#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define vi vector<int>
#define vl vector<ll>
#define vii vector<pair<int,int>>
#define vll vector<pair<ll,ll>>
#define vvi vector<vector<int>>
#define vvl vector<vector<ll>>
#define vvii vector<vector<pair<int,int>>>
#define vvll vector<vector<pair<ll,ll>>>
#define vst vector<string>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define mkunique(x) sort(all(x));(x).erase(unique(all(x)),(x).end())
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod=998244353,MAX=300005,INF=15<<26;

// https://nyaannyaan.github.io/library/math/bigint.hpp.html

#pragma once

#include <algorithm>
#include <cassert>
#include <cmath>
#include <iostream>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

#pragma once

#include <type_traits>
using namespace std;

namespace internal {
template <typename T>
using is_broadly_integral =
typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
is_same_v<T, __uint128_t>,
true_type, false_type>::type;

template <typename T>
using is_broadly_signed =
typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
true_type, false_type>::type;

template <typename T>
using is_broadly_unsigned =
typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
true_type, false_type>::type;

#define ENABLE_VALUE(x) \
template <typename T> \
constexpr bool x##_v = x<T>::value;

ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE

#define ENABLE_HAS_TYPE(var)                                   \
template <class, class = void>                               \
struct has_##var : false_type {};                            \
template <class T>                                           \
struct has_##var<T, void_t<typename T::var>> : true_type {}; \
template <class T>                                           \
constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_VAR(var)                                     \
template <class, class = void>                                \
struct has_##var : false_type {};                             \
template <class T>                                            \
struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
template <class T>                                            \
constexpr auto has_##var##_v = has_##var<T>::value;

}  // namespace internal

#pragma once

template <uint32_t mod>
struct LazyMontgomeryModInt {
    using mint = LazyMontgomeryModInt;
    using i32 = int32_t;
    using u32 = uint32_t;
    using u64 = uint64_t;
    
    static constexpr u32 get_r() {
        u32 ret = mod;
        for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
        return ret;
    }
    
    static constexpr u32 r = get_r();
    static constexpr u32 n2 = -u64(mod) % mod;
    static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
    static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
    static_assert(r * mod == 1, "this code has bugs.");
    
    u32 a;
    
    constexpr LazyMontgomeryModInt() : a(0) {}
    constexpr LazyMontgomeryModInt(const int64_t &b)
    : a(reduce(u64(b % mod + mod) * n2)){};
    
    static constexpr u32 reduce(const u64 &b) {
        return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
    }
    
    constexpr mint &operator+=(const mint &b) {
        if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }
    
    constexpr mint &operator-=(const mint &b) {
        if (i32(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }
    
    constexpr mint &operator*=(const mint &b) {
        a = reduce(u64(a) * b.a);
        return *this;
    }
    
    constexpr mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }
    
    constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
    constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
    constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
    constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
    constexpr bool operator==(const mint &b) const {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr bool operator!=(const mint &b) const {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr mint operator-() const { return mint() - mint(*this); }
    constexpr mint operator+() const { return mint(*this); }
    
    constexpr mint pow(u64 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }
    
    constexpr mint inverse() const {
        int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
        while (y > 0) {
            t = x / y;
            x -= t * y, u -= t * v;
            tmp = x, x = y, y = tmp;
            tmp = u, u = v, v = tmp;
        }
        return mint{u};
    }
    
    friend ostream &operator<<(ostream &os, const mint &b) {
        return os << b.get();
    }
    
    friend istream &operator>>(istream &is, mint &b) {
        int64_t t;
        is >> t;
        b = LazyMontgomeryModInt<mod>(t);
        return (is);
    }
    
    constexpr u32 get() const {
        u32 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }
    
    static constexpr u32 get_mod() { return mod; }
};

