#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 998244353;

template <int mod>
struct Mod_Int {
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    static int get_mod() { return mod; }

    Mod_Int &operator+=(const Mod_Int &p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator-=(const Mod_Int &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator*=(const Mod_Int &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator/=(const Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator++() { return *this += Mod_Int(1); }

    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator--() { return *this -= Mod_Int(1); }

    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator-() const { return Mod_Int(-x); }

    Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }

    Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }

    Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }

    Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }

    bool operator==(const Mod_Int &p) const { return x == p.x; }

    bool operator!=(const Mod_Int &p) const { return x != p.x; }

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }

    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }

    friend istream &operator>>(istream &is, Mod_Int &p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

using mint = Mod_Int<MOD>;

template <typename T>
struct Matrix {
    vector<vector<T>> A;

    Matrix(int m, int n) : A(m, vector<T>(n, 0)) {}

    int height() const { return A.size(); }

    int width() const { return A.front().size(); }

    inline const vector<T> &operator[](int k) const { return A[k]; }

    inline vector<T> &operator[](int k) { return A[k]; }

    static Matrix I(int l) {
        Matrix ret(l, l);
        for (int i = 0; i < l; i++) ret[i][i] = 1;
        return ret;
    }

    Matrix &operator*=(const Matrix &B) {
        int m = height(), n = width(), p = B.width();
        assert(n == B.height());
        Matrix ret(m, p);
        for (int i = 0; i < m; i++) {
            for (int k = 0; k < n; k++) {
                for (int j = 0; j < p; j++) ret[i][j] += A[i][k] * B[k][j];
            }
        }
        swap(A, ret.A);
        return *this;
    }

    Matrix operator*(const Matrix &B) const { return Matrix(*this) *= B; }

    Matrix pow(long long k) const {
        int m = height(), n = width();
        assert(m == n);
        Matrix now = *this, ret = I(n);
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    bool eq(const T &a, const T &b) const {
        return a == b;
        // return abs(a-b) <= EPS;
    }

    pair<int, T> row_reduction(vector<T> &b) { // 行基本変形を用いて簡約化を行い、(rank, det) の組を返す
        int m = height(), n = width(), check = 0, rank = 0;
        T det = 1;
        assert(b.size() == m);
        for (int j = 0; j < n; j++) {
            int pivot = check;
            for (int i = check; i < m; i++) {
                if (A[i][j] != 0) pivot = i;
                // if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら
            }
            if (check != pivot) det *= T(-1);
            swap(A[check], A[pivot]), swap(b[check], b[pivot]);
            if (eq(A[check][j], T(0))) {
                det = T(0);
                continue;
            }
            rank++;
            det *= A[check][j];
            T r = T(1) / A[check][j];
            for (int k = j + 1; k < n; k++) A[check][k] *= r;
            b[check] *= r;
            A[check][j] = T(1);
            for (int i = 0; i < m; i++) {
                if (i == check) continue;
                if (!eq(A[i][j], 0)) {
                    for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[check][k];
                    b[i] -= A[i][j] * b[check];
                }
                A[i][j] = T(0);
            }
            if (++check == m) break;
        }
        return make_pair(rank, det);
    }

    pair<int, T> row_reduction() {
        vector<T> b(height(), T(0));
        return row_reduction(b);
    }

    Matrix inverse() { // 行基本変形によって正方行列の逆行列を求める
        if (height() != width()) return Matrix(0, 0);
        int n = height();
        Matrix ret = I(n);
        for (int j = 0; j < n; j++) {
            int pivot = j;
            for (int i = j; i < n; i++) {
                if (A[i][j] != 0) pivot = i;
                // if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら
            }
            swap(A[j], A[pivot]), swap(ret[j], ret[pivot]);
            if (eq(A[j][j], T(0))) return Matrix(0, 0);
            T r = T(1) / A[j][j];
            for (int k = j + 1; k < n; k++) A[j][k] *= r;
            for (int k = 0; k < n; k++) ret[j][k] *= r;
            A[j][j] = T(1);
            for (int i = 0; i < n; i++) {
                if (i == j) continue;
                if (!eq(A[i][j], T(0))) {
                    for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[j][k];
                    for (int k = 0; k < n; k++) ret[i][k] -= A[i][j] * ret[j][k];
                }
                A[i][j] = T(0);
            }
        }
        return ret;
    }

