/**
 *	author: nok0
 *	created: 2021.04.17 21:31:09
**/
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif

#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif

#pragma region Macros
// rep macro
#define foa(v, a) for(auto &v : a)
#define REPname(a, b, c, d, e, ...) e
#define REP(...) REPname(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__)
#define REP0(x) for(int i = 0; i < (x); ++i)
#define REP1(i, x) for(int i = 0; i < (x); ++i)
#define REP2(i, l, r) for(int i = (l); i < (r); ++i)
#define REP3(i, l, r, c) for(int i = (l); i < (r); i += (c))
#define REPSname(a, b, c, ...) c
#define REPS(...) REPSname(__VA_ARGS__, REPS1, REPS0)(__VA_ARGS__)
#define REPS0(x) for(int i = 1; i <= (x); ++i)
#define REPS1(i, x) for(int i = 1; i <= (x); ++i)
#define RREPname(a, b, c, d, e, ...) e
#define RREP(...) RREPname(__VA_ARGS__, RREP3, RREP2, RREP1, RREP0)(__VA_ARGS__)
#define RREP0(x) for(int i = (x)-1; i >= 0; --i)
#define RREP1(i, x) for(int i = (x)-1; i >= 0; --i)
#define RREP2(i, r, l) for(int i = (r)-1; i >= (l); --i)
#define RREP3(i, r, l, c) for(int i = (r)-1; i >= (l); i -= (c))
#define RREPSname(a, b, c, ...) c
#define RREPS(...) RREPSname(__VA_ARGS__, RREPS1, RREPS0)(__VA_ARGS__)
#define RREPS0(x) for(int i = (x); i >= 1; --i)
#define RREPS1(i, x) for(int i = (x); i >= 1; --i)

// name macro
#define pb push_back
#define eb emplace_back
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template <class T = int>
using V = std::vector<T>;
template <class T = int>
using VV = std::vector<std::vector<T>>;
template <class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;

// input macro
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
	is >> p.first >> p.second;
	return is;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
	for(T &i : v) is >> i;
	return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
	std::string s;
	is >> s;
	__int128_t ret = 0;
	for(int i = 0; i < s.length(); i++)
		if('0' <= s[i] and s[i] <= '9')
			ret = 10 * ret + s[i] - '0';
	a = ret * (s[0] == '-' ? -1 : 1);
	return is;
}
#if __has_include(<atcoder/all>)
std::istream &operator>>(std::istream &is, atcoder::modint998244353 &a) {
	long long v;
	is >> v;
	a = v;
	return is;
}
std::istream &operator>>(std::istream &is, atcoder::modint1000000007 &a) {
	long long v;
	is >> v;
	a = v;
	return is;
}
template <int m>
std::istream &operator>>(std::istream &is, atcoder::static_modint<m> &a) {
	long long v;
	is >> v;
	a = v;
	return is;
}
template <int m>
std::istream &operator>>(std::istream &is, atcoder::dynamic_modint<m> &a) {
	long long v;
	is >> v;
	a = v;
	return is;
}
#endif
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template <class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template <class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &... tail) {
	scan(head);
	INPUT(tail...);
}
}  // namespace scanner
#define VEC(type, name, size)     \
	std::vector<type> name(size); \
	scanner::INPUT(name)
#define VVEC(type, name, h, w)                                    \
	std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
	scanner::INPUT(name)
#define INT(...)     \
	int __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LL(...)            \
	long long __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define STR(...)             \
	std::string __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define CHAR(...)     \
	char __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...)     \
	double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LD(...)              \
	long double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)

