#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
#define UNIQUE(v) sort(ALL(v)),(v).erase(unique(ALL(v)),(v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v,x) int(lower_bound(ALL(v),(x))-(v).begin())
#define UB(v,x) int(upper_bound(ALL(v),(x))-(v).begin())

using ll=long long int;
using ull=unsigned long long;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<typename T,typename U>T ceil(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?(x+y-1)/y:x/y);}
template<typename T,typename U>T floor(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?x/y:(x-y+1)/y);}
template<typename T>int popcnt(T x){return __builtin_popcountll(x);}
template<typename T>int topbit(T x){return (x==0?-1:63-__builtin_clzll(x));}
template<typename T>int lowbit(T x){return (x==0?-1:__builtin_ctzll(x));}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>

class FastIO{
    static constexpr int L=1<<16;
    char rdbuf[L];
    int rdLeft=0,rdRight=0;
    inline void reload(){
        int len=rdRight-rdLeft;
        memmove(rdbuf,rdbuf+rdLeft,len);
        rdLeft=0,rdRight=len;
        rdRight+=fread(rdbuf+len,1,L-len,stdin);
    }
    inline bool skip(){
        for(;;){
            while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;
            if(rdLeft==rdRight){
                reload();
                if(rdLeft==rdRight)return false;
            }
            else break;
        }
        return true;
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    inline bool _read(__int128_t& x){
        if(!skip())return false;
        if(rdLeft+40>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    inline bool _read(__uint128_t& x){
        if(!skip())return false;
        if(rdLeft+40>=rdRight)reload();
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        return true;
    }
    template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        if(rdbuf[rdLeft]!='.')return true;
        rdLeft++;
        T base=.1;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x+=base*(rdbuf[rdLeft++]^48);
            base*=.1;
        }
        if(neg)x=-x;
        return true;
    }
    inline bool _read(char& x){
        if(!skip())return false;
        if(rdLeft+1>=rdRight)reload();
        x=rdbuf[rdLeft++];
        return true;
    }
    inline bool _read(string& x){
        if(!skip())return false;
        for(;;){
            int pos=rdLeft;
            while(pos<rdRight and rdbuf[pos]>' ')pos++;
            x.append(rdbuf+rdLeft,pos-rdLeft);
            if(rdLeft==pos)break;
            rdLeft=pos;
            if(rdLeft==rdRight)reload();
            else break;
        }
        return true;
    }
    template<typename T>inline bool _read(vector<T>& v){
        for(auto& x:v){
            if(!_read(x))return false;
        }
        return true;
    }

    char wtbuf[L],tmp[50];
    int wtRight=0;
    inline void _write(const char& x){
        if(wtRight>L-32)flush();
        wtbuf[wtRight++]=x;
    }
    inline void _write(const string& x){
        for(auto& c:x)_write(c);
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){
        if(wtRight>L-32)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
                switch (sizeof(x)) {
                case 2: _write("32768"); return;
                case 4: _write("2147483648"); return;
                case 8: _write("9223372036854775808"); return;
                }
            }
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    inline void _write(__int128_t x){
        if(wtRight>L-40)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    inline void _write(__uint128_t x){
        if(wtRight>L-40)flush();
        if(x==0){
            _write('0');
            return;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    inline void _write(double x){
        ostringstream oss;
        oss << fixed << setprecision(15) << double(x);
        string s = oss.str();
        _write(s);
    }
    template<typename T>inline void _write(const vector<T>& v){
        rep(i,0,v.size()){
            if(i)_write(' ');
            _write(v[i]);
        }
    }
public:
    FastIO(){}
    ~FastIO(){flush();}
    inline void read(){}
    template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){
        assert(_read(head));
        read(tail...); 
    }
    template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}
    template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){
        _write(head);
        write<ln,true>(tail...); 
        if(space)_write(' ');
    }
    inline void flush(){
        fwrite(wtbuf,1,wtRight,stdout);
        wtRight=0;
    }
};