#pragma once

template <typename mint>
struct NTT {
    static constexpr uint32_t get_pr() {
        uint32_t _mod = mint::get_mod();
        using u64 = uint64_t;
        u64 ds[32] = {};
        int idx = 0;
        u64 m = _mod - 1;
        for (u64 i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                ds[idx++] = i;
                while (m % i == 0) m /= i;
            }
        }
        if (m != 1) ds[idx++] = m;
        
        uint32_t _pr = 2;
        while (1) {
            int flg = 1;
            for (int i = 0; i < idx; ++i) {
                u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
                while (b) {
                    if (b & 1) r = r * a % _mod;
                    a = a * a % _mod;
                    b >>= 1;
                }
                if (r == 1) {
                    flg = 0;
                    break;
                }
            }
            if (flg == 1) break;
            ++_pr;
        }
        return _pr;
    };
    
    static constexpr uint32_t mod = mint::get_mod();
    static constexpr uint32_t pr = get_pr();
    static constexpr int level = __builtin_ctzll(mod - 1);
    mint dw[level], dy[level];
    
    void setwy(int k) {
        mint w[level], y[level];
        w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
        y[k - 1] = w[k - 1].inverse();
        for (int i = k - 2; i > 0; --i)
            w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
        dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
        for (int i = 3; i < k; ++i) {
            dw[i] = dw[i - 1] * y[i - 2] * w[i];
            dy[i] = dy[i - 1] * w[i - 2] * y[i];
        }
    }
    
    NTT() { setwy(level); }
    
    void fft4(vector<mint> &a, int k) {
        if ((int)a.size() <= 1) return;
        if (k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        if (k & 1) {
            int v = 1 << (k - 1);
            for (int j = 0; j < v; ++j) {
                mint ajv = a[j + v];
                a[j + v] = a[j] - ajv;
                a[j] += ajv;
            }
        }
        int u = 1 << (2 + (k & 1));
        int v = 1 << (k - 2 - (k & 1));
        mint one = mint(1);
        mint imag = dw[1];
        while (v) {
            // jh = 0
            {
                int j0 = 0;
                int j1 = v;
                int j2 = j1 + v;
                int j3 = j2 + v;
                for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
                    mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
                }
            }
            // jh >= 1
            mint ww = one, xx = one * dw[2], wx = one;
            for (int jh = 4; jh < u;) {
                ww = xx * xx, wx = ww * xx;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for (; j0 < je; ++j0, ++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
                    t3 = a[j2 + v] * wx;
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
                }
                xx *= dw[__builtin_ctzll((jh += 4))];
            }
            u <<= 2;
            v >>= 2;
        }
    }
    
    void ifft4(vector<mint> &a, int k) {
        if ((int)a.size() <= 1) return;
        if (k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        int u = 1 << (k - 2);
        int v = 1;
        mint one = mint(1);
        mint imag = dy[1];
        while (u) {
            // jh = 0
            {
                int j0 = 0;
                int j1 = v;
                int j2 = v + v;
                int j3 = j2 + v;
                for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
                    mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
                    a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
                    a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
                }
            }
            // jh >= 1
            mint ww = one, xx = one * dy[2], yy = one;
            u <<= 2;
            for (int jh = 4; jh < u;) {
                ww = xx * xx, yy = xx * imag;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for (; j0 < je; ++j0, ++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
                    a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
                    a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
                }
                xx *= dy[__builtin_ctzll(jh += 4)];
            }
            u >>= 4;
            v <<= 2;
        }
        if (k & 1) {
            u = 1 << (k - 1);
            for (int j = 0; j < u; ++j) {
                mint ajv = a[j] - a[j + u];
                a[j] += a[j + u];
                a[j + u] = ajv;
            }
        }
    }
    
    void ntt(vector<mint> &a) {
        if ((int)a.size() <= 1) return;
        fft4(a, __builtin_ctz(a.size()));
    }
    
    void intt(vector<mint> &a) {
        if ((int)a.size() <= 1) return;
        ifft4(a, __builtin_ctz(a.size()));
        mint iv = mint(a.size()).inverse();
        for (auto &x : a) x *= iv;
    }
    
    vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
        int l = a.size() + b.size() - 1;
        if (min<int>(a.size(), b.size()) <= 40) {
            vector<mint> s(l);
            for (int i = 0; i < (int)a.size(); ++i)
                for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
            return s;
        }
        int k = 2, M = 4;
        while (M < l) M <<= 1, ++k;
        setwy(k);
        vector<mint> s(M);
        for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
        fft4(s, k);
        if (a.size() == b.size() && a == b) {
            for (int i = 0; i < M; ++i) s[i] *= s[i];
        } else {
            vector<mint> t(M);
            for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
            fft4(t, k);
            for (int i = 0; i < M; ++i) s[i] *= t[i];
        }
        ifft4(s, k);
        s.resize(l);
        mint invm = mint(M).inverse();
        for (int i = 0; i < l; ++i) s[i] *= invm;
        return s;
    }
    
    void ntt_doubling(vector<mint> &a) {
        int M = (int)a.size();
        auto b = a;
        intt(b);
        mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
        for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;
        ntt(b);
        copy(begin(b), end(b), back_inserter(a));
    }
};

#pragma once

namespace ArbitraryNTT {
using i64 = int64_t;
using u128 = __uint128_t;
constexpr int32_t m0 = 167772161;
constexpr int32_t m1 = 469762049;
constexpr int32_t m2 = 754974721;
using mint0 = LazyMontgomeryModInt<m0>;
using mint1 = LazyMontgomeryModInt<m1>;
using mint2 = LazyMontgomeryModInt<m2>;
constexpr int r01 = mint1(m0).inverse().get();
constexpr int r02 = mint2(m0).inverse().get();
constexpr int r12 = mint2(m1).inverse().get();
constexpr int r02r12 = i64(r02) * r12 % m2;
constexpr i64 w1 = m0;
constexpr i64 w2 = i64(m0) * m1;

template <typename T, typename submint>
vector<submint> mul(const vector<T> &a, const vector<T> &b) {
    static NTT<submint> ntt;
    vector<submint> s(a.size()), t(b.size());
    for (int i = 0; i < (int)a.size(); ++i) s[i] = i64(a[i] % submint::get_mod());
    for (int i = 0; i < (int)b.size(); ++i) t[i] = i64(b[i] % submint::get_mod());
    return ntt.multiply(s, t);
}

template <typename T>
vector<int> multiply(const vector<T> &s, const vector<T> &t, int mod) {
    auto d0 = mul<T, mint0>(s, t);
    auto d1 = mul<T, mint1>(s, t);
    auto d2 = mul<T, mint2>(s, t);
    int n = d0.size();
    vector<int> ret(n);
    const int W1 = w1 % mod;
    const int W2 = w2 % mod;
    for (int i = 0; i < n; i++) {
        int n1 = d1[i].get(), n2 = d2[i].get(), a = d0[i].get();
        int b = i64(n1 + m1 - a) * r01 % m1;
        int c = (i64(n2 + m2 - a) * r02r12 + i64(m2 - b) * r12) % m2;
        ret[i] = (i64(a) + i64(b) * W1 + i64(c) * W2) % mod;
    }
    return ret;
}

template <typename mint>
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
    if (a.size() == 0 && b.size() == 0) return {};
    if (min<int>(a.size(), b.size()) < 128) {
        vector<mint> ret(a.size() + b.size() - 1);
        for (int i = 0; i < (int)a.size(); ++i)
            for (int j = 0; j < (int)b.size(); ++j) ret[i + j] += a[i] * b[j];
        return ret;
    }
    vector<int> s(a.size()), t(b.size());
    for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i].get();
    for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i].get();
    vector<int> u = multiply<int>(s, t, mint::get_mod());
    vector<mint> ret(u.size());
    for (int i = 0; i < (int)u.size(); ++i) ret[i] = mint(u[i]);
    return ret;
}

