#include <bits/stdc++.h>
#include <atcoder/all>

using namespace std;
using namespace atcoder;

#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define Sort(a) (sort((a).begin(), (a).end()))
#define RSort(a) (sort((a).rbegin(), (a).rend()))
#define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end()))

typedef long long int ll;
typedef unsigned long long ul;
typedef long double ld;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef vector<char> vc;
typedef vector<string> vst;
typedef vector<double> vd;
typedef vector<long double> vld;
typedef pair<long long, long long> P;

template<class T> long long sum(const T &a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T &a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T &a){ return *max_element(a.begin(), a.end()); }

const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);

template<class T> inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; }

template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }

template <typename T>
long long binary_search(long long ok, long long ng, T check){
    while(abs(ok - ng) > 1){
        long long mid = (ok + ng) / 2;
        if(check(mid)) ok = mid;
        else ng = mid;
    }
    return ok;
}

template <typename T>
long double binary_search_real(long double ok, long double ng, T check, int iter = 100){
    for(int i = 0; i < iter; ++i){
        long double mid = (ok + ng) / 2;
        if(check(mid)) ok = mid;
        else ng = mid;
    }
    return ok;
}

template <typename T>
long long trisum(T a, T b){
    long long res = ((b - a + 1) * (a + b)) / 2;
    return res;
}

template <typename T>
T intpow(T x, int n){
    T ret = 1;
    while(n > 0) {
        if(n & 1) (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}

template <typename T>
T getReminder(T a, T b){
    if(b == 0) return -1;
    if(a >= 0 && b > 0){
        return a % b;
    } else if(a < 0 && b > 0){
        return ((a % b) + b) % b;
    } else if(a >= 0 && b < 0){
        return a % b;
    } else{
        return (abs(b) - abs(a % b)) % b;
    }
}

template<class T, class U> inline T vin(T &vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T, class U> void inGraph(vector<vector<T>> &G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } }

template <long long Modulus>
struct ModInt{
    long long val;
    static constexpr int mod() { return Modulus; }
    constexpr ModInt(const long long _val = 0) noexcept : val(_val) {
        normalize();
    }
    void normalize(){
        val = (val % Modulus + Modulus) % Modulus;
    }
    inline ModInt &operator+=(const ModInt &rhs) noexcept {
        if(val += rhs.val, val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt &operator-=(const ModInt &rhs) noexcept {
        if(val -= rhs.val, val < 0) val += Modulus;
        return *this;
    }
    inline ModInt &operator*=(const ModInt &rhs) noexcept {
        val = val * rhs.val % Modulus;
        return *this;
    }
    inline ModInt &operator/=(const ModInt &rhs) noexcept {
        val = val * inv(rhs.val).val % Modulus;
        return *this;
    }
    inline ModInt &operator++() noexcept {
        if(++val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt operator++(int) noexcept {
        ModInt t = val;
        if(++val >= Modulus) val -= Modulus;
        return t;
    }
    inline ModInt &operator--() noexcept {
        if(--val < 0) val += Modulus;
        return *this;
    }
    inline ModInt operator--(int) noexcept {
        ModInt t = val;
        if(--val < 0) val += Modulus;
        return t;
    }
    inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; }
    inline ModInt inv(void) const { return inv(val); }
    ModInt pow(long long n) const {
        assert(0 <= n);
        ModInt x = *this, r = 1;
        while(n){
            if(n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    ModInt inv(const long long n) const {
        long long a = n, b = Modulus, u = 1, v = 0;
        while(b){
            long long t = a / b;
            a -= t * b; std::swap(a, b);
            u -= t * v; std::swap(u, v);
        }
        u %= Modulus;
        if(u < 0) u += Modulus;
        return u;
    }
    friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; }
    friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; }
    friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; }
    friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; }
    friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; }
    friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; }
    friend inline std::istream &operator>>(std::istream &is, ModInt &x) noexcept {
        is >> x.val;
        x.normalize();
        return is;
    }
    friend inline std::ostream &operator<<(std::ostream &os, const ModInt &x) noexcept { return os << x.val; }
};
#line 2 "lib/math/crt.hpp"