    vector<vector<T>> Gausiann_elimination(vector<T> b) { // Ax = b の解の 1 つと解空間の基底の組を返す
        int m = height(), n = width();
        row_reduction(b);
        vector<vector<T>> ret;
        vector<int> p(m, n);
        vector<bool> is_zero(n, true);
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (!eq(A[i][j], T(0))) {
                    p[i] = j;
                    break;
                }
            }
            if (p[i] < n)
                is_zero[p[i]] = false;
            else if (!eq(b[i], T(0)))
                return {};
        }
        vector<T> x(n, T(0));
        for (int i = 0; i < m; i++) {
            if (p[i] < n) x[p[i]] = b[i];
        }
        ret.push_back(x);
        for (int j = 0; j < n; j++) {
            if (!is_zero[j]) continue;
            x[j] = T(1);
            for (int i = 0; i < m; i++) {
                if (p[i] < n) x[p[i]] = -A[i][j];
            }
            ret.push_back(x), x[j] = T(0);
        }
        return ret;
    }
};

struct Union_Find_Tree {
    vector<int> data;
    const int n;
    int cnt;

    Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {}

    int root(int x) {
        if (data[x] < 0) return x;
        return data[x] = root(data[x]);
    }

    int operator[](int i) { return root(i); }

    bool unite(int x, int y) {
        x = root(x), y = root(y);
        if (x == y) return false;
        if (data[x] > data[y]) swap(x, y);
        data[x] += data[y], data[y] = x;
        cnt--;
        return true;
    }

    int size(int x) { return -data[root(x)]; }

    int count() { return cnt; };

    bool same(int x, int y) { return root(x) == root(y); }

    void clear() {
        cnt = n;
        fill(begin(data), end(data), -1);
    }
};

template <typename T>
struct Number_Theoretic_Transform {
    static int max_base;
    static T root;
    static vector<T> r, ir;

    Number_Theoretic_Transform() {}

    static void init() {
        if (!r.empty()) return;
        int mod = T::get_mod();
        int tmp = mod - 1;
        root = 2;
        while (root.pow(tmp >> 1) == 1) root++;
        max_base = 0;
        while (tmp % 2 == 0) tmp >>= 1, max_base++;
        r.resize(max_base), ir.resize(max_base);
        for (int i = 0; i < max_base; i++) {
            r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i]  := 1 の 2^(i+2) 乗根
            ir[i] = r[i].inverse();                 // ir[i] := 1/r[i]
        }
    }

    static void ntt(vector<T> &a) {
        init();
        int n = a.size();
        assert((n & (n - 1)) == 0);
        assert(n <= (1 << max_base));
        for (int k = n; k >>= 1;) {
            T w = 1;
            for (int s = 0, t = 0; s < n; s += 2 * k) {
                for (int i = s, j = s + k; i < s + k; i++, j++) {
                    T x = a[i], y = w * a[j];
                    a[i] = x + y, a[j] = x - y;
                }
                w *= r[__builtin_ctz(++t)];
            }
        }
    }

    static void intt(vector<T> &a) {
        init();
        int n = a.size();
        assert((n & (n - 1)) == 0);
        assert(n <= (1 << max_base));
        for (int k = 1; k < n; k <<= 1) {
            T w = 1;
            for (int s = 0, t = 0; s < n; s += 2 * k) {
                for (int i = s, j = s + k; i < s + k; i++, j++) {
                    T x = a[i], y = a[j];
                    a[i] = x + y, a[j] = w * (x - y);
                }
                w *= ir[__builtin_ctz(++t)];
            }
        }
        T inv = T(n).inverse();
        for (auto &e : a) e *= inv;
    }