/**
 * @brief Fast IO
 */
#line 3 "sol.cpp"

#line 2 "library/Convolution/ntt.hpp"

template <typename T> struct NTT {
    static constexpr int rank2 = __builtin_ctzll(T::get_mod() - 1);
    std::array<T, rank2 + 1> root;  // root[i]^(2^i) == 1
    std::array<T, rank2 + 1> iroot; // root[i] * iroot[i] == 1

    std::array<T, std::max(0, rank2 - 2 + 1)> rate2;
    std::array<T, std::max(0, rank2 - 2 + 1)> irate2;

    std::array<T, std::max(0, rank2 - 3 + 1)> rate3;
    std::array<T, std::max(0, rank2 - 3 + 1)> irate3;

    NTT() {
        T g = 2;
        while (g.pow((T::get_mod() - 1) >> 1) == 1) {
            g += 1;
        }
        root[rank2] = g.pow((T::get_mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }

        {
            T prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 2; i++) {
                rate2[i] = root[i + 2] * prod;
                irate2[i] = iroot[i + 2] * iprod;
                prod *= iroot[i + 2];
                iprod *= root[i + 2];
            }
        }
        {
            T prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 3; i++) {
                rate3[i] = root[i + 3] * prod;
                irate3[i] = iroot[i + 3] * iprod;
                prod *= iroot[i + 3];
                iprod *= root[i + 3];
            }
        }
    }

    void ntt(std::vector<T> &a, bool type = 0) {
        int n = int(a.size());
        int h = __builtin_ctzll((unsigned int)n);

        if (type) {
            int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
            while (len) {
                if (len == 1) {
                    int p = 1 << (h - len);
                    T irot = 1;
                    for (int s = 0; s < (1 << (len - 1)); s++) {
                        int offset = s << (h - len + 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::get_mod() + l.v - r.v) *
                                irot.v;
                            ;
                        }
                        if (s + 1 != (1 << (len - 1)))
                            irot *= irate2[__builtin_ctzll(~(unsigned int)(s))];
                    }
                    len--;
                } else {
                    // 4-base
                    int p = 1 << (h - len);
                    T irot = 1, iimag = iroot[2];
                    for (int s = 0; s < (1 << (len - 2)); s++) {
                        T irot2 = irot * irot;
                        T irot3 = irot2 * irot;
                        int offset = s << (h - len + 2);
                        for (int i = 0; i < p; i++) {
                            auto a0 = 1ULL * a[i + offset + 0 * p].v;
                            auto a1 = 1ULL * a[i + offset + 1 * p].v;
                            auto a2 = 1ULL * a[i + offset + 2 * p].v;
                            auto a3 = 1ULL * a[i + offset + 3 * p].v;

                            auto a2na3iimag =
                                1ULL * T((T::get_mod() + a2 - a3) * iimag.v).v;