template <typename T>
vector<u128> multiply_u128(const vector<T> &s, const vector<T> &t) {
    if (s.size() == 0 && t.size() == 0) return {};
    if (min<int>(s.size(), t.size()) < 128) {
        vector<u128> ret(s.size() + t.size() - 1);
        for (int i = 0; i < (int)s.size(); ++i)
            for (int j = 0; j < (int)t.size(); ++j) ret[i + j] += i64(s[i]) * t[j];
        return ret;
    }
    auto d0 = mul<T, mint0>(s, t);
    auto d1 = mul<T, mint1>(s, t);
    auto d2 = mul<T, mint2>(s, t);
    int n = d0.size();
    vector<u128> ret(n);
    for (int i = 0; i < n; i++) {
        i64 n1 = d1[i].get(), n2 = d2[i].get();
        i64 a = d0[i].get();
        i64 b = (n1 + m1 - a) * r01 % m1;
        i64 c = ((n2 + m2 - a) * r02r12 + (m2 - b) * r12) % m2;
        ret[i] = a + b * w1 + u128(c) * w2;
    }
    return ret;
}
}  // namespace ArbitraryNTT

namespace MultiPrecisionIntegerImpl {
struct TENS {
    static constexpr int offset = 30;
    constexpr TENS() : _tend() {
        _tend[offset] = 1;
        for (int i = 1; i <= offset; i++) {
            _tend[offset + i] = _tend[offset + i - 1] * 10.0;
            _tend[offset - i] = 1.0 / _tend[offset + i];
        }
    }
    long double ten_ld(int n) const {
        assert(-offset <= n and n <= offset);
        return _tend[n + offset];
    }
    
private:
    long double _tend[offset * 2 + 1];
};
}  // namespace MultiPrecisionIntegerImpl

// 0 は neg=false, dat={} として扱う
struct MultiPrecisionInteger {
    using M = MultiPrecisionInteger;
    inline constexpr static MultiPrecisionIntegerImpl::TENS tens = {};
    
    static constexpr int D = 1000000000;
    static constexpr int logD = 9;
    bool neg;
    vector<int> dat;
    
    MultiPrecisionInteger() : neg(false), dat() {}
    
    MultiPrecisionInteger(bool n, const vector<int>& d) : neg(n), dat(d) {}
    
    template <typename I,
    enable_if_t<internal::is_broadly_integral_v<I>>* = nullptr>
    MultiPrecisionInteger(I x) : neg(false) {
        if constexpr (internal::is_broadly_signed_v<I>) {
            if (x < 0) neg = true, x = -x;
        }
        while (x) dat.push_back(x % D), x /= D;
    }
    
    MultiPrecisionInteger(const string& S) : neg(false) {
        assert(!S.empty());
        if (S.size() == 1u && S[0] == '0') return;
        int l = 0;
        if (S[0] == '-') ++l, neg = true;
        for (int ie = S.size(); l < ie; ie -= logD) {
            int is = max(l, ie - logD);
            long long x = 0;
            for (int i = is; i < ie; i++) x = x * 10 + S[i] - '0';
            dat.push_back(x);
        }
        while(!dat.empty() and dat.back() == 0) dat.pop_back();
    }
    
    friend M operator+(const M& lhs, const M& rhs) {
        if (lhs.neg == rhs.neg) return {lhs.neg, _add(lhs.dat, rhs.dat)};
        if (_leq(lhs.dat, rhs.dat)) {
            // |l| <= |r|
            auto c = _sub(rhs.dat, lhs.dat);
            bool n = _is_zero(c) ? false : rhs.neg;
            return {n, c};
        }
        auto c = _sub(lhs.dat, rhs.dat);
        bool n = _is_zero(c) ? false : lhs.neg;
        return {n, c};
    }
    friend M operator-(const M& lhs, const M& rhs) { return lhs + (-rhs); }
    
    friend M operator*(const M& lhs, const M& rhs) {
        auto c = _mul(lhs.dat, rhs.dat);
        bool n = _is_zero(c) ? false : (lhs.neg ^ rhs.neg);
        return {n, c};
    }
    friend pair<M, M> divmod(const M& lhs, const M& rhs) {
        auto dm = _divmod_newton(lhs.dat, rhs.dat);
        bool dn = _is_zero(dm.first) ? false : lhs.neg != rhs.neg;
        bool mn = _is_zero(dm.second) ? false : lhs.neg;
        return {M{dn, dm.first}, M{mn, dm.second}};
    }
    friend M operator/(const M& lhs, const M& rhs) {
        return divmod(lhs, rhs).first;
    }
    friend M operator%(const M& lhs, const M& rhs) {
        return divmod(lhs, rhs).second;
    }
    
