// https://github.com/edon8618/mylib

// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2")

#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;



// #include <boost/multiprecision/cpp_int.hpp>
// using namespace boost::multiprecision;

#define ll long long
#define ld long double
#define rep(i, n) for (ll i = 0; i < (ll)(n); ++i)
#define vi vector<int>
#define vl vector<ll>
#define vd vector<double>
// #define vb vector<bool>
// #define vs vector<string>
#define vc vector<char>
#define ull unsigned long long
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()

template<class T, class U>
inline bool chmax(T &a, const U &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T, class U>
inline bool chmin(T &a, const U &b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}


// #define ll int
// #define ll int128_t
// #define ll int256_t
// #define ll cpp_int


constexpr ll inf = (1ll << 60);
// constexpr ll inf = (1 << 30);
// const double PI=3.1415926535897932384626433832795028841971;

uint32_t xor_x = 123456789, xor_y = 362436069, xor_z = 521288629, xor_w = 88675123;
inline uint32_t xor_next() {
    uint32_t t = xor_x ^ (xor_x << 11);
    xor_x = xor_y; xor_y = xor_z; xor_z = xor_w;
    return xor_w = (xor_w ^ (xor_w >> 19)) ^ (t ^ (t >> 8));
}
inline int rnd(int max_val) { return xor_next() % max_val; }


struct Timer {
    std::chrono::steady_clock::time_point start_time;

    Timer() {
        reset();
    }

    // 測定の起点リセット用
    void reset() {
        start_time = std::chrono::steady_clock::now();
    }

    // スタートからの経過時間をミリ秒(msec)で返す
    long long get_ms() const {
        auto now = std::chrono::steady_clock::now();
        return std::chrono::duration_cast<std::chrono::milliseconds>(now - start_time).count();
    }
};

struct I128Hash {
    size_t operator()(__int128_t a) const {
        uint64_t x = (uint64_t)a ^ (uint64_t)((__uint128_t)a>>64);
        x ^= x >> 30; x *= 0xbf58476d1ce4e5b9ULL;
        x ^= x >> 27; x *= 0x94d049bb133111ebULL;
        return x ^ (x >> 31);
    }
};



// vl fact;
// ll kai(ll n){
//     fact.resize(n,1);
//     rep(i,n-1)fact[i+1]=fact[i]*(i+1);
// }

// using mint = ld;
// using mint = modint998244353;//static_modint<998244353>
// using mint = modint1000000007;//static_modint<1000000007>
// using mint = static_modint<922267487>;   // 多分落とされにくい NOT ntt-friendly
// using mint = static_modint<469762049>;   // ntt-friendly
// using mint = static_modint<167772161>;   // ntt-friendly
// using mint = modint;//mint::set_mod(mod);

// ll const mod=1000000007ll;
// ll const mod=998244353ll;
// ll modrui(ll a,ll b,ll mod){
//     a%=mod;
//     if(b==0)return 1;
//     if(b%2==1) return a*modrui(a*a%mod,b/2,mod)%mod;
//     return modrui(a*a%mod,b/2,mod)%mod;
// }

// void incr(vl &v,ll n){//　n進法
//     ll k=v.size();
//     v[k-1]++;
//     ll now=k-1;
//     while (v[now]>=n)
//     {
//         v[now]=0;
//         if(now==0)break;
//         v[now-1]++;
//         now--;
//     }
//     return;
// }

// vector<mint> fact,invf;
// void init_modfact(ll sz){
//     fact.resize(sz);
//     invf.resize(sz);
//     fact[0]=1;
//     rep(i,sz-1){
//         fact[i+1]=fact[i]*(i+1);
//     }
//     invf[sz-1]=1/fact[sz-1];
//     for(ll i=sz-2; i>=0; i--){
//         invf[i]=invf[i+1]*(i+1);
//     }
// }
// mint choose(ll n,ll r){
//     if(n<r || r<0 || n<0)return 0;
//     return fact[n]*invf[r]*invf[n-r];
// }

// vector<mint> modpow,invpow;
// void init_modpow(ll x,ll sz){
//     mint inv=1/mint(x);
//     modpow.assign(sz,1);
//     invpow.assign(sz,1);
//     rep(i,sz-1){
//         modpow[i+1]=modpow[i]*x;
//         invpow[i+1]=invpow[i]*inv;
//     }
// }
// long long phi(long long n) {// O(sqrt(n))
//     long long res = n;
//     for (long long i = 2; i * i <= n; i++) {
//         if (n % i == 0) {
//             res -= res / i;
//             while (n % i == 0) n /= i;
//         }
//     }
//     if (n > 1) res -= res / n;
//     return res;
// }


