453375946},{172363179,-341796807,-358731843,23526613,0,1}} };
mint coefs[DEG1][TRM2][DEG2] = {
{{-98806613,151442388,495571897,-215412272,-3737820,-118111394,414057114,20286198,31756520},{36293288,-145212441,262940279,32550437,246904529,-109890253,42857485,490257135,-29694154},{-347934625,-189127641,-154456220,-363346658,339250367,354292385,-327919633,-68376518,-336417980},{-304172696,60758356,-83916697,-241679383,271420646,-419452961,-106924421,163459356,-432745437},{143460120,-285605640,-298209651,273079607,-288487680,203789184,-284627540,81169785,340542712},{88247074,213006617,-360699930,-94588063,290970245,-323269054,441058370,-61666442,-45426671},{93997984,-128096500,-414976950,-423488242,169027982,119742730,-55886376,225621531,201142436},{436050445,236891548,64659605,-28234595,83510285,253974338,-183211595,407949958,-492133745},{408843053,-151593549,391638061,-325474382,-391723826,38925025,60596596,-258700996,-237023688}},
{{53805687,331258565,136722925,-157059108,-87285769,-96493156,77002646,177245899,124238246},{-374696093,51512102,-165513203,-417432728,234183778,384184404,-228377636,386074937,-80794151},{-377467479,370722125,-229491859,223980307,-430484099,-406821011,353792719,-372702735,248476492},{397888561,-156899255,-464425023,175826949,-224983691,-439160035,409610097,429910736,-86888190},{-442713188,-401718544,324698177,400797208,387257343,-284459300,-44819584,-227610724,-161588302},{277088329,-273742149,152340070,407661190,-90792188,292295690,87015390,370169728,416158833},{-24556819,-480885323,-314715863,266308415,161377696,-448710547,425151942,476130060,80794151},{-332694701,-47610269,-299067442,365334182,100952934,-422092280,-120256205,-186155394,-248476492},{128131960,-498128077,277878004,-423442336,219054208,421256228,40880638,-53062500,-291920587}},
{{-422632936,-130161541,-7003897,479414629,-226575725,390336444,-423645815,365667886,-428620745},{-334880612,-70503322,226713099,-74685633,5221417,-126099357,-258674975,-449380162,95402474},{173671238,322243590,387447104,160352788,-364409220,24240924,247019213,-25042878,142758517},{-364508888,-184433092,-136360902,-226117392,267436632,-252590179,351660656,378007471,-333563465},{-237512039,377571517,218991882,96385916,174622201,252823132,-495007502,-161473632,190804948},{488810364,-18710640,148666126,198935581,149985801,-319367408,10273226,-382418519,380919508},{-359557411,76885024,-328200321,46317578,-450218687,-97787926,-103170957,-90051583,-95402474},{53422542,271238656,-11471297,-202039847,-148241011,183755027,115025003,453791210,-142758517},{117503536,146004077,71338155,-462757027,310517275,-55310657,-443478856,-89099793,190459754}},
{{-467031536,200555657,-74892646,-213860411,182481825,-118501742,385675785,-106939443,0},{-359394656,25511043,228567597,-468065269,-221954033,2638480,436283838,-452730249,0},{-434017540,-433390045,303364580,-209604658,-470525570,105259173,206897342,-167213231,0},{-183009040,-404846642,-437116508,452779574,-352295355,-14583548,-427643767,406237187,0},{-486590159,-97684662,206431507,234395742,427944221,444622221,-474680461,189941983,0},{-86512349,-239575135,-266696434,195768962,-51821343,83885697,347954769,356292201,0},{-242733752,-185378156,257898926,-383001612,-224640501,-274047299,16313540,-261062336,0},{-337465654,-106826670,164616909,-140335004,-409474429,-367971601,-420327878,-309799139,0},{-46837324,-336857666,394949080,-154623208,-49093620,138698619,-70473168,345273027,0}},