/**
 * @brief Chinese Remainder Theorem (中国剰余定理)
 * @docs docs/math/crt.md
 */

#include <numeric>
#line 10 "lib/math/crt.hpp"

namespace CRT{
    inline long long mod(long long a, long long m){
        return (a % m + m) % m;
    }

    long long extGCD(long long a, long long b, long long &x, long long &y){
        if(b == 0){
            x = 1;
            y = 0;
            return a;
        }
        long long d = extGCD(b, a % b, y, x);
        y -= a / b * x;
        return d;
    }

    std::pair<long long, long long> chineseRem(const std::vector<long long> &b, const std::vector<long long> &m) {
        long long r = 0, M = 1;
        for(int i = 0; i < (int) b.size(); i++){
            long long p, q;
            long long d = extGCD(M, m[i], p, q);
            if((b[i] - r) % d != 0) return {0, -1};
            long long tmp = (b[i] - r) / d * p % (m[i] / d);
            r += M * tmp;
            M *= m[i] / d;
        }
        r %= M;
        if(r < 0) r += M;
        return {r, M};
    }

    // not coprime
    long long preGarner(std::vector<long long> &b, std::vector<long long> &m, const long long MOD){
        long long res = 1;
        int n = b.size();
        for(int i = 0; i < n; i++){
            for(int j = 0; j < i; j++){
                long long g = std::gcd(m[i], m[j]);
                if((b[i] - b[j]) % g != 0) return -1;
                m[i] /= g, m[j] /= g;
                // gcd の分だけ被ってるので振り分ける
                long long gi = std::gcd(m[i], g), gj = g / gi;
                do{
                    g = std::gcd(gi, gj);
                    gi *= g, gj /= g;
                }while(g != 1);
                m[i] *= gi, m[j] *= gj;
                b[i] %= m[i], b[j] %= m[j];
            }
        }
        for(auto x : m) (res *= x) %= MOD;
        return res;
    }

    long long garner(const std::vector<long long> &b, const std::vector<long long> &m, const long long MOD){
        std::vector<long long> tm = m;
        tm.push_back(MOD);
        auto inv = [&](long long a, long long m) -> long long {
            long long x, y;
            extGCD(a, m, x, y);
            return mod(x, m);
        };
        int n = b.size();
        std::vector<long long> coeffs(n + 1, 1), constants(n + 1, 0);
        for(int i = 0; i < n; i++){
            // solve "coeffs[i] * t[i] + constants[i] = b[i] (mod. m[i])
            long long t = mod((b[i] - constants[i]) * inv(coeffs[i], tm[i]), tm[i]);
            for(int j = i + 1; j < n + 1; j++){
                (constants[j] += t * coeffs[j]) %= tm[j];
                (coeffs[j] *= tm[i]) %= tm[j];
            }
        }
        return constants[n];
    }

    // ax + b ≡ 0 (mod m)
    long long modEquation(long long a, long long b, long long m, bool is_positive = false){
        a %= m; b %= m;
        b = (m - b) % m;
        long long g = std::gcd(a, m);
        if(b % g != 0) return -1;
        a /= g; b /= g; m /= g;
        if(is_positive && b == 0){
            return m;
        }
        long long x, y;
        extGCD(a, m, x, y);
        return (b * x % m + m) % m;
    }
}
#line 9 "lib/convolution/ntt.hpp"

#line 11 "lib/convolution/ntt.hpp"

namespace NTT{

    // @param n `0 <= n`
    // @return minimum non-negative `x` s.t. `n <= 2**x`
    int ceil_pow2(int n) {
        int x = 0;
        while((1U << x) < (unsigned int) (n)) x++;
        return x;
    }

    // @param n `1 <= n`
    // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
    int bsf(unsigned int n) {
        return __builtin_ctz(n);
    }

    int primitive_root(int m) {
        if(m == 2) return 1;
        if(m == 167772161) return 3;
        if(m == 469762049) return 3;
        if(m == 754974721) return 11;
        if(m == 998244353) return 3;
        return 1;
    }

    template <typename T>
    void butterfly(std::vector<T> &a){
        int g = primitive_root(T::mod());
        int n = int(a.size());
        int h = ceil_pow2(n);