    M& operator+=(const M& rhs) { return (*this) = (*this) + rhs; }
    M& operator-=(const M& rhs) { return (*this) = (*this) - rhs; }
    M& operator*=(const M& rhs) { return (*this) = (*this) * rhs; }
    M& operator/=(const M& rhs) { return (*this) = (*this) / rhs; }
    M& operator%=(const M& rhs) { return (*this) = (*this) % rhs; }
    
    M operator-() const {
        if (is_zero()) return *this;
        return {!neg, dat};
    }
    M operator+() const { return *this; }
    friend M abs(const M& m) { return {false, m.dat}; }
    bool is_zero() const { return _is_zero(dat); }
    
    friend bool operator==(const M& lhs, const M& rhs) {
        return lhs.neg == rhs.neg && lhs.dat == rhs.dat;
    }
    friend bool operator!=(const M& lhs, const M& rhs) {
        return lhs.neg != rhs.neg || lhs.dat != rhs.dat;
    }
    friend bool operator<(const M& lhs, const M& rhs) {
        if (lhs == rhs) return false;
        return _neq_lt(lhs, rhs);
    }
    friend bool operator<=(const M& lhs, const M& rhs) {
        if (lhs == rhs) return true;
        return _neq_lt(lhs, rhs);
    }
    friend bool operator>(const M& lhs, const M& rhs) {
        if (lhs == rhs) return false;
        return _neq_lt(rhs, lhs);
    }
    friend bool operator>=(const M& lhs, const M& rhs) {
        if (lhs == rhs) return true;
        return _neq_lt(rhs, lhs);
    }
    
    // a * 10^b (1 <= |a| < 10) の形で渡す
    // 相対誤差：10^{-16} ~ 10^{-19} 程度 (処理系依存)
    pair<long double, int> dfp() const {
        if (is_zero()) return {0, 0};
        int l = max<int>(0, _size() - 3);
        int b = logD * l;
        string prefix{};
        for (int i = _size() - 1; i >= l; i--) {
            prefix += _itos(dat[i], i != _size() - 1);
        }
        b += prefix.size() - 1;
        long double a = 0;
        for (auto& c : prefix) a = a * 10.0 + (c - '0');
        a *= tens.ten_ld(-((int)prefix.size()) + 1);
        a = clamp<long double>(a, 1.0, nextafterl(10.0, 1.0));
        if (neg) a = -a;
        return {a, b};
    }
    string to_string() const {
        if (is_zero()) return "0";
        string res;
        if (neg) res.push_back('-');
        for (int i = _size() - 1; i >= 0; i--) {
            res += _itos(dat[i], i != _size() - 1);
        }
        return res;
    }
    long double to_ld() const {
        auto [a, b] = dfp();
        if (-tens.offset <= b and b <= tens.offset) {
            return a * tens.ten_ld(b);
        }
        return a * powl(10, b);
    }
    long long to_ll() const {
        long long res = _to_ll(dat);
        return neg ? -res : res;
    }
    __int128_t to_i128() const {
        __int128_t res = _to_i128(dat);
        return neg ? -res : res;
    }
    
    friend istream& operator>>(istream& is, M& m) {
        string s;
        is >> s;
        m = M{s};
        return is;
    }
    
    friend ostream& operator<<(ostream& os, const M& m) {
        return os << m.to_string();
    }
    
    // 内部の関数をテスト
    static void _test_private_function(const M&, const M&);
    
