|FPS|[fps.cpp](fps.cpp)|形式的べき級数|

using vm = vector<mint>;

struct fps : vm {

#define d (*this)

#define s int(vm::size())

template<class...Args> fps(Args...args): vm(args...) {}

fps(initializer_list<mint> a): vm(a.begin(),a.end()) {}

void rsz(int n) { if (s < n) resize(n);}

mint& operator[](int i) { rsz(i+1); return vm::operator[](i);}

mint operator[](int i) const { return i<s ? vm::operator[](i) : 0;}

mint operator()(mint x) const {

mint r;

for (int i = s-1; i >= 0; --i) r = r*x+d[i];

return r;

}

fps operator-() const { fps r(d); rep(i,s) r[i] = -r[i]; return r;}

fps& operator+=(const fps& a) { rsz(a.size()); rep(i,a.size()) d[i] += a[i]; return d;}

fps& operator-=(const fps& a) { rsz(a.size()); rep(i,a.size()) d[i] -= a[i]; return d;}

fps& operator*=(const fps& a) { return d = convolution(d, a);}

fps& operator*=(mint a) { rep(i,s) d[i] *= a; return *this;}

fps& operator/=(mint a) { rep(i,s) d[i] /= a; return *this;}

fps operator+(const fps& a) const { return fps(d) += a;}

fps operator-(const fps& a) const { return fps(d) -= a;}

fps operator*(const fps& a) const { return fps(d) *= a;}

fps operator*(mint a) const { return fps(d) *= a;}

fps operator/(mint a) const { return fps(d) /= a;}

fps integ() const {

fps r;

rep(i,s) r[i+1] = d[i]/(i+1);

return r;

}

#undef s

#undef d

};

ostream& operator<<(ostream&o,const fps&a) {

rep(i,a.size()) o<<(i?" ":"")<<a[i].val();

return o;

}