                            a[i + offset] = a0 + a1 + a2 + a3;
                            a[i + offset + 1 * p] =
                                (a0 + (T::get_mod() - a1) + a2na3iimag) *
                                irot.v;
                            a[i + offset + 2 * p] =
                                (a0 + a1 + (T::get_mod() - a2) +
                                 (T::get_mod() - a3)) *
                                irot2.v;
                            a[i + offset + 3 * p] =
                                (a0 + (T::get_mod() - a1) +
                                 (T::get_mod() - a2na3iimag)) *
                                irot3.v;
                        }
                        if (s + 1 != (1 << (len - 2)))
                            irot *= irate3[__builtin_ctzll(~(unsigned int)(s))];
                    }
                    len -= 2;
                }
            }
            T e = T(n).inv();
            for (auto &x : a)
                x *= e;
        } else {
            int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
            while (len < h) {
                if (h - len == 1) {
                    int p = 1 << (h - len - 1);
                    T rot = 1;
                    for (int s = 0; s < (1 << len); s++) {
                        int offset = s << (h - len);
                        for (int i = 0; i < p; i++) {
                            auto l = a[i + offset];
                            auto r = a[i + offset + p] * rot;
                            a[i + offset] = l + r;
                            a[i + offset + p] = l - r;
                        }
                        if (s + 1 != (1 << len))
                            rot *= rate2[__builtin_ctzll(~(unsigned int)(s))];
                    }
                    len++;
                } else {
                    // 4-base
                    int p = 1 << (h - len - 2);
                    T rot = 1, imag = root[2];
                    for (int s = 0; s < (1 << len); s++) {
                        T rot2 = rot * rot;
                        T rot3 = rot2 * rot;
                        int offset = s << (h - len);
                        for (int i = 0; i < p; i++) {
                            auto mod2 = 1ULL * T::get_mod() * T::get_mod();
                            auto a0 = 1ULL * a[i + offset].v;
                            auto a1 = 1ULL * a[i + offset + p].v * rot.v;
                            auto a2 = 1ULL * a[i + offset + 2 * p].v * rot2.v;
                            auto a3 = 1ULL * a[i + offset + 3 * p].v * rot3.v;
                            auto a1na3imag =
                                1ULL * T(a1 + mod2 - a3).v * imag.v;
                            auto na2 = mod2 - a2;
                            a[i + offset] = a0 + a2 + a1 + a3;
                            a[i + offset + 1 * p] =
                                a0 + a2 + (2 * mod2 - (a1 + a3));
                            a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                            a[i + offset + 3 * p] =
                                a0 + na2 + (mod2 - a1na3imag);
                        }
                        if (s + 1 != (1 << len))
                            rot *= rate3[__builtin_ctzll(~(unsigned int)(s))];
                    }
                    len += 2;
                }
            }
        }
    }
    vector<T> mult(const vector<T> &a, const vector<T> &b) {
        if (a.empty() or b.empty())
            return vector<T>();
        int as = a.size(), bs = b.size();
        int n = as + bs - 1;
        if (as <= 30 or bs <= 30) {
            if (as > 30)
                return mult(b, a);
            vector<T> res(n);
            rep(i, 0, as) rep(j, 0, bs) res[i + j] += a[i] * b[j];
            return res;
        }
        int m = 1;
        while (m < n)
            m <<= 1;
        vector<T> res(m);
        rep(i, 0, as) res[i] = a[i];
        ntt(res);
        if (a == b)
            rep(i, 0, m) res[i] *= res[i];
        else {
            vector<T> c(m);
            rep(i, 0, bs) c[i] = b[i];
            ntt(c);
            rep(i, 0, m) res[i] *= c[i];
        }
        ntt(res, 1);
        res.resize(n);
        return res;
    }
};

/**
 * @brief Number Theoretic Transform
 */
#line 2 "library/Math/modint.hpp"

template <int mod = 1000000007> struct fp {
    int v;
    static constexpr int get_mod() { return mod; }
    int inv() const {
        int tmp, a = v, b = mod, x = 1, y = 0;
        while (b)
            tmp = a / b, a -= tmp * b, swap(a, b), x -= tmp * y, swap(x, y);
        if (x < 0) {
            x += mod;
        }
        return x;
    }
    fp(ll x = 0) : v(x >= 0 ? x % mod : (mod - (-x) % mod) % mod) {}
    fp operator-() const { return fp() - *this; }
    fp pow(ll t) {
        assert(t >= 0);
        fp res = 1, b = *this;
        while (t) {
            if (t & 1)
                res *= b;
            b *= b;
            t >>= 1;
        }
        return res;
    }
    fp &operator+=(const fp &x) {
        if ((v += x.v) >= mod)
            v -= mod;
        return *this;
    }
    fp &operator-=(const fp &x) {
        if ((v += mod - x.v) >= mod)
            v -= mod;
        return *this;
    }
    fp &operator*=(const fp &x) {
        v = ll(v) * x.v % mod;
        return *this;
    }
    fp &operator/=(const fp &x) {
        v = ll(v) * x.inv() % mod;
        return *this;
    }
    fp operator+(const fp &x) const { return fp(*this) += x; }
    fp operator-(const fp &x) const { return fp(*this) -= x; }
    fp operator*(const fp &x) const { return fp(*this) *= x; }
    fp operator/(const fp &x) const { return fp(*this) /= x; }
    bool operator==(const fp &x) const { return v == x.v; }
    bool operator!=(const fp &x) const { return v != x.v; }
    friend istream &operator>>(istream &is, fp &x) { return is >> x.v; }
    friend ostream &operator<<(ostream &os, const fp &x) { return os << x.v; }
};