private:
    // size
    int _size() const { return dat.size(); }
    // a == b
    static bool _eq(const vector<int>& a, const vector<int>& b) { return a == b; }
    // a < b
    static bool _lt(const vector<int>& a, const vector<int>& b) {
        if (a.size() != b.size()) return a.size() < b.size();
        for (int i = a.size() - 1; i >= 0; i--) {
            if (a[i] != b[i]) return a[i] < b[i];
        }
        return false;
    }
    // a <= b
    static bool _leq(const vector<int>& a, const vector<int>& b) {
        return _eq(a, b) || _lt(a, b);
    }
    // a < b (s.t. a != b)
    static bool _neq_lt(const M& lhs, const M& rhs) {
        assert(lhs != rhs);
        if (lhs.neg != rhs.neg) return lhs.neg;
        bool f = _lt(lhs.dat, rhs.dat);
        if (f) return !lhs.neg;
        return lhs.neg;
    }
    // a == 0
    static bool _is_zero(const vector<int>& a) { return a.empty(); }
    // a == 1
    static bool _is_one(const vector<int>& a) {
        return (int)a.size() == 1 && a[0] == 1;
    }
    // 末尾 0 を削除
    static void _shrink(vector<int>& a) {
        while (a.size() && a.back() == 0) a.pop_back();
    }
    // 末尾 0 を削除
    void _shrink() {
        while (_size() && dat.back() == 0) dat.pop_back();
    }
    // a + b
    static vector<int> _add(const vector<int>& a, const vector<int>& b) {
        vector<int> c(max(a.size(), b.size()) + 1);
        for (int i = 0; i < (int)a.size(); i++) c[i] += a[i];
        for (int i = 0; i < (int)b.size(); i++) c[i] += b[i];
        for (int i = 0; i < (int)c.size() - 1; i++) {
            if (c[i] >= D) c[i] -= D, c[i + 1]++;
        }
        _shrink(c);
        return c;
    }
    // a - b
    static vector<int> _sub(const vector<int>& a, const vector<int>& b) {
        assert(_leq(b, a));
        vector<int> c{a};
        int borrow = 0;
        for (int i = 0; i < (int)a.size(); i++) {
            if (i < (int)b.size()) borrow += b[i];
            c[i] -= borrow;
            borrow = 0;
            if (c[i] < 0) c[i] += D, borrow = 1;
        }
        assert(borrow == 0);
        _shrink(c);
        return c;
    }
    // a * b (fft)
    static vector<int> _mul_fft(const vector<int>& a, const vector<int>& b) {
        if (a.empty() || b.empty()) return {};
        auto m = ArbitraryNTT::multiply_u128(a, b);
        vector<int> c;
        c.reserve(m.size() + 3);
        __uint128_t x = 0;
        for (int i = 0;; i++) {
            if (i >= (int)m.size() && x == 0) break;
            if (i < (int)m.size()) x += m[i];
            c.push_back(x % D);
            x /= D;
        }
        _shrink(c);
        return c;
    }
    // a * b (naive)
    static vector<int> _mul_naive(const vector<int>& a, const vector<int>& b) {
        if (a.empty() || b.empty()) return {};
        vector<long long> prod(a.size() + b.size() - 1 + 1);
        for (int i = 0; i < (int)a.size(); i++) {
            for (int j = 0; j < (int)b.size(); j++) {
                long long p = 1LL * a[i] * b[j];
                prod[i + j] += p;
                if (prod[i + j] >= (4LL * D * D)) {
                    prod[i + j] -= 4LL * D * D;
                    prod[i + j + 1] += 4LL * D;
                }
            }
        }
        vector<int> c(prod.size() + 1);
        long long x = 0;
        int i = 0;
        for (; i < (int)prod.size(); i++) x += prod[i], c[i] = x % D, x /= D;
        while (x) c[i] = x % D, x /= D, i++;
        _shrink(c);
        return c;
    }
    // a * b
    static vector<int> _mul(const vector<int>& a, const vector<int>& b) {