// output-macro
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
	for(int i = 0; i < int(a.size()); ++i) {
		if(i) os << " ";
		os << a[i];
	}
	return os;
}
std::ostream &operator<<(std::ostream &dest, __int128_t &value) {
	std::ostream::sentry s(dest);
	if(s) {
		__uint128_t tmp = value < 0 ? -value : value;
		char buffer[128];
		char *d = std::end(buffer);
		do {
			--d;
			*d = "0123456789"[tmp % 10];
			tmp /= 10;
		} while(tmp != 0);
		if(value < 0) {
			--d;
			*d = '-';
		}
		int len = std::end(buffer) - d;
		if(dest.rdbuf()->sputn(d, len) != len) {
			dest.setstate(std::ios_base::badbit);
		}
	}
	return dest;
}
#if __has_include(<atcoder/all>)
std::ostream &operator<<(std::ostream &os, const atcoder::modint998244353 &a) { return os << a.val(); }
std::ostream &operator<<(std::ostream &os, const atcoder::modint1000000007 &a) { return os << a.val(); }
template <int m>
std::ostream &operator<<(std::ostream &os, const atcoder::static_modint<m> &a) { return os << a.val(); }
template <int m>
std::ostream &operator<<(std::ostream &os, const atcoder::dynamic_modint<m> &a) { return os << a.val(); }
#endif
template <class T>
void print(const T a) { std::cout << a << '\n'; }
template <class Head, class... Tail>
void print(Head H, Tail... T) {
	std::cout << H << ' ';
	print(T...);
}
template <class T>
void printel(const T a) { std::cout << a << '\n'; }
template <class T>
void printel(const std::vector<T> &a) {
	for(const auto &v : a)
		std::cout << v << '\n';
}
template <class Head, class... Tail>
void printel(Head H, Tail... T) {
	std::cout << H << '\n';
	printel(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
void err(const bool b = true) {
	if(b) {
		std::cout << "-1\n", exit(0);
	}
}

//debug macro
namespace debugger {
template <class T>
void view(const std::vector<T> &a) {
	std::cerr << "{ ";
	for(const auto &v : a) {
		std::cerr << v << ", ";
	}
	std::cerr << "\b\b }";
}
template <class T>
void view(const std::vector<std::vector<T>> &a) {
	std::cerr << "{\n";
	for(const auto &v : a) {
		std::cerr << "\t";
		view(v);
		std::cerr << "\n";
	}
	std::cerr << "}";
}
template <class T, class U>
void view(const std::vector<std::pair<T, U>> &a) {
	std::cerr << "{\n";
	for(const auto &p : a) std::cerr << "\t(" << p.first << ", " << p.second << ")\n";
	std::cerr << "}";
}
template <class T, class U>
void view(const std::map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &p : m) std::cerr << "\t[" << p.first << "] : " << p.second << "\n";
	std::cerr << "}";
}
template <class T, class U>
void view(const std::pair<T, U> &p) { std::cerr << "(" << p.first << ", " << p.second << ")"; }
template <class T>
void view(const std::set<T> &s) {
	std::cerr << "{ ";
	for(auto &v : s) {
		view(v);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <class T>
void view(const T &e) { std::cerr << e; }
}  // namespace debugger
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
	debugger::view(H);
	std::cerr << ", ";
	debug_out(T...);
}
#define debug(...)                                                \
	do {                                                          \
		std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
		debug_out(__VA_ARGS__);                                   \
		std::cerr << "\b\b]\n";                                   \
	} while(false)
#else
#define debug(...) (void(0))
#endif

// vector macro
template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
	std::sort(a.begin(), a.end());
	a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
	auto res = a;
	UNIQUE(res);
	for(auto &v : a)
		v = lb(res, v);
	return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a) std::sort((a).begin(), (a).end())
#define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x) {
	for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v -= x;
}
template <class T>
void MUL(std::vector<T> &a, const T x) {
	for(auto &v : a) v *= x;
}
template <class T>
void DIV(std::vector<T> &a, const T x) {
	for(auto &v : a) v /= x;
}

// math macro
template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
	T ret = 1;
	while(n) {
		if(n & 1) ret *= a;
		a *= a;
		n >>= 1;
	}
	return ret;
}
// modpow
long long POW(long long a, long long n, const int mod) {
	long long ret = 1;
	while(n) {
		if(n & 1) (ret *= a) %= mod;
		(a *= a) %= mod;
		n >>= 1;
	}
	return ret;
}

// others
struct fast_io {
	fast_io() {
		ios::sync_with_stdio(false);
		cin.tie(nullptr);
		cout << fixed << setprecision(15);
	}
} fast_io_;
const int inf = 1e9;
const ll INF = 1e18;
#pragma endregion