    static vector<T> convolve(vector<T> a, vector<T> b) {
        if (a.empty() || b.empty()) return {};
        int k = (int)a.size() + (int)b.size() - 1, n = 1;
        while (n < k) n <<= 1;
        a.resize(n), b.resize(n);
        ntt(a), ntt(b);
        for (int i = 0; i < n; i++) a[i] *= b[i];
        intt(a), a.resize(k);
        return a;
    }
};

template <typename T>
int Number_Theoretic_Transform<T>::max_base = 0;

template <typename T>
T Number_Theoretic_Transform<T>::root = T();

template <typename T>
vector<T> Number_Theoretic_Transform<T>::r = vector<T>();

template <typename T>
vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();

using NTT = Number_Theoretic_Transform<mint>;

template <typename T>
struct Formal_Power_Series : vector<T> {
    using NTT_ = Number_Theoretic_Transform<T>;
    using vector<T>::vector;

    Formal_Power_Series(const vector<T> &f) : vector<T>(f) {}

    // f(x) mod x^n
    Formal_Power_Series pre(int n) const {
        Formal_Power_Series ret(begin(*this), begin(*this) + min((int)this->size(), n));
        ret.resize(n, 0);
        return ret;
    }

    // f(1/x)x^{n-1}
    Formal_Power_Series rev(int n = -1) const {
        Formal_Power_Series ret = *this;
        if (n != -1) ret.resize(n, 0);
        reverse(begin(ret), end(ret));
        return ret;
    }

    void normalize() {
        while (!this->empty() && this->back() == 0) this->pop_back();
    }

    Formal_Power_Series operator-() const {
        Formal_Power_Series ret = *this;
        for (int i = 0; i < (int)ret.size(); i++) ret[i] = -ret[i];
        return ret;
    }

    Formal_Power_Series &operator+=(const T &t) {
        if (this->empty()) this->resize(1, 0);
        (*this)[0] += t;
        return *this;
    }

    Formal_Power_Series &operator+=(const Formal_Power_Series &g) {
        if (g.size() > this->size()) this->resize(g.size());
        for (int i = 0; i < (int)g.size(); i++) (*this)[i] += g[i];
        this->normalize();
        return *this;
    }

    Formal_Power_Series &operator-=(const T &t) {
        if (this->empty()) this->resize(1, 0);
        *this[0] -= t;
        return *this;
    }

    Formal_Power_Series &operator-=(const Formal_Power_Series &g) {
        if (g.size() > this->size()) this->resize(g.size());
        for (int i = 0; i < (int)g.size(); i++) (*this)[i] -= g[i];
        this->normalize();
        return *this;
    }

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

    Formal_Power_Series &operator*=(const Formal_Power_Series &g) {
        if (empty(*this) || empty(g)) {
            this->clear();
            return *this;
        }
        return *this = NTT_::convolve(*this, g);
    }

    Formal_Power_Series &operator/=(const T &t) {
        assert(t != 0);
        T inv = t.inverse();
        return *this *= inv;
    }

    // f(x) を g(x) で割った商
    Formal_Power_Series &operator/=(const Formal_Power_Series &g) {
        if (g.size() > this->size()) {
            this->clear();
            return *this;
        }
        int n = this->size(), m = g.size();
        return *this = (rev() * g.rev().inv(n - m + 1)).pre(n - m + 1).rev();
    }

    // f(x) を g(x) で割った余り
    Formal_Power_Series &operator%=(const Formal_Power_Series &g) { return *this -= (*this / g) * g; }

    // f(x)/x^k
    Formal_Power_Series &operator<<=(int k) {
        Formal_Power_Series ret(k, 0);
        ret.insert(end(ret), begin(*this), end(*this));
        return *this = ret;
    }

    // f(x)x^k
    Formal_Power_Series &operator>>=(int k) {
        Formal_Power_Series ret;
        ret.insert(end(ret), begin(*this) + k, end(*this));
        return *this = ret;
    }