        static bool first = true;
        static T sum_e[30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
        if(first){
            first = false;
            T es[30], ies[30];  // es[i]^(2^(2+i)) == 1
            int cnt2 = bsf(T::mod() - 1);
            T e = T(g).pow((T::mod() - 1) >> cnt2), ie = e.inv();
            for(int i = cnt2; i >= 2; i--){
                // e^(2^i) == 1
                es[i - 2] = e;
                ies[i - 2] = ie;
                e *= e;
                ie *= ie;
            }
            T now = 1;
            for(int i = 0; i <= cnt2 - 2; i++){
                sum_e[i] = es[i] * now;
                now *= ies[i];
            }
        }
        for(int ph = 1; ph <= h; ph++){
            int w = 1 << (ph - 1), p = 1 << (h - ph);
            T now = 1;
            for(int s = 0; s < w; s++){
                int offset = s << (h - ph + 1);
                for(int i = 0; i < p; i++){
                    auto l = a[i + offset];
                    auto r = a[i + offset + p] * now;
                    a[i + offset] = l + r;
                    a[i + offset + p] = l - r;
                }
                now *= sum_e[bsf(~(unsigned int) (s))];
            }
        }
    }

    template <typename T>
    void butterfly_inv(std::vector<T> &a) {
        int g = primitive_root(T::mod());
        int n = int(a.size());
        int h = ceil_pow2(n);

        static bool first = true;
        static T sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
        if(first){
            first = false;
            T es[30], ies[30];  // es[i]^(2^(2+i)) == 1
            int cnt2 = bsf(T::mod() - 1);
            T e = T(g).pow((T::mod() - 1) >> cnt2), ie = e.inv();
            for(int i = cnt2; i >= 2; i--){
                // e^(2^i) == 1
                es[i - 2] = e;
                ies[i - 2] = ie;
                e *= e;
                ie *= ie;
            }
            T now = 1;
            for(int i = 0; i <= cnt2 - 2; i++){
                sum_ie[i] = ies[i] * now;
                now *= es[i];
            }
        }

        for(int ph = h; ph >= 1; ph--){
            int w = 1 << (ph - 1), p = 1 << (h - ph);
            T inow = 1;
            for(int s = 0; s < w; s++){
                int offset = s << (h - ph + 1);
                for(int i = 0; i < p; i++){
                    auto l = a[i + offset];
                    auto r = a[i + offset + p];
                    a[i + offset] = l + r;
                    a[i + offset + p] = (unsigned long long) (T::mod() + l.val - r.val) * inow.val;
                }
                inow *= sum_ie[bsf(~(unsigned int) (s))];
            }
        }
    }

    template <typename T>
    std::vector<T> convolution(std::vector<T> a, std::vector<T> b){
        int n = int(a.size()), m = int(b.size());
        if(!n || !m) return {};
        if(std::min(n, m) <= 60) {
            if(n < m) {
                std::swap(n, m);
                std::swap(a, b);
            }
            std::vector<T> ans(n + m - 1);
            for(int i = 0; i < n; i++){
                for(int j = 0; j < m; j++){
                    ans[i + j] += a[i] * b[j];
                }
            }
            return ans;
        }
        int z = 1 << ceil_pow2(n + m - 1);
        a.resize(z);
        butterfly(a);
        b.resize(z);
        butterfly(b);
        for(int i = 0; i < z; i++){
            a[i] *= b[i];
        }
        butterfly_inv(a);
        a.resize(n + m - 1);
        T iz = T(z).inv();
        for(int i = 0; i < n + m - 1; i++) a[i] *= iz;
        return a;
    }

    template <typename T>
    std::vector<T> convolution_mod(const std::vector<T> &a, const std::vector<T> &b, const long long MOD){
        if(MOD == 998244353){
            return convolution(a, b);
        }
        constexpr long long m0 = 167772161;
        constexpr long long m1 = 469762049;
        constexpr long long m2 = 754974721;
        using mint0 = ModInt<m0>;
        using mint1 = ModInt<m1>;
        using mint2 = ModInt<m2>;
        int n = a.size(), m = b.size();
        std::vector<mint0> a0(n), b0(m);
        std::vector<mint1> a1(n), b1(m);
        std::vector<mint2> a2(n), b2(m);
        for(int i = 0; i < n; i++){
            a0[i] = a[i].val;
            a1[i] = a[i].val;
            a2[i] = a[i].val;
        }
        for(int i = 0; i < m; i++){
            b0[i] = b[i].val;
            b1[i] = b[i].val;
            b2[i] = b[i].val;
        }
        auto c0 = convolution(a0, b0);
        auto c1 = convolution(a1, b1);
        auto c2 = convolution(a2, b2);
        std::vector<T> ret(n + m - 1);
        for(int i = 0; i < n + m - 1; i++){
            ret[i] = CRT::garner({c0[i].val, c1[i].val, c2[i].val}, {m0, m1, m2}, MOD);
        }
        return ret;
    }
};
#line 11 "lib/polynomial/formal_power_series.hpp"

template <typename T>
struct FormalPowerSeries : std::vector<T> {
    using std::vector<T>::vector;
    using FPS = FormalPowerSeries;