#pragma region Math Formal Power Series
enum Mode {
	FAST = 1,
	NAIVE = -1,
};
template <class T, Mode mode = FAST>
struct FormalPowerSeries : std::vector<T> {
	using std::vector<T>::vector;
	using std::vector<T>::size;
	using std::vector<T>::resize;
	using std::vector<T>::begin;
	using std::vector<T>::insert;
	using std::vector<T>::erase;
	using F = FormalPowerSeries;
	using S = std::vector<std::pair<int, T>>;

	F &operator+=(const F &g) {
		for(int i = 0; i < int(std::min((*this).size(), g.size())); i++) (*this)[i] += g[i];
		return *this;
	}

	F &operator+=(const T &t) {
		assert(int((*this).size()));
		(*this)[0] += t;
		return *this;
	}

	F &operator-=(const F &g) {
		for(int i = 0; i < int(std::min((*this).size(), g.size())); i++) (*this)[i] -= g[i];
		return *this;
	}

	F &operator-=(const T &t) {
		assert(int((*this).size()));
		(*this)[0] -= t;
		return *this;
	}

	F &operator*=(const T &t) {
		for(int i = 0; i < int((*this).size()); ++i) (*this)[i] *= t;
		return *this;
	}

	F &operator/=(const T &t) {
		T div = t.inv();
		for(int i = 0; i < int((*this).size()); ++i) (*this)[i] *= div;
		return *this;
	}

	F &operator>>=(const int sz) {
		assert(sz >= 0);
		int n = (*this).size();
		(*this).erase((*this).begin(), (*this).begin() + std::min(sz, n));
		(*this).resize(n);
		return *this;
	}

	F &operator<<=(const int sz) {
		assert(sz >= 0);
		int n = (*this).size();
		(*this).insert((*this).begin(), sz, T(0));
		(*this).resize(n);
		return *this;
	}

	F &operator%=(const F &g) { return *this -= *this / g * g; }

	F &operator=(const std::vector<T> &v) {
		int n = (*this).size();
		for(int i = 0; i < n; ++i) (*this)[i] = v[i];
		return *this;
	}

	F operator-() const {
		F ret = *this;
		return ret * -1;
	}

	F &operator*=(const F &g) {
		if(mode == FAST) {
			int n = (*this).size();
			auto tmp = atcoder::convolution(*this, g);
			for(int i = 0; i < n; ++i) (*this)[i] = tmp[i];
			return *this;
		} else {
			int n = (*this).size(), m = g.size();
			for(int i = n - 1; i >= 0; --i) {
				(*this)[i] *= g[0];
				for(int j = 1; j < std::min(i + 1, m); j++)
					(*this)[i] += (*this)[i - j] * g[j];
			}
			return *this;
		}
	}

	F &operator/=(const F &g) {
		if((*this).size() < g.size()) {
			(*this).assign((*this).size(), T(0));
			return *this;
		}
		if(mode == FAST) {
			int old = (*this).size();
			int n = (*this).size() - g.size() + 1;
			*this = ((*this).rev().pre(n) * g.rev().inv(n));
			(*this).rev_inplace();
			(*this).resize(old);
			return *this;
		} else {
			assert(g[0] != T(0));
			T ig0 = g[0].inv();
			int n = (*this).size(), m = g.size();
			for(int i = 0; i < n; ++i) {
				for(int j = 1; j < std::min(i + 1, m); ++j)
					(*this)[i] -= (*this)[i - j] * g[j];
				(*this)[i] *= ig0;
			}
			return *this;
		}
	}

	F &operator*=(S g) {
		int n = (*this).size();
		auto [d, c] = g.front();
		if(!d)
			g.erase(g.begin());
		else
			c = 0;
		for(int i = n - 1; i >= 0; --i) {
			(*this)[i] *= c;
			for(auto &[j, b] : g) {
				if(j > i) break;
				(*this)[i] += (*this)[i - j] * b;
			}
		}
		return *this;
	}

	F &operator/=(S g) {
		int n = (*this).size();
		auto [d, c] = g.front();
		assert(!d and c != 0);
		T ic = c.inv();
		g.erase(g.begin());
		for(int i = 0; i < n; ++i) {
			for(auto &[j, b] : g) {
				if(j > i) break;
				(*this)[i] -= (*this)[i - j] * b;
			}
			(*this)[i] *= ic;
		}
		return *this;
	}

