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struct poly {
vector<ll> data;
poly(int deg = 0) : data(1 + deg) {}
poly(initializer_list<ll> _data) : data(_data) {}
int size() const { return ssize(data); }
void trim() {
for (ll& x : data) x = (x % mod + mod) % mod;
while (size() > 1 && data.back() == 0) data.pop_back();
}
ll& operator[](int x) { return data[x]; }
const ll& operator[](int x) const { return data[x]; }
ll operator()(int x) const {
ll res = 0;
for (int i = size() - 1; i >= 0; i--)
res = (res * x + data[i]) % mod;
return res % mod;
}
poly& operator+=(const poly& o) {
if (size() < o.size()) data.resize(o.size());
for (int i = 0; i < o.size(); i++)
data[i] = (data[i] + o[i]) % mod;
return *this;
}
poly operator*(const poly& o) const {
poly res(size() + o.size() - 1);
for (int i = 0; i < size(); i++) {
for (int j = 0; j < o.size(); j++) {
res[i + j] += (data[i] * o[j]) % mod;
}}
res.trim();
return res;
}
//return p(x+a)
poly operator<<(ll a) const {
poly res(size() - 1);
for (int i = size() - 1; i >= 0; i--) {
for (int j = size() - i - 1; j >= 1; j--)
res[j] = (res[j] * a + res[j - 1]) % mod;
res[0] = (res[0] * a + data[i]) % mod;
}
return res;
}
pair<poly, poly> divmod(const poly& d) const {
int i = size() - d.size();
if (i <= 0) return {{}, *this};
poly s(i + 1), r = *this;
ll inv = multInv(d.data.back(), mod);
for (; i >= 0; i--) {
s[i] = (r.data.back() * inv) % mod;
r.data.pop_back();
for (int j = 0; i + j < r.size(); j++) {
r[i + j] = (r.data[i + j] - s[i] * d[j]) % mod;
}}
s.trim(); r.trim();
return {s, r};
}
};
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