    // deg 次として初期化
    FPS pre(int deg) const {
        FPS res(std::begin(*this), std::begin(*this) + std::min((int) this->size(), deg));
        if((int) res.size() < deg) res.resize(deg, T(0));
        return res;
    }

    // deg 次として反転
    FPS rev(int deg = -1) const {
        FPS res(*this);
        if(deg != -1) res.resize(deg, T(0));
        std::reverse(std::begin(res), std::end(res));
        return res;
    }

    int notZeroCount() const {
        int res = 0;
        for(auto x : *this){
            if(x != T(0)) res++;
        }
        return res;
    }

    int maxDeg() const {
        for(int i = (int) this->size() - 1; i >= 0; i--){
            if((*this)[i] != T(0)) return i;
        }
        return -1;
    }

    void shrink() {
        while(this->size() && this->back() == T(0)) this->pop_back();
    }

    std::vector<std::pair<int, T>> sparseFormat() const {
        std::vector<std::pair<int, T>> res;
        for(int i = 0; i < (int) this->size(); i++){
            if((*this)[i] != T(0)) res.emplace_back(i, (*this)[i]);
        }
        return res;
    }

    FPS operator+(const T &rhs) const { return FPS(*this) += rhs; }
    FPS operator+(const FPS &rhs) const { return FPS(*this) += rhs; }
    FPS operator-(const T &rhs) const { return FPS(*this) -= rhs; }
    FPS operator-(const FPS &rhs) const { return FPS(*this) -= rhs; }
    FPS operator*(const T &rhs) const { return FPS(*this) *= rhs; }
    FPS operator*(const FPS &rhs) const { return FPS(*this) *= rhs; }
    FPS operator/(const T &rhs) const { return FPS(*this) /= rhs; }
    FPS operator/(const FPS &rhs) const { return FPS(*this) /= rhs; }
    FPS operator%(const FPS &rhs) const { return FPS(*this) %= rhs; }
    FPS operator-() const {
        FPS res(this->size());
        for(int i = 0; i < (int) this->size(); i++) res[i] = -(*this)[i];
        return res;
    }

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

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

    FPS &operator*=(const T &rhs){
        for(auto &x : *this) x *= rhs;
        return *this;
    }

    FPS &operator/=(const T &rhs){
        for(auto &x : *this) x /= rhs;
        return *this;
    }

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

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

    FPS &operator*=(const FPS &rhs) noexcept {
        long long len1 = this->notZeroCount(), len2 = rhs.notZeroCount();
        // Sparse な場合
        if(len1 * len2 <= 60LL * (long long) std::max(this->size(), rhs.size())){
            std::vector<std::pair<int, T>> rhs_sparse = rhs.sparseFormat();
            return *this = this->multiply_naive(rhs_sparse);
        }
        auto res = NTT::convolution_mod(*this, rhs, T::mod());
        return *this = {std::begin(res), std::end(res)};
    }

    // f/g = f * (g.inv())
    FPS &operator/=(const FPS &rhs) noexcept {
        if(this->size() < rhs.size()) return *this = FPS();
        const int n = this->size() - rhs.size() + 1;
        return *this = (rev().pre(n) * rhs.rev().inv(n)).pre(n).rev(n);
    }

    FPS &operator%=(const FPS &rhs) noexcept {
        return *this -= (*this / rhs) * rhs;
    }

    FPS operator>>(int deg) const {
        if((int) this->size() <= deg) return {};
        FPS res(*this);
        res.erase(std::begin(res), std::begin(res) + deg);
        return res;
    }

    FPS operator<<(int deg) const {
        FPS res(*this);
        res.insert(std::begin(res), deg, T(0));
        return res;
    }

    // 微分
    FPS diff() const {
        const int n = this->size();
        FPS res(std::max(0, n - 1));
        for(int i = 1; i < n; i++) res[i - 1] = (*this)[i] * T(i);
        return res;
    }

    // 積分
    FPS integral() const {
        const int n = this->size();
        FPS res(n + 1);
        res[0] = T(0);
        for(int i = 0; i < n; i++) res[i + 1] = (*this)[i] / T(i + 1);
        return res;
    }