{{-337431110,228205185,101781782,43605098,-372791024,-236288921,303253983,0,0},{231614897,-53592907,-288142337,-327143721,128283519,408205817,-321508719,0,0},{-248677006,55703091,116629618,311314361,-239933963,-62651376,-343374490,0,0},{-485701468,246976328,171884964,-229552963,-195097444,122333601,486650838,0,0},{7737297,354894683,-197137869,-364980802,-153172304,-101070227,-406237227,0,0},{-146069229,-352523472,328326839,-125749769,470623988,-245997037,133292674,0,0},{229666151,370606425,-485606940,-239803412,195136511,-405499829,-417774122,0,0},{433387133,187913263,794861,-366053251,-275953683,-249617430,-487858965,0,0},{-6751641,-70914757,11386917,-393405752,-242888728,-229414605,53556021,0,0}},
{{-53109870,-53798785,-160263126,213568014,264006876,-303340280,0,0,0},{-356722100,349526595,-229014208,-123575994,85827658,328053872,0,0,0},{-363316869,-496962221,-124295306,224748991,24010930,480623444,0,0,0},{-267036111,417955429,-407344184,432824942,216402149,-244878803,0,0,0},{-322610311,-101318868,-71193447,-111259665,-221395960,401590548,0,0,0},{-281317082,450922763,321932201,-116303741,-21405199,75594468,0,0,0},{-146718170,386418064,412810038,89545170,334993259,-29273967,0,0,0},{26898601,-76150160,-260367079,11417204,-383087180,-303599154,0,0,0},{-369035612,50112612,-478819515,484996465,-299352533,-404770128,0,0,0}},
{{-48454038,355185053,-429661783,243044863,267780094,0,0,0,0},{112618898,-158367953,432292908,-470916700,297054008,0,0,0,0},{-83397055,-5719286,-375313427,-135366259,369209916,0,0,0,0},{-144304589,-120465195,155463618,-481365420,477530154,0,0,0,0},{-487343525,461124770,74519024,-171689669,-179785692,0,0,0,0},{-445057626,-221250636,329531647,-363591509,-368692232,0,0,0,0},{442865972,-432735127,-441016104,-9631324,-202341887,0,0,0,0},{-472796266,283670163,-53591057,-421177212,23764317,0,0,0,0},{-394029895,-458424891,209568672,-19739317,315481329,0,0,0,0}},
{{-107345966,-77624966,-146344728,267866391,0,0,0,0,0},{486011992,-429372375,-436485000,-410538611,0,0,0,0,0},{-423809753,80277377,31921666,-327190881,0,0,0,0,0},{339840305,-292448661,454784636,-315826509,0,0,0,0,0},{127778314,128911655,-268913238,184604936,0,0,0,0,0},{-405527489,-305790943,409895791,458412457,0,0,0,0,0},{-326925950,25192272,251529943,-101257255,0,0,0,0,0},{222903373,463932558,268894975,220251450,0,0,0,0,0},{-3,-499999997,-4,-500000003,0,0,0,0,0}},
{{0,0,0,0,0,0,0,0,0},{412552036,-349982766,464267225,0,0,0,0,0,0},{-137462033,-316540182,-250043154,0,0,0,0,0,0},{20275590,-195298957,357155181,0,0,0,0,0,0},{-427270198,90390742,357155190,0,0,0,0,0,0},{240758645,-64120530,464267227,0,0,0,0,0,0},{410284535,330884990,178577591,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0}} };
// --------------------------------------------------------------
vm res(TRM2 - 1);
// i1 方向に tbl[..][0], ..., tbl[..][TRM2-2] を延長する．
dump("------- solve_1D -------");
rep(i2, TRM2 - 1) {
dump("--- i2:", i2, "---");
vm seq; int offset = 0;
rep(i1, sz(tbl)) {
if (sz(tbl[i1]) <= i2) {
if (offset == i1) {
offset = i1 + 1;
continue;
}
else {
break;
}
}
seq.emplace_back(tbl[i1][i2]);
}
if (N - offset < 0) continue;
solve_1D(seq, N - offset, coefs1[i2]);
//dump("seq:", seq);
res[i2] = seq[N - offset];
}
vm pow_i1s(DEG1);
pow_i1s[0] = 1;
repi(d1, 1, DEG1 - 1) pow_i1s[d1] = pow_i1s[d1 - 1] * (N - TRM1 + 1);
// i2 方向に tbl[N][..] を延長する．
res.resize(M + 1);
repi(i2, TRM2 - 1, M) {
// 0 除算回避
if (i2 * 2 == N) { res[i2] = z1[i2]; continue; }
if (i2 == N && N % 2 == 0) { res[i2] = z2[i2 / 2]; continue; }
if (i2 == N && N % 2 == 1) { res[i2] = z3[i2 / 2]; continue; }
if (i2 == N + 1 && N % 2 == 0) { res[i2] = z4[i2 / 2]; continue; }