        if (_is_zero(a) || _is_zero(b)) return {};
        if (_is_one(a)) return b;
        if (_is_one(b)) return a;
        if (min<int>(a.size(), b.size()) <= 128) {
            return a.size() < b.size() ? _mul_naive(b, a) : _mul_naive(a, b);
        }
        return _mul_fft(a, b);
    }
    // 0 <= A < 1e18, 1 <= B < 1e9
    static pair<vector<int>, vector<int>> _divmod_li(const vector<int>& a,
                                                     const vector<int>& b) {
        assert(0 <= (int)a.size() && (int)a.size() <= 2);
        assert((int)b.size() == 1);
        long long va = _to_ll(a);
        int vb = b[0];
        return {_integer_to_vec(va / vb), _integer_to_vec(va % vb)};
    }
    // 0 <= A < 1e18, 1 <= B < 1e18
    static pair<vector<int>, vector<int>> _divmod_ll(const vector<int>& a,
                                                     const vector<int>& b) {
        assert(0 <= (int)a.size() && (int)a.size() <= 2);
        assert(1 <= (int)b.size() && (int)b.size() <= 2);
        long long va = _to_ll(a), vb = _to_ll(b);
        return {_integer_to_vec(va / vb), _integer_to_vec(va % vb)};
    }
    // 1 <= B < 1e9
    static pair<vector<int>, vector<int>> _divmod_1e9(const vector<int>& a,
                                                      const vector<int>& b) {
        assert((int)b.size() == 1);
        if (b[0] == 1) return {a, {}};
        if ((int)a.size() <= 2) return _divmod_li(a, b);
        vector<int> quo(a.size());
        long long d = 0;
        int b0 = b[0];
        for (int i = a.size() - 1; i >= 0; i--) {
            d = d * D + a[i];
            assert(d < 1LL * D * b0);
            int q = d / b0, r = d % b0;
            quo[i] = q, d = r;
        }
        _shrink(quo);
        return {quo, d ? vector<int>{int(d)} : vector<int>{}};
    }
    // 0 <= A, 1 <= B
    static pair<vector<int>, vector<int>> _divmod_naive(const vector<int>& a,
                                                        const vector<int>& b) {
        if (_is_zero(b)) {
            cerr << "Divide by Zero Exception" << endl;
            exit(1);
        }
        assert(1 <= (int)b.size());
        if ((int)b.size() == 1) return _divmod_1e9(a, b);
        if (max<int>(a.size(), b.size()) <= 2) return _divmod_ll(a, b);
        if (_lt(a, b)) return {{}, a};
        // B >= 1e9, A >= B
        int norm = D / (b.back() + 1);
        vector<int> x = _mul(a, {norm});
        vector<int> y = _mul(b, {norm});
        int yb = y.back();
        vector<int> quo(x.size() - y.size() + 1);
        vector<int> rem(x.end() - y.size(), x.end());
        for (int i = quo.size() - 1; i >= 0; i--) {
            if (rem.size() < y.size()) {
                // do nothing
            } else if (rem.size() == y.size()) {
                if (_leq(y, rem)) {
                    quo[i] = 1, rem = _sub(rem, y);
                }
            } else {
                assert(y.size() + 1 == rem.size());
                long long rb = 1LL * rem[rem.size() - 1] * D + rem[rem.size() - 2];
                int q = rb / yb;
                vector<int> yq = _mul(y, {q});
                // 真の商は q-2 以上 q+1 以下だが自信が無いので念のため while を回す
                while (_lt(rem, yq)) q--, yq = _sub(yq, y);
                rem = _sub(rem, yq);
                while (_leq(y, rem)) q++, rem = _sub(rem, y);
                quo[i] = q;
            }
            if (i) rem.insert(begin(rem), x[i - 1]);
        }
        _shrink(quo), _shrink(rem);
        auto [q2, r2] = _divmod_1e9(rem, {norm});
        assert(_is_zero(r2));
        return {quo, q2};
    }
    