    // {lhs / rhs, lhs % rhs}
    std::pair<FPS, FPS> division(const FPS &rhs) const {
        FPS q = *this / rhs;
        FPS r = *this - q * rhs;
        q.shrink(), r.shrink();
        return {q, r};
    }

    FPS multiply_naive(const std::vector<std::pair<int, T>> &rhs, int deg = -1){
        if(deg == -1) deg = this->size() + (rhs.back().first + 1) - 1;
        FPS res(deg, T(0));
        for(auto &[i, x] : this->sparseFormat()){
            for(auto &[j, y] : rhs){
                if(i + j >= deg) break;
                res[i + j] += x * y;
            }
        }
        return *this = {std::begin(res), std::end(res)};
    }

    FPS divide_naive(const std::vector<std::pair<int, T>> &rhs){
        assert(!rhs.empty());
        if((int) this->size() < (rhs.back().first + 1)) return FPS();
        auto [i0, x0] = rhs[0];
        assert(i0 == 0 && x0 != T(0));
        T x0_inv = T(1) / x0;
        for(int i = 0; i < (int) this->size(); i++){
            for(int i2 = 1; i2 < (int) rhs.size(); i2++){
                auto &[j, y] = rhs[i2];
                if(i < j) break;
                (*this)[i] -= (*this)[i - j] * y;
            }
            (*this)[i] *= x0_inv;
        }
        return *this;
    }

    // fg = 1 (mod x^n) となる g
    FPS inv(int deg = -1) const {
        assert((*this)[0] != T(0));
        if(deg == -1) deg = this->size();
        // g_p mod x^k から g mod x^2k を求める
        // (g - g_p)^2 = g^2 - 2 g g_p + (g_p)^2 = 0 (mod x^2k)
        // fg^2 - 2fg g_p + f (g_p)^2
        // = g - 2(g_p) + f (g_p)^2 = 0 (mod x^2k)
        // g = 2(g_p) - f (g_p)^2 (mod x^2k)
        FPS res({T(1) / (*this)[0]});
        for(int i = 1; i < deg; i <<= 1) {
            res = (res + res - res * res * pre(i << 1)).pre(i << 1);
        }
        return res.pre(deg);
    }

    // g = log f となる g
    FPS log(int deg = -1) const {
        assert((*this)[0] == T(1));
        if(deg == -1) deg = this->size();
        // log f = integral((f' / f) dx)
        return (this->diff() * this->inv(deg)).pre(deg - 1).integral().pre(deg);
    }

    // g = exp(f) となる g
    FPS exp(int deg = -1) const {
        assert((*this)[0] == T(0));
        if(deg == -1) deg = this->size();
        // g_p mod x^k から g mod x^2k をニュートン法で求める
        // log g = f (mod x^n) であるから、
        // g = g_p - (log g_p - f)/(log' g_p)
        //   = g_p(1 - log g_p + f) (mod x^2k)
        FPS res({T(1)});
        for(int i = 1; i < deg; i <<= 1) {
            res = (res * (-res.log(i << 1) + pre(i << 1) + T(1))).pre(i << 1);
        }
        return res.pre(deg);
    }

    // g = f^k となる g
    FPS pow(long long k, int deg = -1) const {
        if(deg == -1) deg = this->size();
        if(k == 0){
            FPS res(deg, T(0));
            res[0] = T(1);
            return res;
        }
        // f^k = exp(log f)^k = exp(k log f)
        // log を計算するのに定数項が 1 である必要があるので調整する
        // 最も低次の項を a x^i として、(f / (a x^i))^k を計算してから (a x^i)^k を掛ける
        for(int i = 0; i < (int) this->size(); i++){
            if(k * i > deg) return FPS(deg, T(0));
            if((*this)[i] != T(0)){
                T inv_i = T(1) / (*this)[i];
                FPS res = ((((*this) * inv_i) >> i).log(deg) * k).exp(deg) * ((*this)[i].pow(k));
                res = (res << (k * i)).pre(deg);
                return res;
            }
        }
        return *this;
    }

    long long sqrtT(const T a) const {
        const long long p = T::mod();
        if(a == T(0) || a == T(1)) return a.val;
        if(a.pow((p - 1) / 2) != T(1)) return -1LL;
        T b = 1;
        while(b.pow((p - 1) / 2) == 1) b++;
        // p - 1 = m 2^e
        long long m = p - 1;
        int e = 0;
        while(m % 2 == 0) m >>= 1, e++;
        // x = a^((m + 1) / 2) (mod p)
        T x = a.pow((m - 1) / 2);
        // y = a^{-1} x^2 (mod p)
        T y = (a * x) * x;
        x *= a;
        T z = b.pow(m);
        while(y != 1){
            int j = 0;
            T t = y;
            while(t != 1){
                t *= t;
                j++;
            }
            z = z.pow(1LL << (e - j - 1));
            x *= z;
            z *= z;
            y *= z;
            e = j;
        }
        return x.val;
    }