template <typename T> T Inv(ll n) {
    static const int md = T::get_mod();
    static vector<T> buf({0, 1});
    assert(n > 0);
    n %= md;
    while (SZ(buf) <= n) {
        int k = SZ(buf), q = (md + k - 1) / k;
        buf.push_back(buf[k * q - md] * q);
    }
    return buf[n];
}

template <typename T> T Fact(ll n, bool inv = 0) {
    static const int md = T::get_mod();
    static vector<T> buf({1, 1}), ibuf({1, 1});
    assert(n >= 0 and n < md);
    while (SZ(buf) <= n) {
        buf.push_back(buf.back() * SZ(buf));
        ibuf.push_back(ibuf.back() * Inv<T>(SZ(ibuf)));
    }
    return inv ? ibuf[n] : buf[n];
}

template <typename T> T nPr(int n, int r, bool inv = 0) {
    if (n < 0 || n < r || r < 0)
        return 0;
    return Fact<T>(n, inv) * Fact<T>(n - r, inv ^ 1);
}
template <typename T> T nCr(int n, int r, bool inv = 0) {
    if (n < 0 || n < r || r < 0)
        return 0;
    return Fact<T>(n, inv) * Fact<T>(r, inv ^ 1) * Fact<T>(n - r, inv ^ 1);
}
template <typename T> T nHr(int n, int r, bool inv = 0) {
    return nCr<T>(n + r - 1, r, inv);
}

/**
 * @brief Modint
 */
#line 4 "library/Convolution/arbitrary.hpp"

using M1 = fp<1045430273>;
using M2 = fp<1051721729>;
using M3 = fp<1053818881>;
NTT<fp<1045430273>> N1;
NTT<fp<1051721729>> N2;
NTT<fp<1053818881>> N3;
const M2 r_12 = M2(M1::get_mod()).inv();
const M3 r_13 = M3(M1::get_mod()).inv();
const M3 r_23 = M3(M2::get_mod()).inv();
const M3 r_1323 = r_13 * r_23;
template <typename T>
vector<T> ArbitraryMult(const vector<int> &a, const vector<int> &b) {
    if (a.empty() or b.empty())
        return vector<T>();
    int n = a.size() + b.size() - 1;
    vector<T> res(n);
    if (min(a.size(), b.size()) <= 60) {
        rep(i, 0, a.size()) rep(j, 0, b.size()) res[i + j] += T(a[i]) * b[j];
        return res;
    }
    vector<int> vals[3];
    vector<M1> a1(ALL(a)), b1(ALL(b)), c1 = N1.mult(a1, b1);
    vector<M2> a2(ALL(a)), b2(ALL(b)), c2 = N2.mult(a2, b2);
    vector<M3> a3(ALL(a)), b3(ALL(b)), c3 = N3.mult(a3, b3);
    for (M1 x : c1)
        vals[0].push_back(x.v);
    for (M2 x : c2)
        vals[1].push_back(x.v);
    for (M3 x : c3)
        vals[2].push_back(x.v);
    T w1(M1::get_mod()), w2 = w1 * T(M2::get_mod());
    rep(i, 0, n) {
        T p = vals[0][i];
        T q = (vals[1][i] + M2::get_mod() - p) * r_12.v % M2::get_mod();
        T r = ((vals[2][i] + M3::get_mod() - p) * r_1323.v +
               (M3::get_mod() - q) * r_23.v) %
              M3::get_mod();
        res[i] = (p + q * w1 + r * w2);
    }
    return res;
}