//https://qandori.github.io/cp-library/lightweight/convolution/convolution.hpp.html
#line 1 "convolution/convolution_light.hpp"



#line 1 "components/fps_light_ntt.hpp"



#include <algorithm>
#include <bit>
#include <cassert>
#include <cstddef>
#include <type_traits>
#include <vector>
#line 1 "math/mint.hpp"


#line 4 "math/mint.hpp"
#include <istream>
#include <ostream>
#line 7 "math/mint.hpp"

#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif

namespace mint_detail {
template <class I>
constexpr bool mint_integral = std::is_integral_v<I>
#if defined(__SIZEOF_INT128__)
							   || std::is_same_v<I, __int128> || std::is_same_v<I, unsigned __int128>
#endif
	;
struct Mint {
	using mint = Mint;
	unsigned v = 0;
	static constexpr unsigned mod() { return 998244353; }
	[[gnu::always_inline]] static unsigned reduce(unsigned long long x) {
		return (x + (unsigned long long)(unsigned(x) * 998244351u) * mod()) >> 32;
	}
	[[gnu::always_inline]] Mint() = default;
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	Mint(I x) {
		long long r = x % (long long)mod();
		if (r < 0) r += mod();
		v = reduce((unsigned long long)r * 932051910);
	}
	[[gnu::always_inline]] static Mint raw(unsigned x) {
		Mint a;
		a.v = reduce((unsigned long long)x * 932051910);
		return a;
	}
	[[gnu::always_inline]] static Mint word(unsigned x) {
		Mint a;
		a.v = x;
		return a;
	}
	[[gnu::always_inline]] unsigned val() const {
		unsigned r = reduce(v);
		return r < mod() ? r : r - mod();
	}
	friend std::istream &operator>>(std::istream &is, Mint &x) {
		long long value;
		if (is >> value) x = Mint(value);
		return is;
	}
	friend std::ostream &operator<<(std::ostream &os, const Mint &x) {
		return os << x.val();
	}
	[[gnu::always_inline]] Mint &operator+=(Mint b) {
		v += b.v;
		if (v >= 2 * mod()) v -= 2 * mod();
		return *this;
	}
	[[gnu::always_inline]] Mint &operator-=(Mint b) {
		v -= b.v;
		if (v >> 31) v += 2 * mod();
		return *this;
	}
	[[gnu::always_inline]] Mint &operator*=(Mint b) {
		v = reduce((unsigned long long)v * b.v);
		return *this;
	}
	Mint &operator/=(Mint b) { return *this *= b.inv(); }
	Mint &operator++() { return *this += Mint(1); }
	Mint &operator--() { return *this -= Mint(1); }
	Mint operator++(int) {
		Mint a = *this;
		++*this;
		return a;
	}
	Mint operator--(int) {
		Mint a = *this;
		--*this;
		return a;
	}
	[[gnu::always_inline]] Mint operator+() const { return *this; }
	[[gnu::always_inline]] Mint operator-() const { return word(v ? 2 * mod() - v : 0); }
	[[gnu::always_inline]] Mint operator+(Mint b) const { return Mint(*this) += b; }
	[[gnu::always_inline]] Mint operator-(Mint b) const { return Mint(*this) -= b; }
	[[gnu::always_inline]] Mint operator*(Mint b) const { return Mint(*this) *= b; }
	Mint operator/(Mint b) const { return Mint(*this) /= b; }
	[[gnu::always_inline]] bool operator==(Mint b) const { return (v < mod() ? v : v - mod()) == (b.v < mod() ? b.v : b.v - mod()); }
	[[gnu::always_inline]] bool operator!=(Mint b) const { return !(*this == b); }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	friend Mint operator+(I a, Mint b) { return Mint(a) + b; }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	friend Mint operator-(I a, Mint b) { return Mint(a) - b; }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	friend Mint operator*(I a, Mint b) { return Mint(a) * b; }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	friend Mint operator/(I a, Mint b) { return Mint(a) / b; }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	friend bool operator==(I a, Mint b) { return Mint(a) == b; }
	template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
	friend bool operator!=(I a, Mint b) { return Mint(a) != b; }
	Mint pow(long long n) const {
		assert(n >= 0);
		if (!n) return Mint(1);
		Mint r(1), a = *this;
		for (; n > 1; n >>= 1, a *= a)
			if (n & 1) r *= a;
		return r * a;
	}
	[[gnu::noinline]] Mint inv() const {
		assert(*this != Mint(0));
		Mint a2 = *this * *this, a3 = a2 * *this;
		Mint a7 = a3 * a3 * *this;
		Mint a31 = a7;
		for (int i = 0; i < 2; ++i) a31 *= a31;
		a31 *= a3;
		Mint r = a7;
		for (int i = 0; i < 3; ++i) r *= r;
		r *= a3;
		r *= r;
		for (int j = 0; j < 4; ++j) {
			for (int i = 0; i < 5; ++i) r *= r;
			r *= a31;
		}
		for (int i = 0; i < 3; ++i) r *= r;
		return r * a7;
	}
};
} // namespace mint_detail

using mint = mint_detail::Mint;
using fps_mint = mint;