if (i2 == N + 1 && N % 2 == 1) { res[i2] = z5[(i2 - 1) / 2]; continue; }
mint dnm = 0;
mint pow_i2 = 1;
rep(d2, DEG2) {
rep(d1, DEG1) {
dnm += coefs[d1][0][d2] * pow_i1s[d1] * pow_i2;
}
pow_i2 *= i2 - TRM2 + 1;
}
mint num = 0;
repi(t2, 1, TRM2 - 1) {
mint pow_i2 = 1;
rep(d2, DEG2) {
rep(d1, DEG1) {
num += coefs[d1][t2][d2] * pow_i1s[d1] * pow_i2 * res[i2 - t2];
}
pow_i2 *= i2 - TRM2 + 1 + t2;
}
}
// dnm * tbl[N][i2] + num = 0 を解く．分母 0 に注意！
if (dnm == 0) {
dump("DIVISION BY ZERO at i1 =", N, "i2 =", i2);
Assert(dnm != 0);
}
res[i2] = -num / dnm;
}
return res;
}
vvm tbl = {
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40},
{1,6,19,37,61,91,127,169,217,271,331,397,469,547,631,721,817,919,1027,1141,1261,1387,1519,1657,1801,1951,2107,2269,2437,2611,2791,2977,3169,3367,3571,3781,3997,4219,4447,4681},
{1,8,27,64,125,216,343,512,729,1000,1331,1728,2197,2744,3375,4096,4913,5832,6859,8000,9261,10648,12167,13824,15625,17576,19683,21952,24389,27000,29791,32768,35937,39304,42875,46656,50653,54872,59319,64000},
{1,10,51,180,501,1131,2221,3951,6531,10201,15231,21921,30601,41631,55401,72331,92871,117501,146731,181101,221181,267571,320901,381831,451051,529281,617271,715801,825681,947751,1082881,1231971,1395951,1575781,1772451,1986981,2220421,2473851,2748381,3045151},
{1,12,73,284,835,2036,4347,8408,15069,25420,40821,62932,93743,135604,191255,263856,357017,474828,621889,803340,1024891,1292852,1614163,1996424,2447925,2977676,3595437,4311748,5137959,6086260,7169711,8402272,9798833,11375244,13148345,15135996,17357107,19831668,22580779,25626680},
{1,14,99,476,1765,5418,14407,33839,71835,140505,257069,445117,736009,1170415,1799995,2689219,3917327,5580429,7793745,10693985,14441869,19224787,25259599,32795575,42117475,53548769,67454997,84247269,104385905,128384215,156812419,190301707,229548439,275318485,328451705,389866569,460564917,541636859,634265815,739733695},
{1,16,129,704,2875,9456,26411,65024,144909,298000,573661,1045056,1816919,3034864,4896375,7663616,11678201,17378064,25316569,36184000,50831571,70298096,95839459,128961024,171453125,225429776,293370741,378167104,483170479,612246000,769829231,960987136,191483242,467847177,797448618,188575922,650519517,193660123,829562118,571071972},
{1,18,163,996,4645,17718,57799,166344,432073,1027351,2262853,4665259,9083725,16831423,29869081,51038083,84351319,135350605,211540123,322905961,482532463,707326729,18863228,444361166,17807727,781241229,786208468,95411580,784560031,944444115,683247096,129113494,432991862,771770905,351728534,412313980,230283716,124212698,459402898,653211837},
{1,20,201,1360,7001,29112,101941,310472,843471,2084752,4760723,10167312,20505043,39357332,72354003,128069584,219214133,364183164,589042693,930035504,436705438,175747890,235706564,732649276,816968713,681467993,570905284,793186930,732414240,864005518,772131845,169722862,921317010,69049527,862091291,789871282,619436821,437326618,696354075,267720788},
{1,22,243,1804,10165,46530,180775,614680,1871145,5188590,13286043,31735023,71282113,151590693,307025643,595289971,109940848,998067142,484703752,905893322,752684748,728784814,825055209,414576419,372584327,226227954,339800519,141863245,401515367,561966889,140546045,205323454,939662701,307215269,831169051,502936676,836936208,89673724,662989354,713076623},
{1,24,289,2336,14305,71000,297381,1081088,3486591,10154440,27100491,67081312,155545403,340670344,709621235,413986297,708384583,7534229,968656869,608015415,462684087,811376715,971363711,692240880,671630650,222856333,130293757,734535523,296768196,699930913,553367144,777875225,759384263,172011712,585079502,983863555,350515533,469816803,144297520,24875525},