/**
 * @brief Arbitrary Mod Convolution
 */
#line 3 "library/Math/bigint.hpp"

template <int D> struct bigint {
    using u128 = __uint128_t;
    static const int B = pow(10, D);
    int sign = 0;
    vector<int> v;
    static int get_D() { return D; }
    static int get_B() { return B; }
    bigint(ll x = 0) {
        if (x < 0)
            x *= -1, sign = 1;
        while (x) {
            v.push_back(x % B);
            x /= B;
        }
    }
    bigint(string s) {
        if (s[0] == '-')
            s.erase(s.begin()), sign = 1;
        int add = 0, cnt = 0, base = 1;
        while (s.size()) {
            if (cnt == D) {
                v.push_back(add);
                cnt = 0;
                add = 0;
                base = 1;
            }
            add = (s.back() - '0') * base + add;
            cnt++;
            base *= 10;
            s.pop_back();
        }
        if (add)
            v.push_back(add);
    }
    bigint operator-() const {
        bigint res = *this;
        res.sign ^= 1;
        return res;
    }
    bigint abs() const {
        bigint res = *this;
        res.sign = 0;
        return res;
    }
    int &operator[](const int i) { return v[i]; }
    int size() const { return v.size(); }
    void norm() {
        rep(i, 0, v.size() - 1) {
            if (v[i] >= 0) {
                v[i + 1] += v[i] / B;
                v[i] %= B;
            } else {
                int c = (-v[i] + B - 1) / B;
                v[i] += c * B;
                v[i + 1] -= c;
            }
        }
        while (!v.empty() and v.back() >= B) {
            int c = v.back() / B;
            v.back() %= B;
            v.push_back(c);
        }
        while (!v.empty() and v.back() == 0)
            v.pop_back();
    }
    string to_str() const {
        string res;
        if (v.empty())
            return "0";
        if (sign)
            res += '-';
        res += to_string(v.back());
        for (int i = v.size() - 2; i >= 0; i--) {
            string add;
            int w = v[i];
            rep(_, 0, D) {
                add += ('0' + (w % 10));
                w /= 10;
            }
            reverse(ALL(add));
            res += add;
        }
        return res;
    }
    friend istream &operator>>(istream &is, bigint<D> &x) {
        string tmp;
        is >> tmp;
        x = bigint(tmp);
        return is;
    }
    friend ostream &operator<<(ostream &os, bigint<D> x) {
        os << x.to_str();
        return os;
    }
    bigint &operator<<=(const int &x) {
        if (!v.empty()) {
            vector<int> add(x, 0);
            v.insert(v.begin(), ALL(add));
        }
        return *this;
    }
    bigint &operator>>=(const int &x) {
        v = vector<int>(v.begin() + min(x, (int)v.size()), v.end());
        return *this;
    }
    bigint &operator+=(const bigint &x) {
        if (sign != x.sign) {
            *this -= (-x);
            return *this;
        }
        if ((int)v.size() < (int)x.size())
            v.resize(x.size(), 0);
        rep(i, 0, x.size()) { v[i] += x.v[i]; }
        norm();
        return *this;
    }
    bigint &operator-=(const bigint &x) {
        if (sign != x.sign) {
            *this += (-x);
            return *this;
        }
        if (abs() < x.abs()) {
            *this = x - (*this);
            sign ^= 1;
            return *this;
        }
        rep(i, 0, x.size()) { v[i] -= x.v[i]; }
        norm();
        return *this;
    }
    bigint &operator*=(const bigint &x) {
        sign ^= x.sign;
        auto v1 = ArbitraryMult<u128>(v, x.v);
        u128 add = 0;
        v.clear();
        for (int i = 0;; i++) {
            if (i >= v1.size() and add == 0)
                break;
            if (i < v1.size())
                add += v1[i];