	F operator+(const F &g) const { return F(*this) += g; }

	F operator+(const T &t) const { return F(*this) += t; }

	F operator-(const F &g) const { return F(*this) -= g; }

	F operator-(const T &t) const { return F(*this) -= t; }

	F operator*(const F &g) const { return F(*this) *= g; }

	F operator*(const T &t) const { return F(*this) *= t; }

	F operator/(const F &g) const { return F(*this) /= g; }

	F operator/(const T &t) const { return F(*this) /= t; }

	F operator%(const F &g) const { return F(*this) %= g; }

	F operator*=(const S &g) const { return F(*this) *= g; }

	F operator/=(const S &g) const { return F(*this) /= g; }

	F pre(int d) const { return F((*this).begin(), (*this).begin() + std::min((int)(*this).size(), d)); }

	F &shrink() {
		while(!(*this).empty() and (*this).back() == T(0)) (*this).pop_back();
		return *this;
	}

	F &rev_inplace() {
		reverse((*this).begin(), (*this).end());
		return *this;
	}
	F rev() const { return F(*this).rev_inplace(); }

	// *=(1 + cz^d)
	F &multiply(const int d, const T c) {
		int n = (*this).size();
		if(c == T(1))
			for(int i = n - d - 1; i >= 0; --i)
				(*this)[i + d] += (*this)[i];
		else if(c == T(-1))
			for(int i = n - d - 1; i >= 0; --i)
				(*this)[i + d] -= (*this)[i];
		else
			for(int i = n - d - 1; i >= 0; --i)
				(*this)[i + d] += (*this)[i] * c;
		return *this;
	}
	// /=(1 + cz^d)
	F &divide(const int d, const T c) {
		int n = (*this).size();
		if(c == T(1))
			for(int i = 0; i < n - d; ++i) (*this)[i + d] -= (*this)[i];
		else if(c == T(-1))
			for(int i = 0; i < n - d; ++i) (*this)[i + d] += (*this)[i];
		else
			for(int i = 0; i < n - d; ++i) (*this)[i + d] -= (*this)[i] * c;
		return *this;
	}

	//Ο(N)
	T eval(const T &t) const {
		int n = (*this).size();
		T res = 0, tmp = 1;
		for(int i = 0; i < n; ++i) res += (*this)[i] * tmp, tmp *= t;
		return res;
	}

	F inv(int deg = -1) const {
		int n = (*this).size();
		assert(mode == FAST and n and (*this)[0] != 0);
		if(deg == -1) deg = n;
		assert(deg > 0);
		F res{(*this)[0].inv()};
		while(int(res.size()) < deg) {
			int m = res.size();
			F f((*this).begin(), (*this).begin() + std::min(n, m * 2)), r(res);
			f.resize(m * 2), atcoder::internal::butterfly(f);
			r.resize(m * 2), atcoder::internal::butterfly(r);
			for(int i = 0; i < m * 2; ++i) f[i] *= r[i];
			atcoder::internal::butterfly_inv(f);
			f.erase(f.begin(), f.begin() + m);
			f.resize(m * 2), atcoder::internal::butterfly(f);
			for(int i = 0; i < m * 2; ++i) f[i] *= r[i];
			atcoder::internal::butterfly_inv(f);
			T iz = T(m * 2).inv();
			iz *= -iz;
			for(int i = 0; i < m; ++i) f[i] *= iz;
			res.insert(res.end(), f.begin(), f.begin() + m);
		}
		res.resize(deg);
		return res;
	}

	//Ο(N)
	F &diff_inplace() {
		int n = (*this).size();
		for(int i = 1; i < n; ++i) (*this)[i - 1] = (*this)[i] * i;
		(*this)[n - 1] = 0;
		return *this;
	}
	F diff() const { F(*this).diff_inplace(); }

	//Ο(N)
	F &integral_inplace() {
		int n = (*this).size(), mod = T::mod();
		std::vector<T> inv(n);
		{
			inv[1] = 1;
			for(int i = 2; i < n; ++i)
				inv[i] = T(mod) - inv[mod % i] * (mod / i);
		}
		for(int i = n - 2; i >= 0; --i) (*this)[i + 1] = (*this)[i] * inv[i + 1];
		(*this)[0] = 0;
		return *this;
	}
	F integral() const { return F(*this).integral_inplace(); }