    // g^2 = f となる g
    FPS sqrt(int deg = -1) const {
        if(this->empty()) return {};
        if(deg == -1) deg = this->size();
        // inv を計算するのに定数項が非零である必要があるので調整する
        if((*this)[0] == T(0)){
            for(int i = 1; i < (int) this->size(); i++){
                if((*this)[i] == T(0)) continue;
                if(i & 1) return {};
                FPS res = (*this >> i).sqrt();
                if(res.empty()) return {};
                res = res.pre(deg - i / 2) << (i / 2);
                return res;
            }
            FPS res(deg, T(0));
            return res;
        }
        // g_p mod x^k から g mod x^2k をニュートン法で求める
        // g^2 = f (mod x^n) であるから、
        // g = g_p - ((g_p)^2 - f)/((g_p^2)')
        //   = g_p - ((g_p)^2 - f)/(2 g_p)
        //   = 1/2 * (g_p + f/g_p (mod x^2k)
        long long sqrt0 = sqrtT((*this)[0]);
        if(sqrt0 == -1) return {};
        FPS res({T(sqrt0)});
        T inv2 = T(1) / T(2);
        for(int i = 1; i < deg; i <<= 1) {
            res = (res + pre(i << 1) * res.inv(i << 1)) * inv2;
        }
        return res.pre(deg);
    }
};
#line 11 "lib/polynomial/bostan_mori.hpp"

// [x^n] f(x)/g(x) : O(d log d log n)
template <typename T>
T bostan_mori(long long n, FormalPowerSeries<T> f, FormalPowerSeries<T> g){
    using FPS = FormalPowerSeries<T>;
    assert(n >= 0);
    g.shrink();
    assert(!g.empty());
    {
        int h = 0;
        while(g[h] == T(0)) h++;
        g.erase(g.begin(), g.begin() + h);
        n += h;
    }

    if((int) g.size() == 1){
        return ((int) f.size() > n) ? f[n] / g[0] : T(0);
    }

    while(n > 0){
        FPS tmp_g = g;
        for(int i = 1; i < (int) g.size(); i += 2){
            tmp_g[i] *= -1;
        }
        FPS u = f * tmp_g;
        for(int i = 0; i < (int) f.size(); i++){
            f[i] = u[i * 2 + n % 2];
        }
        f.resize(((int) u.size() + 1 - (n % 2)) / 2);
        tmp_g *= g;
        for(int i = 0; i < (int) g.size(); i++){
            g[i] = tmp_g[i * 2];
        }
        n >>= 1;
    }
    return f[0] / g[0];
}

// a_i = sum_{j = 1}^{d} a_{i - j} * c[j] を満たす数列の k (0-indexed) 番目の項を求める
template <typename T>
T findKthTerm(const std::vector<T> &init, const std::vector<T> &c, long long k){
    using FPS = FormalPowerSeries<T>;
    assert((int) init.size() + 1 == (int) c.size());
    FPS f(init.size()), g(c.size());
    for(int i = 0; i < (int) init.size(); i++){
        f[i] = init[i];
    }
    g[0] = 1;
    for(int i = 1; i < (int) c.size(); i++){
        g[i] = c[i] * T(-1);
    }
    f *= g;
    f.resize(init.size());
    return bostan_mori(k, f, g);
}

using mint = ModInt<MOD>;

ll T;

void input(){
    in(T);
}

using FPS = FormalPowerSeries<mint>;

void solve(){
    ll n, q; in(n, q);
    FPS a(n);
    rep(i, n) in(a[i]);
    while(q--){
        ll t; in(t);
        if(t == 1){
            ll k, x; in(k, x);
            FPS f = {mint(1), mint(-k)};
            a *= f.pow(x, n).inv(n);
            a.resize(n);
        }else{
            ll x; in(x);
            x--;
            out(a[x]);
        }
    }
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);

    T = 1;
    // input();
    while(T--) solve();
}