            v.push_back(add % B);
            add /= B;
        }
        return *this;
    }
    bigint &operator/=(const bigint &x) {
        bigint a = abs(), b = x.abs();
        sign ^= x.sign;
        if (a < b)
            return *this = bigint();
        if (b == bigint(1))
            return *this = a;
        int d = a.size() - b.size() + 1;
        bigint inv(1LL * B * B / b.v.back()), pre;
        int cur = 2, bcur = 1;
        pre = bigint(0);
        while (inv != pre or bcur < b.size()) {
            bcur = min(bcur << 1, b.size());
            bigint c;
            c.v = vector<int>(b.v.end() - bcur, b.v.end());
            pre = inv;
            inv *= ((bigint(2) << (cur + bcur - 1)) - inv * c);
            cur = min(cur << 1, d);
            inv.v = vector<int>(inv.v.end() - cur, inv.v.end());
        }
        inv.v = vector<int>(inv.v.end() - d, inv.v.end());
        bigint res = a * inv;
        res >>= (a.size());
        bigint mul = res * b;
        while (mul + b <= a) {
            res += bigint(1);
            mul += b;
        }
        v = res.v;
        return *this;
    }
    bigint &operator%=(const bigint &x) {
        bigint div = (*this) / x;
        (*this) -= div * x;
        return *this;
    }
    bigint square() {
        bigint res = *this;
        res.sign = 0;
        auto v1 = ArbitraryMult<u128>(v, v);
        res.v.assign(v1.size(), 0);
        rep(i, 0, v1.size()) {
            ll val = v1[i];
            for (int j = i; val; j++) {
                if (j == (int)res.v.size())
                    res.v.push_back(0);
                res.v[j] += val % B;
                val /= B;
            }
        }
        res.norm();
        return res;
    }
    bigint mul(ll x) {
        bigint res = *this;
        if (x < 0)
            res.sign ^= 1, x *= -1;
        for (int i = res.v.size() - 1; i >= 0; i--)
            res.v[i] *= x;
        res.norm();
        return res;
    }
    bigint div(ll x) {
        bigint res = *this;
        if (x < 0)
            res.sign ^= 1, x *= -1;
        for (int i = res.v.size() - 1; i >= 0; i--) {
            if (res.v[i] % x != 0 and i != 0) {
                res.v[i - 1] += B * (res.v[i] % x);
            }
            res.v[i] /= x;
        }
        res.norm();
        return res;
    }
    bigint operator<<(const int &x) const { return bigint(*this) <<= x; }
    bigint operator>>(const int &x) const { return bigint(*this) >>= x; }
    bigint operator+(const bigint &x) const { return bigint(*this) += x; }
    bigint operator-(const bigint &x) const { return bigint(*this) -= x; }
    bigint operator*(const bigint &x) const { return bigint(*this) *= x; }
    bigint operator/(const bigint &x) const { return bigint(*this) /= x; }
    bigint operator%(const bigint &x) const { return bigint(*this) %= x; }
    bool operator<(const bigint &x) const {
        if (sign != x.sign)
            return sign > x.sign;
        if ((int)v.size() != (int)x.size()) {
            if (sign)
                return (int)x.size() < (int)v.size();
            else
                return (int)v.size() < (int)x.size();
        }
        for (int i = v.size() - 1; i >= 0; i--)
            if (v[i] != x.v[i]) {
                if (sign)
                    return x.v[i] < v[i];
                else
                    return v[i] < x.v[i];
            }
        return false;
    }
    bool operator>(const bigint &x) const { return x < *this; }
    bool operator<=(const bigint &x) const { return !(*this > x); }
    bool operator>=(const bigint &x) const { return !(*this < x); }
    bool operator==(const bigint &x) const {
        return !(*this < x) and !(*this > x);
    }
    bool operator!=(const bigint &x) const { return !(*this == x); }
};
typedef bigint<9> Bigint;