	//Ο(NlogN)
	F &log_inplace() {
		int n = (*this).size();
		assert(n and (*this)[0] == 1);
		F f_inv = (*this).inv();
		(*this).diff_inplace();
		(*this) *= f_inv;
		(*this).integral_inplace();
		return *this;
	}
	F log() const { return F(*this).log_inplace(); }

	//Ο(NlogN)
	F &deriv_inplace() {
		int n = (*this).size();
		assert(n);
		for(int i = 2; i < n; ++i) (*this)[i] *= i;
		(*this).erase((*this).begin());
		(*this).push_back(0);
		return *this;
	}
	F deriv() const { return F(*this).deriv_inplace(); }

	//Ο(NlogN)
	F &exp_inplace() {
		int n = (*this).size();
		assert(n and (*this)[0] == 0);
		F g{1};
		(*this)[0] = 1;
		F h_drv((*this).deriv());
		for(int m = 1; m < n; m *= 2) {
			F f((*this).begin(), (*this).begin() + m);
			f.resize(2 * m), atcoder::internal::butterfly(f);
			auto mult_f = [&](F &p) {
				p.resize(2 * m);
				atcoder::internal::butterfly(p);
				for(int i = 0; i < 2 * m; ++i) p[i] *= f[i];
				atcoder::internal::butterfly_inv(p);
				p /= 2 * m;
			};
			if(m > 1) {
				F g_(g);
				g_.resize(2 * m), atcoder::internal::butterfly(g_);
				for(int i = 0; i < 2 * m; ++i) g_[i] *= g_[i] * f[i];
				atcoder::internal::butterfly_inv(g_);
				T iz = T(-2 * m).inv();
				g_ *= iz;
				g.insert(g.end(), g_.begin() + m / 2, g_.begin() + m);
			}
			F t((*this).begin(), (*this).begin() + m);
			t.deriv_inplace();
			{
				F r{h_drv.begin(), h_drv.begin() + m - 1};
				mult_f(r);
				for(int i = 0; i < m; ++i) t[i] -= r[i] + r[m + i];
			}
			t.insert(t.begin(), t.back());
			t.pop_back();
			t *= g;
			F v((*this).begin() + m, (*this).begin() + std::min(n, 2 * m));
			v.resize(m);
			t.insert(t.begin(), m - 1, 0);
			t.push_back(0);
			t.integral_inplace();
			for(int i = 0; i < m; ++i) v[i] -= t[m + i];
			mult_f(v);
			for(int i = 0; i < std::min(n - m, m); ++i)
				(*this)[m + i] = v[i];
		}
		return *this;
	}
	F exp() const { return F(*this).exp_inplace(); }

	//Ο(NlogN)
	F &pow_inplace(long long k) {
		int n = (*this).size(), l = 0;
		assert(k >= 0);
		if(!k) {
			for(int i = 0; i < n; ++i) (*this)[i] = !i;
			return *this;
		}
		while(l < n and (*this)[l] == 0) ++l;
		if(l > (n - 1) / k or l == n) return *this = F(n);
		T c = (*this)[l];
		(*this).erase((*this).begin(), (*this).begin() + l);
		(*this) /= c;
		(*this).log_inplace();
		(*this).resize(n - l * k);
		(*this) *= k;
		(*this).exp_inplace();
		(*this) *= c.pow(k);
		(*this).insert((*this).begin(), l * k, 0);
		return *this;
	}
	F pow(const long long k) const { return F(*this).pow_inplace(k); }