{1,26,339,2964,19605,104910,474215,1866280,6539625,20758530,60511803,163786428,415382397,994338281,260193819,903157973,195605819,399138699,403813892,705357736,863671220,633366671,16287203,559023634,307650625,939789755,723458153,106029393,918344566,392182541,437844858,916760194,976319702,895505269,325505958,305030994,991390344,681980966,413338598,223550663},
{1,28,393,3696,26265,150780,729905,3066968,11422251,38322580,117380131,331910448,874684707,165706790,73073960,309535267,117884549,416342677,656230766,755419258,620617087,969546997,422293003,163526185,900131210,370719570,326163510,718205500,834308502,332742703,597902961,591693243,466728279,680205092,257942893,266230559,520678348,168521279,102792133,289658714},
{1,30,451,4540,34501,211546,1092231,4892536,19439241,69690006,228509259,692897076,960751942,217709231,141557428,499036480,184622865,785948861,427820047,642206371,460229836,984744981,581901786,780936648,306603433,770632620,880009099,135379683,552385284,721432419,441574823,287688769,32766536,274060523,538455658,437084050,226858985,824708055,625857587,456151283},
{1,32,513,5504,44545,290592,1594369,7579136,31898043,120811360,417094139,326538361,921273686,856112666,336172519,136000022,453001994,658085485,36735776,747039001,939887522,939021568,421651894,790896050,825419098,54998744,438499099,670459841,339545599,519490681,426984301,842407793,615134774,757145310,4872255,816564853,224479689,850536911,522574564,166065010},
{1,34,579,6596,56645,391782,2276743,11450248,50940297,203891370,744170955,504056126,838996636,6047309,710825814,417252479,472487324,347092189,180947277,197257496,631772355,778000569,334472808,690270877,882531830,367288119,631801515,684086783,55844214,256655053,677174812,650261992,2668506,849793813,168041696,25918845,49036888,134883668,872928398,222882599},
{1,36,649,7824,71065,519492,3188017,16915008,79305553,334088600,281236862,520425036,800941863,306193541,479494415,512154267,916329807,848171189,654862203,375827748,297771211,666146092,455337711,180219143,686246227,540361713,995877841,355665929,862594983,144011323,481006499,490502125,843961657,214490632,91514151,686520858,422035139,764408534,291106955,681655152},
{1,38,723,9196,88085,678642,4386151,24489176,120709737,534152510,150489261,963115411,367021376,959024041,112943753,111814874,128504077,869647520,186648829,113948318,87825311,628396651,253622684,157377664,762052576,212120117,409584493,429252267,394573144,809886106,918372836,911924458,720065884,760019842,420565346,855681509,549337043,63876022,212496130,181335179},
{1,40,801,10720,108001,874728,5939521,34814848,180013761,834876008,519333016,629091397,917305361,925012307,105901665,972170766,86148956,979288338,55582009,837772846,398876864,777839176,966068819,85614347,145635957,265541953,81917602,323675242,417003473,756465875,908892618,388403464,400943526,194288379,163743376,636510563,419868208,643938944,720410824,14852745},
{1,42,883,12404,131125,1113854,7928103,48682472,263511081,278400843,632794616,785434818,381816458,634380288,284957308,232260742,644641754,295493300,792778,191982598,3956231,94544338,326027200,884967917,21999170,802890825,461962906,284292047,937865001,994948702,123260479,127613361,66332297,297948121,291516179,58507577,678636828,524804817,514661979,524099445},
{1,44,969,14256,157785,1402764,10444721,67055296,379248849,921160773,832356225,249880213,401024118,225406661,559035196,854519088,6682481,815098836,895996641,996327102,891163767,920734317,734463270,700175710,860317853,795613016,717381165,462912233,111175378,186507629,650863758,554438350,523706928,621908261,257007259,157587811,138793906,992173726,107404262,357327563},