struct Bigfloat {
    Bigint v;
    int p = 0;
    Bigfloat() {}
    Bigfloat(const ll &_v) { v = Bigint(_v); }
    Bigfloat(const Bigint &_v, int _p = 0) : v(_v), p(_p) {}
    void set(int _p) {
        if (p < _p) {
            v >>= (_p - p);
        } else {
            v <<= (p - _p);
        }
        p = _p;
    }
    Bigint to_int() const {
        if (p < 0)
            return v >> (-p);
        else
            return v << p;
    }
    Bigfloat &operator+=(const Bigfloat &x) {
        if (p > x.p)
            set(x.p), v += x.v;
        else
            v += x.v << (x.p - p);
        return *this;
    }
    Bigfloat &operator-=(const Bigfloat &x) {
        if (p > x.p)
            set(x.p), v -= x.v;
        else
            v -= x.v << (x.p - p);
        return *this;
    }
    Bigfloat square() {
        Bigfloat res = *this;
        res.p *= 2;
        res.v = res.v.square();
        return res;
    }
    Bigfloat mul(ll x) {
        Bigfloat res = *this;
        res.v = v.mul(x);
        return res;
    }
    Bigfloat div(ll x) {
        Bigfloat res = *this;
        res.v = v.div(x);
        return res;
    }
    Bigfloat &operator*=(const Bigfloat &x) {
        p += x.p;
        v *= x.v;
        return *this;
    }
    Bigfloat &operator/=(const Bigfloat &x) {
        p -= x.p;
        v /= x.v;
        return *this;
    }
    Bigfloat operator+(const Bigfloat &x) const { return Bigfloat(*this) += x; }
    Bigfloat operator-(const Bigfloat &x) const { return Bigfloat(*this) -= x; }
    Bigfloat operator*(const Bigfloat &x) const { return Bigfloat(*this) *= x; }
    Bigfloat operator/(const Bigfloat &x) const { return Bigfloat(*this) /= x; }
    string to_str() {
        string res = v.abs().to_str();
        int d = Bigint::get_D();
        if (p * d > 0)
            res += string(p * d, '0');
        else if (-p * d >= 1 and -p * d < (int)res.size()) {
            res = res.substr(0, (int)res.size() + p * d) + '.' +
                  res.substr((int)res.size() + p * d);
        } else if (-p * d >= (int)res.size())
            res = "0." + string(-p * d - (int)res.size(), '0') + res;
        if (v.sign) {
            res.insert(res.begin(), '-');
        }
        return res;
    }
    friend ostream &operator<<(ostream &os, Bigfloat x) {
        os << x.to_str();
        return os;
    }
};

Bigfloat sqrt(ll n, int d) {
    Bigfloat res(Bigint((ll)sqrt(1LL * Bigint::get_B() * Bigint::get_B() / n)),
                 -1),
        pre;
    int cur = 1;
    while (pre.v != res.v) {
        cur = min(cur << 1, d);
        pre = res;
        Bigfloat add = Bigfloat(1) - res.square().mul(n);
        add.set(-cur);
        res += (res * add).div(2);
        res.set(-cur);
    }
    return res.mul(n);
}

/**
 * @brief Big Integer(Float)
 */
#line 2 "library/Math/fraction.hpp"