	//Ο(NlogN)
	F sqrt(int deg = -1) const {
		auto SQRT = [&](T t) {
			int mod = T::mod();
			if(t == 0 or t == 1) return t;
			int v = (mod - 1) / 2;
			if(t.pow(v) != 1) return T(-1);
			int q = mod - 1, m = 0;
			while(~q & 1) q >>= 1, m++;
			std::mt19937 mt;
			T z = mt();
			while(z.pow(v) != mod - 1) z = mt();
			T c = z.pow(q), u = t.pow(q), r = t.pow((q + 1) / 2);
			for(; m > 1; m--) {
				T tmp = u.pow(1 << (m - 2));
				if(tmp != 1) r = r * c, u = u * c * c;
				c = c * c;
			}
			return T(std::min(r.val(), mod - r.val()));
		};
		int n = (*this).size();
		if(deg == -1) deg = n;
		if((*this)[0] == 0) {
			for(int i = 1; i < n; i++) {
				if((*this)[i] != 0) {
					if(i & 1) return F(0);
					if(deg - i / 2 <= 0) break;
					auto ret = (*this);
					ret >>= i;
					ret.resize(n - i);
					ret = ret.sqrt(deg - i / 2);
					if(ret.empty()) return F(0);
					ret <<= (i / 2);
					ret.resize(deg);
					return ret;
				}
			}
			return F(deg);
		}
		auto sqr = SQRT((*this)[0]);
		if(sqr * sqr != (*this)[0]) return F(0);
		F ret{sqr};
		T ti = T(1) / T(2);
		for(int i = 1; i < deg; i <<= 1) {
			auto u = (*this);
			u.resize(i << 1);
			ret = (ret.inv(i << 1) * u + ret) * ti;
		}
		ret.resize(deg);
		return ret;
	}

	void sparse_pow(const int n, const int d, const T c, const int k);
	void sparse_pow_inv(const int n, const int d, const T c, const int k);
	void stirling_first(int n);
	void stirling_second(int n);
	std::vector<T> multipoint_evaluation(const std::vector<T> &p);
};
#pragma endregion

template <class F>
F Berlekamp_Massey(const F &a) {
	using T = typename F::value_type;
	int n = a.size();
	F c{-1}, c2{0};
	T r2 = 1;
	int i2 = -1;
	for(int i = 0; i < n; i++) {
		T r = 0;
		int d = c.size();
		for(int j = 0; j < d; j++) r += c[j] * a[i - j];
		if(r == 0) continue;
		T coef = -r / r2;
		int d2 = c2.size();
		if(d - i >= d2 - i2) {
			for(int j = 0; j < d2; j++)
				c[j + i - i2] += c2[j] * coef;
		} else {
			F tmp(c);
			c.resize(d2 + i - i2);
			for(int j = 0; j < d2; j++) c[j + i - i2] += c2[j] * coef;
			c2 = std::move(tmp);
			i2 = i, r2 = r;
		}
	}
	return {c.begin() + 1, c.end()};
}

//return generating function of a, s.t. F(x) = P(x) / Q(x)
template <class F>
std::pair<F, F> find_generating_function(F a) {
	auto q = Berlekamp_Massey(a);
	int d = q.size();
	a.resize(d);
	q.insert(q.begin(), 1);
	for(int i = 1; i < (int)q.size(); i++) q[i] *= -1;
	a *= q;
	return {a, q};
}

//return [x^k] p(x) / q(x)
template <class T, Mode mode>
T compute_Kthterm(FormalPowerSeries<T, mode> p, FormalPowerSeries<T, mode> q, long long k) {
	int d = q.size();
	assert(q[0] == 1 and p.size() + 1 <= d);
	while(k) {
		auto q_minus = q;
		for(int i = 1; i < d; i += 2)
			q_minus[i] *= -1;
		p.resize(2 * d);
		q.resize(2 * d);
		p *= q_minus;
		q *= q_minus;
		for(int i = 0; i < d - 1; i++)
			p[i] = p[(i << 1) | (k & 1)];
		for(int i = 0; i < d; i++)
			q[i] = q[i << 1];
		p.resize(d - 1);
		q.resize(d);
		k >>= 1;
	}
	return p[0];
}

template <class T, Mode mode>
T compute_Kthterm(std::pair<FormalPowerSeries<T, mode>, FormalPowerSeries<T, mode>> f, long long k) { return compute_Kthterm(f.first, f.second, k); }
using fps = FormalPowerSeries<modint1000000007, NAIVE>;

void main_() {
	INT(n);
	fps a = {
	    1, 12, 65, 172, 297, 456, 649, 876, 1137, 1432, 1761, 2124, 2521, 2952, 3417};
	auto f = find_generating_function(a);
	print(compute_Kthterm(f, n));
}

int main() {
	int t = 1;
	//cin >> t;
	while(t--) main_();
	return 0;
}