{1,46,1059,16284,188325,1748874,13596359,91096376,537400521,837810136,591327120,674268983,342691535,194562095,981966990,205927510,824008576,259127171,930666898,91268065,640583444,589688936,691751211,459963291,613797793,604619152,476089912,759363092,91791365,932115288,170303029,40776841,763318464,351094732,898879243,41844296,69554864,731345122,853757112,385705003},
{1,48,1153,18496,223105,2160304,17505537,122198272,750695169,125905812,555043061,820639157,834895512,304961259,613693996,44137590,152653661,759077468,158077476,976907134,296919518,752562105,671638569,170481719,99659308,833266097,347009389,967466805,737023396,733573333,139330773,699775600,767695590,951793998,563309640,973748137,385121983,517231826,957019103,96096871},
{1,50,1251,20900,262501,2645910,22311751,162015560,34908994,911509975,592458841,968141052,626379863,838832815,765068468,55727685,564217481,185779089,80270499,186490927,46497813,868628581,202471848,482697810,708092282,722046640,164758037,960696241,323674434,710306979,839130719,284095248,930347629,334775585,940425722,617485636,79101125,690629397,611035375,602650399},
{1,52,1353,23504,306905,3215316,28172977,212500288,409424842,355843804,859812613,420412492,14933393,469745464,794316340,726179594,970603149,87998888,562454825,209796560,608841319,661476196,677723496,929166733,118756655,29249457,350082331,251752820,132224199,34451936,208705352,989603137,200541338,476172051,372665451,93859216,140536348,313183931,453689324,68326578},
{1,54,1459,26316,356725,3878946,35267239,275940504,897865634,663134273,878790683,159015774,594361659,89441109,653634506,642525318,72157435,871731288,687351285,35782289,883963466,880259763,862782869,601576048,216328963,628846605,60856517,680408420,615439574,497351151,668399214,282408228,350913096,19712966,123400879,18554252,386881591,533785549,373885911,24564170},
{1,56,1569,29344,412385,4648056,43794241,355001984,528808115,89808008,631732957,669539407,422916833,106719594,809678609,947805913,375577228,583382180,648136094,899710093,663841893,68811845,612633922,955218147,470452416,694945240,101122433,811288900,368127076,181571011,443084222,626293292,99540782,468213454,663108288,770253931,519652632,587388377,136160051,523150216},
{1,58,1683,32596,474325,5534766,53977063,452773288,336583380,955199503,676740461,978012818,70469044,600105471,556620267,552370488,558963272,224127518,392263046,842614707,935845683,713045622,997511401,489378701,263509915,700721701,672812163,146021889,903857504,278149373,442163315,357400663,356464217,293563732,985728217,402388996,180253630,347080161,496421533,125352845},
{1,60,1801,36080,543001,6552092,66063921,572814272,362170933,653953809,285893759,940647031,989128886,659703394,816429125,770302353,92382704,570200456,507306035,744161108,954532109,362823729,255217608,676920353,728186562,931389383,418879847,223533408,831160564,159111388,512791401,705241694,554747425,468621341,442903950,379202448,60099951,271271630,846351797,313594289},
{1,62,1923,39804,618885,7713978,80329991,719208184,654193382,670318117,610165678,836706461,766482364,415314630,891447142,633296126,595469611,452067632,708147000,815494671,936180464,484217924,391703691,496636562,841348137,903179930,302777182,894742343,355420928,723573286,317472375,766038487,229071225,274339588,937374599,562756822,441777149,778982933,864063505,484402550},