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

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

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

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

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

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

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

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

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

    Formal_Power_Series operator<<(int k) const { return Formal_Power_Series(*this) <<= k; }

    Formal_Power_Series operator>>(int k) const { return Formal_Power_Series(*this) >>= k; }

    // f(c)
    T val(const T &c) const {
        T ret = 0;
        for (int i = (int)this->size() - 1; i >= 0; i--) ret *= c, ret += (*this)[i];
        return ret;
    }

    // df/dx
    Formal_Power_Series derivative() const {
        if (empty(*this)) return *this;
        int n = this->size();
        Formal_Power_Series ret(n - 1);
        for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * i;
        return ret;
    }

    // ∫f(x)dx
    Formal_Power_Series integral() const {
        if (empty(*this)) return *this;
        int n = this->size();
        vector<T> inv(n + 1, 0);
        inv[1] = 1;
        int mod = T::get_mod();
        for (int i = 2; i <= n; i++) inv[i] = -inv[mod % i] * T(mod / i);
        Formal_Power_Series ret(n + 1, 0);
        for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] * inv[i + 1];
        return ret;
    }

    // 1/f(x) mod x^n (f[0] != 0)
    Formal_Power_Series inv(int n = -1) const {
        assert((*this)[0] != 0);
        if (n == -1) n = this->size();
        Formal_Power_Series ret(1, (*this)[0].inverse());
        for (int m = 1; m < n; m <<= 1) {
            Formal_Power_Series f = pre(2 * m), g = ret;
            f.resize(2 * m), g.resize(2 * m);
            NTT_::ntt(f), NTT_::ntt(g);
            Formal_Power_Series h(2 * m);
            for (int i = 0; i < 2 * m; i++) h[i] = f[i] * g[i];
            NTT_::intt(h);
            for (int i = 0; i < m; i++) h[i] = 0;
            NTT_::ntt(h);
            for (int i = 0; i < 2 * m; i++) h[i] *= g[i];
            NTT_::intt(h);
            for (int i = 0; i < m; i++) h[i] = 0;
            ret -= h;
        }
        ret.resize(n);
        return ret;
    }

    // log(f(x)) mod x^n (f[0] = 1)
    Formal_Power_Series log(int n = -1) const {
        assert((*this)[0] == 1);
        if (n == -1) n = this->size();
        Formal_Power_Series ret = (derivative() * inv(n)).pre(n - 1).integral();
        ret.resize(n);
        return ret;
    }

    // exp(f(x)) mod x^n (f[0] = 0)
    Formal_Power_Series exp(int n = -1) const {
        assert((*this)[0] == 0);
        if (n == -1) n = this->size();
        vector<T> inv(2 * n + 1, 0);
        inv[1] = 1;
        int mod = T::get_mod();
        for (int i = 2; i <= 2 * n; i++) inv[i] = -inv[mod % i] * T(mod / i);

        auto inplace_integral = [inv](Formal_Power_Series &f) {
            if (empty(f)) return;
            int n = f.size();
            f.insert(begin(f), 0);
            for (int i = 1; i <= n; i++) f[i] *= inv[i];
        };

        auto inplace_derivative = [](Formal_Power_Series &f) {
            if (empty(f)) return;
            int n = f.size();
            f.erase(begin(f));
            for (int i = 0; i < n - 1; i++) f[i] *= T(i + 1);
        };