template <typename T> struct Frac {
    T a, b;
    Frac(T _a = 0) { init(_a, 1); }
    Frac(T _a, T _b) { init(_a, _b); }
    Frac &init(T _a, T _b) {
        // T g = GCD(_a, _b);
        a = _a, b = _b;
        if (b < 0)
            a = -a, b = -b;
        return *this;
    }
    Frac inv() const { return Frac(b, a); }
    Frac operator-() const { return Frac(-a, b); }
    Frac &operator+=(const Frac &x) { return init(a * x.b + x.a * b, b * x.b); }
    Frac &operator-=(const Frac &x) { return init(a * x.b - x.a * b, b * x.b); }
    Frac &operator*=(const Frac &x) { return init(a * x.a, b * x.b); }
    Frac &operator/=(const Frac &x) { return init(a * x.b, b * x.a); }
    Frac operator+(const Frac &x) const { return Frac(*this) += x; }
    Frac operator-(const Frac &x) const { return Frac(*this) -= x; }
    Frac operator*(const Frac &x) const { return Frac(*this) *= x; }
    Frac operator/(const Frac &x) const { return Frac(*this) /= x; }
    bool operator<(const Frac &x) const { return a * x.b < b * x.a; }
    bool operator>(const Frac &x) const { return x < *this; }
    bool operator<=(const Frac &x) const { return !(x < *this); }
    bool operator>=(const Frac &x) const { return !(*this < x); }
    bool operator==(const Frac &x) const { return (*this <= x and x <= *this); }
    bool operator!=(const Frac &x) const { return !(*this == x); }
    T GCD(T a, T b) {
        if (b == 0)
            return a;
        else
            return GCD(b, a % b);
    }
};
template <typename T> Frac<T> between(const Frac<T> &x, const Frac<T> &y) {
    if (x.a < x.b and y.b < y.a)
        return Frac(1);
    else if (x.b <= x.a) {
        T add = floor(x.a / x.b);
        return between(x - add, y - add) + add;
    } else
        return between(y.inv(), x.inv()).inv();
}

/**
 * @brief Fraction
 * @docs docs/fraction.md
 */
#line 6 "sol.cpp"

FastIO io;
int main() {
    auto yes = [&] {
        io.write("Yes");
        exit(0);
    };
    auto no = [&] {
        io.write("No");
        exit(0);
    };

    int n;
    io.read(n);
    vector<ll> a(n), b(n), c(n), d(n);
    io.read(a, b, c, d);

    using fr = Frac<Bigint>;
    using P = pair<fr, fr>;
    vector<int> ord1(n), ord2(n);
    iota(ALL(ord1), 0);
    iota(ALL(ord2), 0);
    sort(ALL(ord1),
         [&](int i, int j) { return fr(b[i], a[i]) < fr(b[j], a[j]); });
    sort(ALL(ord2),
         [&](int i, int j) { return fr(d[i], c[i]) < fr(d[j], c[j]); });

    vector<P> L({{fr(0), fr(0)}}), U = L;
    for (auto &i : ord1) {
        fr x = L.back().first + fr(a[i]);
        fr y = L.back().second + fr(b[i]);
        L.push_back({x, y});
    }
    for (auto &i : ord2) {
        fr x = U.back().first + fr(c[i]);
        fr y = U.back().second + fr(d[i]);
        U.push_back({x, y});
    }

    rep(i, 0, SZ(U)) {
        rep(j, 0, SZ(L) - 1) {
            P pq = {L[j + 1].first - L[j].first, L[j + 1].second - L[j].second};
            P pr = {U[i].first - L[j].first, U[i].second - L[j].second};
            if (pq.first * pr.second - pq.second * pr.first < fr(0))
                no();
        }
    }

    if (ord1 == ord2)
        yes();

    // cerr << "CP3" << '\n';
    fr x, y;
    rep(i, 0, n - 1) {
        auto [xi2, yi2] = L[i + 2];
        auto direct = (yi2 - y) / (xi2 - x);
        fr mx(inf);
        rep(i, 0, SZ(U)) {
            if (x < U[i].first and U[i].first < xi2) {
                chmin(mx, (U[i].second - y) / (U[i].first - x));
            }
        }
        if (mx == fr(inf) or direct <= mx)
            yes();

        // pass
        auto [xi1, yi1] = L[i + 1];
        auto nslope = (yi1 - y) / (xi1 - x);
        if (mx == nslope) {
            x = xi1, y = yi1;
            continue;
        }
        auto nx = (mx * x - nslope * xi1 - y + yi1) / (mx - nslope);
        auto ny = mx * (nx - x) + y;
        // io.write(nx.a.to_str(), nx.b.to_str());
        x = nx, y = ny;
    }
    no();
    return 0;
}