{1,64,2049,43776,702465,9035328,97079297,896617472,270019024,594530516,875014304,321886429,925075247,106872227,413633992,938377253,566062593,848662439,254245732,397676616,871610825,913594801,301265434,511704298,210319090,462247905,319044346,118183380,605639260,253919181,837557707,766961731,172515187,800980978,159004696,897586637,533116731,912616623,767693359,375707842},
{1,66,2179,48004,794245,10532038,116646663,110343425,276979914,141529447,611074260,807974986,54936648,86884115,607390334,959401572,64921787,446744975,36320017,309751348,858499464,579321075,596462675,377866129,385594521,475835658,516561953,960764871,852650564,73693721,414776746,472895822,265124371,767074750,465033260,696640252,606732467,690336941,171597358,742470114},
{1,68,2313,52496,894745,12221028,139399729,366389817,753713156,172222510,924826217,343875449,206787076,348607839,42882281,609674180,633997532,812058088,878195527,564192052,740398448,467898549,259068576,423347880,305856984,64008428,948332183,345462153,374834906,351624614,735279272,546141104,298931207,147090427,536365159,804410785,558345541,661427068,483898886,697070429},
{1,70,2451,57260,1004501,14120274,165741031,671530577,791633543,717569202,814617922,83319574,633982099,189377007,580867127,233423581,477095286,256757098,31150657,634680573,752532652,476456061,813983745,301623962,527053626,377374105,81522360,255395036,720009950,924384563,543573914,538906293,159931419,787245666,310143074,15284168,257130666,177625731,834919621,123122249},
{1,72,2593,62304,1124065,16248840,196110145,33381746,496545859,5748590,537935707,435873196,153174862,976533968,746778095,561068796,271587656,5440033,218212551,59317419,595694518,666680132,638009749,291742254,631492183,351592435,433205645,931973640,888912417,957905532,963623374,394664222,134593791,724205195,556787609,735167317,23469814,321236177,796219510,627794147},
{1,74,2739,67636,1254005,18626910,230985895,460477786,990405391,492699833,36384123,10193019,599241077,728949900,452261949,760108833,592765278,869792967,168580781,421107580,726678820,648451977,89653632,936902793,728437228,253076968,141040897,824818687,820918845,436818481,165071086,443762361,503771541,209795504,960385285,526038666,375020309,648438851,116188968,719014523},
{1,76,2889,73264,1394905,21275820,270888625,962352306,413235469,896340686,425424635,472001777,81435866,409626836,590838678,803209453,156083550,618641788,657015529,901440335,118474526,93750191,584425600,896224695,236669306,537387540,520994296,16829165,828857812,489127582,958181360,87127326,933883914,602914197,733302034,420250541,165095921,402466567,422249787,504171421},
{1,78,3043,79196,1547365,24218090,316382535,549623459,925211227,234787368,556552682,453979087,7416723,498479425,498944932,892993056,852286052,627011383,902668693,806388098,447582250,611693585,889041312,931051059,664957231,45717599,802110028,918479892,646446851,277888647,768957329,470749011,728908035,648167992,451175769,910788272,757883680,157137635,606745138,411834579} };
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変数係数線形漸化式を復元する．
//【使い方】
// 1. vm tbl = naive() を実装する．
// 2. coefs = embed_coefs(tbl, TRM1_ini, DEG1_ini, TRM2_ini, DEG2_ini, LLL); を実行する．
// 3. 出力を solve() 内に貼る．
// 4. solve(tbl, n, m, [coefs]) で勝手に tbl[n][0..m] を求めてくれる．
// 愚直解を用意する．再計算がイヤなら埋め込む．
//auto tbl = naive();
//return 0;
// (2i, i) のところだけ抜き出して 1D P-recursive する．
{
if (0) {
int N = 50;
z1.resize(N);
rep(i, N) {
dump("i:", i);
z1[i] = naive_sub(i * 2, i);
}
string eb;
eb += "vm z1 = {";
rep(i, sz(z1)) {
eb += to_string(z1[i].val()) + ",";
}
eb.pop_back();
eb += "};\n";
cout << eb;
}
// 引数：seq, TRM_ini, DEG_ini, LLL?