        Formal_Power_Series ret{1, this->size() > 1 ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
        for (int m = 2; m < n; m *= 2) {
            auto y = ret;
            y.resize(2 * m);
            NTT_::ntt(y);
            z1 = z2;
            Formal_Power_Series z(m);
            for (int i = 0; i < m; i++) z[i] = y[i] * z1[i];
            NTT_::intt(z);
            fill(begin(z), begin(z) + m / 2, 0);
            NTT_::ntt(z);
            for (int i = 0; i < m; i++) z[i] *= -z1[i];
            NTT_::intt(z);
            c.insert(end(c), begin(z) + m / 2, end(z));
            z2 = c, z2.resize(2 * m);
            NTT_::ntt(z2);
            Formal_Power_Series x(begin(*this), begin(*this) + min((int)this->size(), m));
            inplace_derivative(x);
            x.resize(m, 0);
            NTT_::ntt(x);
            for (int i = 0; i < m; i++) x[i] *= y[i];
            NTT_::intt(x);
            x -= ret.derivative(), x.resize(2 * m);
            for (int i = 0; i < m - 1; i++) x[m + i] = x[i], x[i] = 0;
            NTT_::ntt(x);
            for (int i = 0; i < 2 * m; i++) x[i] *= z2[i];
            NTT_::intt(x);
            x.pop_back();
            inplace_integral(x);
            for (int i = m; i < min((int)this->size(), 2 * m); i++) x[i] += (*this)[i];
            fill(begin(x), begin(x) + m, 0);
            NTT_::ntt(x);
            for (int i = 0; i < 2 * m; i++) x[i] *= y[i];
            NTT_::intt(x);
            ret.insert(end(ret), begin(x) + m, end(x));
        }
        ret.resize(n);
        return ret;
    }

    // f(x)^k mod x^n
    Formal_Power_Series pow(long long k, int n = -1) const {
        if (n == -1) n = this->size();
        int m = this->size();
        for (int i = 0; i < m; i++) {
            if ((*this)[i] == 0) continue;
            T inv = (*this)[i].inverse();
            Formal_Power_Series g(m - i, 0);
            for (int j = i; j < m; j++) g[j - i] = (*this)[j] * inv;
            g = (g.log(n) * k).exp(n) * ((*this)[i].pow(k));
            Formal_Power_Series ret(n, 0);
            if (i > 0 && k > n / i) return ret;
            long long d = i * k;
            for (int j = 0; j + d < n && j < g.size(); j++) ret[j + d] = g[j];
            return ret;
        }
        Formal_Power_Series ret(n, 0);
        if (k == 0) ret[0] = 1;
        return ret;
    }

    // √f(x) mod x^n (存在しなければ空)
    Formal_Power_Series sqrt(int n = -1) const {
        if (n == -1) n = this->size();
        int mod = T::get_mod();

        auto sqrt_mod = [mod](const T &a) {
            if (mod == 2) return a;
            int s = mod - 1, t = 0;
            while (s % 2 == 0) s /= 2, t++;
            T root = 2;
            while (root.pow((mod - 1) / 2) == 1) root++;
            T x = a.pow((s + 1) / 2);
            T u = root.pow(s);
            T y = x * x * a.inverse();
            while (y != 1) {
                int k = 0;
                T z = y;
                while (z != 1) k++, z *= z;
                for (int i = 0; i < t - k - 1; i++) u *= u;
                x *= u, u *= u, y *= u;
                t = k;
            }
            return x;
        };

        if ((*this)[0] == 0) {
            for (int i = 1; i < (int)this->size(); i++) {
                if ((*this)[i] != 0) {
                    if (i & 1) return {};
                    if ((*this)[i].pow((mod - 1) / 2) != 1) return {};
                    if (n <= i / 2) break;
                    return ((*this) >> i).sqrt(n - i / 2) << (i / 2);
                }
            }
            return Formal_Power_Series(n, 0);
        }
        if ((*this)[0].pow((mod - 1) / 2) != 1) return {};
        T tw = T(2).inverse();
        Formal_Power_Series ret{sqrt_mod((*this)[0])};
        for (int m = 1; m < n; m *= 2) {
            Formal_Power_Series g = (*this).pre(m * 2) * ret.inv(m * 2);
            g.resize(2 * m);
            ret = (ret + g) * tw;
        }
        ret.resize(n);
        return ret;
    }