    // 0 <= A, 1 <= B
    static pair<vector<int>, vector<int>> _divmod_dc(const vector<int>& a,
                                                     const vector<int>& b);
    
    // 1 / a を 絶対誤差 B^{-deg} で求める
    static vector<int> _calc_inv(const vector<int>& a, int deg) {
        assert(!a.empty() && D / 2 <= a.back() and a.back() < D);
        int k = deg, c = a.size();
        while (k > 64) k = (k + 1) / 2;
        vector<int> z(c + k + 1);
        z.back() = 1;
        z = _divmod_naive(z, a).first;
        while (k < deg) {
            vector<int> s = _mul(z, z);
            s.insert(begin(s), 0);
            int d = min(c, 2 * k + 1);
            vector<int> t{end(a) - d, end(a)}, u = _mul(s, t);
            u.erase(begin(u), begin(u) + d);
            vector<int> w(k + 1), w2 = _add(z, z);
            copy(begin(w2), end(w2), back_inserter(w));
            z = _sub(w, u);
            z.erase(begin(z));
            k *= 2;
        }
        z.erase(begin(z), begin(z) + k - deg);
        return z;
    }
    
    static pair<vector<int>, vector<int>> _divmod_newton(const vector<int>& a,
                                                         const vector<int>& b) {
        if (_is_zero(b)) {
            cerr << "Divide by Zero Exception" << endl;
            exit(1);
        }
        if ((int)b.size() <= 64) return _divmod_naive(a, b);
        if ((int)a.size() - (int)b.size() <= 64) return _divmod_naive(a, b);
        int norm = D / (b.back() + 1);
        vector<int> x = _mul(a, {norm});
        vector<int> y = _mul(b, {norm});
        int s = x.size(), t = y.size();
        int deg = s - t + 2;
        vector<int> z = _calc_inv(y, deg);
        vector<int> q = _mul(x, z);
        q.erase(begin(q), begin(q) + t + deg);
        vector<int> yq = _mul(y, {q});
        while (_lt(x, yq)) q = _sub(q, {1}), yq = _sub(yq, y);
        vector<int> r = _sub(x, yq);
        while (_leq(y, r)) q = _add(q, {1}), r = _sub(r, y);
        _shrink(q), _shrink(r);
        auto [q2, r2] = _divmod_1e9(r, {norm});
        assert(_is_zero(r2));
        return {q, q2};
    }
    
    // int -> string
    // 先頭かどうかに応じて zero padding するかを決める
    static string _itos(int x, bool zero_padding) {
        assert(0 <= x && x < D);
        string res;
        for (int i = 0; i < logD; i++) {
            res.push_back('0' + x % 10), x /= 10;
        }
        if (!zero_padding) {
            while (res.size() && res.back() == '0') res.pop_back();
            assert(!res.empty());
        }
        reverse(begin(res), end(res));
        return res;
    }
    
    // convert ll to vec
    template <typename I,
    enable_if_t<internal::is_broadly_integral_v<I>>* = nullptr>
    static vector<int> _integer_to_vec(I x) {
        if constexpr (internal::is_broadly_signed_v<I>) {
            assert(x >= 0);
        }
        vector<int> res;
        while (x) res.push_back(x % D), x /= D;
        return res;
    }
    
    static long long _to_ll(const vector<int>& a) {
        long long res = 0;
        for (int i = (int)a.size() - 1; i >= 0; i--) res = res * D + a[i];
        return res;
    }
    
    static __int128_t _to_i128(const vector<int>& a) {
        __int128_t res = 0;
        for (int i = (int)a.size() - 1; i >= 0; i--) res = res * D + a[i];
        return res;
    }
    
    static void _dump(const vector<int>& a, string s = "") {
        if (!s.empty()) cerr << s << " : ";
        cerr << "{ ";
        for (int i = 0; i < (int)a.size(); i++) cerr << a[i] << ", ";
        cerr << "}" << endl;
    }
};

using bigint = MultiPrecisionInteger;

/**
 * @brief 多倍長整数
 */

//有理数

bigint gcdd(bigint a,bigint b){
    if(b==0) return a;
    return gcdd(b,a%b);
}

bigint abss(bigint a){
    if(a>=0) return a;
    else return -a;
}

int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    ll Q;cin>>Q;
    ll mi=-INF,sum=0;
    bigint a=1,b=0;
    while(Q--){
        ll t,i,d;cin>>t>>i>>d;
        chmax(mi,t-sum);
        
        bigint g=gcdd(a,i);
        if(b%g!=((t-sum)%g+g)%g){
            cout<<-1<<endl;
            return 0;
        }
        
        while(b%i!=((t-sum)%i+i)%i){
            b+=a;
        }
        
        a=a/gcdd(a,i)*i;
        sum+=d;
        //cout<<mi<<" "<<sum<<" "<<a<<" "<<b<<endl;
    }
    
    while(b<mi) b+=a;
    
    cout<<b<<endl;
}