auto coefs = embed_coefs_1D(z1, 1, 1, 0);
solve_1D(z1, 2000, coefs);
//return 0;
}
// (2i, 2i) のところだけ抜き出して 1D P-recursive する．
{
if (0) {
int N = 50;
z2.resize(N);
rep(i, N) {
dump("i:", i);
z2[i] = naive_sub(2 * i, 2 * i);
}
string eb;
eb += "vm z2 = {";
rep(i, sz(z2)) {
eb += to_string(z2[i].val()) + ",";
}
eb.pop_back();
eb += "};\n";
cout << eb;
}
// 引数：seq, TRM_ini, DEG_ini, LLL?
auto coefs = embed_coefs_1D(z2, 1, 1, 0);
solve_1D(z2, 2000, coefs);
//return 0;
}
// (2i+1, 2i+1) のところだけ抜き出して 1D P-recursive する．
{
if (0) {
int N = 80;
z3.resize(N);
rep(i, N) {
dump("i:", i);
z3[i] = naive_sub(2 * i + 1, 2 * i + 1);
}
string eb;
eb += "vm z3 = {";
rep(i, sz(z3)) {
eb += to_string(z3[i].val()) + ",";
}
eb.pop_back();
eb += "};\n";
cout << eb;
}
// 引数：seq, TRM_ini, DEG_ini, LLL?
auto coefs = embed_coefs_1D(z3, 1, 1, 0);
solve_1D(z3, 2000, coefs);
//return 0;
}
// (2i, 2i+1) のところだけ抜き出して 1D P-recursive する．
{
if (0) {
int N = 50;
z4.resize(N);
rep(i, N) {
dump("i:", i);
z4[i] = naive_sub(2 * i, 2 * i + 1);
}
string eb;
eb += "vm z4 = {";
rep(i, sz(z4)) {
eb += to_string(z4[i].val()) + ",";
}
eb.pop_back();
eb += "};\n";
cout << eb;
}
// 引数：seq, TRM_ini, DEG_ini, LLL?
auto coefs = embed_coefs_1D(z4, 1, 1, 0);
solve_1D(z4, 2000, coefs);
//return 0;
}
// (2i+1, 2i+2) のところだけ抜き出して 1D P-recursive する．
{
if (0) {
int N = 80;
z5.resize(N);
rep(i, N) {
dump("i:", i);
z5[i] = naive_sub(2 * i + 1, 2 * i + 2);
}
string eb;
eb += "vm z5 = {";
rep(i, sz(z5)) {
eb += to_string(z5[i].val()) + ",";
}
eb.pop_back();
eb += "};\n";
cout << eb;
}
// 引数：seq, TRM_ini, DEG_ini, LLL?
auto coefs = embed_coefs_1D(z5, 1, 1, 0);
solve_1D(z5, 2000, coefs);
//return 0;
}
// 愚直解を渡して変数係数線形漸化式の係数を得る．再計算がイヤなら埋め込む．
// 引数：tbl, DEG1_ini, TRM2_ini, DEG2_ini, LLL?
// auto [coefs1, coefs] = embed_coefs_2D(tbl, 9, 9, 9, 0);
// 0 除算チェック
//repi(n, 1, 50) {
// int m = 100;
// auto seq = solve_2D(tbl, n, m, coefs1, coefs);
//}
//return 0;
int n, m;
cin >> n >> m;
// 2 次元数列 tbl を元に seq = tbl[n][0..m] を計算する．
// 整理すると綺麗な式になるなら FullSimplify[] すると速くなる．
// auto seq = solve_2D(tbl, n, m, coefs1, coefs);
auto seq = solve_2D(tbl, n, m);
//dump(seq);
mint res = seq[m];
EXIT(res);
}