    // f(x+c)
    Formal_Power_Series Taylor_shift(T c) const {
        int n = this->size();
        vector<T> ifac(n, 1);
        Formal_Power_Series f(n), g(n);
        for (int i = 0; i < n; i++) {
            f[n - 1 - i] = (*this)[i] * ifac[n - 1];
            if (i < n - 1) ifac[n - 1] *= i + 1;
        }
        ifac[n - 1] = ifac[n - 1].inverse();
        for (int i = n - 1; i > 0; i--) ifac[i - 1] = ifac[i] * i;
        T pw = 1;
        for (int i = 0; i < n; i++) {
            g[i] = pw * ifac[i];
            pw *= c;
        }
        f *= g;
        Formal_Power_Series b(n);
        for (int i = 0; i < n; i++) b[i] = f[n - 1 - i] * ifac[i];
        return b;
    }
};

using fps = Formal_Power_Series<mint>;

template <typename T>
vector<Formal_Power_Series<T>> subproduct_tree(const vector<T> &xs) {
    int n = xs.size();
    int k = 1;
    while (k < n) k <<= 1;
    vector<Formal_Power_Series<T>> g(2 * k, {1});
    for (int i = 0; i < n; i++) g[k + i] = {-xs[i], 1};
    for (int i = k - 1; i > 0; i--) g[i] = g[2 * i] * g[2 * i + 1];
    return g;
}

template <typename T>
Formal_Power_Series<T> polynomial_interpolation(const vector<T> &xs, const vector<T> &ys) {
    int n = xs.size();
    assert(ys.size() == n);
    vector<Formal_Power_Series<T>> g = subproduct_tree(xs);
    int k = g.size() / 2;
    vector<Formal_Power_Series<T>> f(2 * k);
    f[1] = g[1].derivative();
    for (int i = 2; i < k + n; i++) f[i] = f[i / 2] % g[i];
    for (int i = 0; i < n; i++) f[k + i][0] = ys[i] / f[k + i][0];
    for (int i = k - 1; i > 0; i--) f[i] = f[2 * i] * g[2 * i + 1] + f[2 * i + 1] * g[2 * i];
    f[1].resize(n);
    return f[1];
}

using mat = Matrix<mint>;

mint calc(vector<vector<mint>> A, int c) {
    int n = sz(A);
    mat B(n, n);
    rep(i, n) rep(j, n) B[i][j] = A[i][j];
    rep(i, n) {
        rep(j, n) {
            if (i != j && A[i][j] == 0) {
                B[i][j] -= c;
                B[i][i] += c;
            }
        }
    }
    rep(j, n) B[n - 1][j] = 0, B[j][n - 1] = 0;
    B[n - 1][n - 1] = 1;
    return B.row_reduction().second;
}

int main() {
    int N, M;
    cin >> N >> M;

    Union_Find_Tree uf(N);

    vector<vector<mint>> A(N, vector<mint>(N, 0));
    rep(i, M) {
        int u, v;
        cin >> u >> v;
        u--, v--;
        A[u][v]--, A[u][u]++;
        A[v][u]--, A[v][v]++;
        uf.unite(u, v);
    }

    if (uf.count() >= 2) {
        mat B(N, N);
        rep(i, N) rep(j, N) B[i][j] = A[i][j];
        vector<int> c;
        rep(i, N) {
            if (uf[i] == i) {
                c.eb(uf.size(i));
                rep(j, N) B[i][j] = 0, B[j][i] = 0;
                B[i][i] = 1;
            }
        }
        mint ans = B.row_reduction().second;
        int res = N * N;
        sort(rall(c));
        each(e, c) res -= e * e;
        if (c[0] == c[1]) {
            int K = 0;
            each(e, c) {
                if (e == c[0]) K++;
            }
            res -= 2 * c[0] * c[0];
            ans *= c[0] * c[0] * K * (K - 1) / 2;
        } else {
            int K = 0;
            each(e, c) {
                if (e == c[1]) K++;
            }
            res -= 2 * c[0] * c[1];
            ans *= c[0] * c[1] * K;
        }
        cout << res << '\n' << ans << '\n';
    } else {
        vector<mint> xs, ys;
        rep(i, N + 1) xs.eb(i), ys.eb(calc(A, i));
        auto f = polynomial_interpolation(xs, ys);
        cout << "0\n" << f[0] + f[1] << '\n';
    }
}