#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC pop_options
#endif


#line 11 "components/fps_light_ntt.hpp"

#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
#include <immintrin.h>
#endif

#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif

namespace fps_light_detail {
using std::size_t;
using Series = std::vector<mint>;
static_assert(sizeof(mint) == sizeof(unsigned) && std::is_trivially_copyable_v<mint>);
inline bool simd_available() {
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
	return __builtin_cpu_supports("avx2");
#else
	return false;
#endif
}
template<bool Inverse>
void scalar_stage(mint *a, size_t n, size_t h, const mint *roots) {
	for (size_t start = 0; start < n; start += h * 2)
		for (size_t j = 0; j < h; ++j) {
			mint x = a[start + j], y = a[start + j + h];
			if constexpr (Inverse) y *= roots[j];
			a[start + j] = x + y;
			a[start + j + h] = x - y;
			if constexpr (!Inverse) a[start + j + h] *= roots[j];
		}
}

#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
__attribute__((target("avx2")))
inline __m256i product(__m256i x, __m256i y) {
	const auto p = _mm256_set1_epi32(mint::mod());
	auto even = _mm256_mul_epu32(x, y);
	auto odd = _mm256_mul_epu32(_mm256_srli_epi64(x, 32), _mm256_srli_epi64(y, 32));
	auto q = _mm256_mullo_epi32(_mm256_mullo_epi32(x, y), _mm256_set1_epi32(998244351));
	even = _mm256_srli_epi64(_mm256_add_epi64(even, _mm256_mul_epu32(q, p)), 32);
	odd = _mm256_add_epi64(odd, _mm256_mul_epu32(_mm256_srli_epi64(q, 32), p));
	return _mm256_blend_epi32(even, odd, 0xaa);
}

__attribute__((target("avx2")))
inline __m256i fixed_product(__m256i x, __m256i w, __m256i q) {
	auto even = _mm256_mul_epu32(x, q);
	auto odd = _mm256_mul_epu32(_mm256_srli_epi64(x, 32), _mm256_srli_epi64(q, 32));
	q = _mm256_blend_epi32(_mm256_srli_epi64(even, 32), odd, 0xaa);
	return _mm256_sub_epi32(_mm256_mullo_epi32(x, w), _mm256_mullo_epi32(q, _mm256_set1_epi32(mint::mod())));
}

__attribute__((target("avx2")))
inline void pointwise_avx2(mint *a, const mint *b, size_t n) {
	size_t i = 0;
	for (; i + 8 <= n; i += 8) {
		auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
		auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(b + i));
		_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), product(x, y));
	}
	for (; i < n; ++i) a[i] *= b[i];
}

__attribute__((target("avx2")))
inline void scale_avx2(mint *a, size_t n, mint factor) {
	size_t i = 0;
	unsigned value = factor.val();
	const auto f = _mm256_set1_epi32(value);
	const auto q = _mm256_set1_epi32((static_cast<unsigned long long>(value) << 32) / mint::mod());
	for (; i + 8 <= n; i += 8) {
		auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
		_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), fixed_product(x, f, q));
	}
	for (; i < n; ++i) a[i] *= factor;
}

__attribute__((target("avx2")))
inline __m256i sum_vec(__m256i x, __m256i y) {
	auto z = _mm256_add_epi32(x, y);
	return _mm256_min_epu32(z, _mm256_sub_epi32(z, _mm256_set1_epi32(2 * mint::mod())));
}

__attribute__((target("avx2")))
inline __m256i diff_vec(__m256i x, __m256i y) {
	auto z = _mm256_sub_epi32(x, y);
	return _mm256_min_epu32(z, _mm256_add_epi32(z, _mm256_set1_epi32(2 * mint::mod())));
}

template<int Half, bool Inverse>
__attribute__((target("avx2"), always_inline))
inline __m256i leaf_stage(__m256i x, const unsigned *w, const unsigned *q) {
	constexpr int mask = Half == 4 ? 0xf0 : Half == 2 ? 0xcc : 0xaa;
	__m256i factor{}, quotient{};
	if constexpr (Half == 4) {
		factor = _mm256_broadcastsi128_si256(_mm_loadu_si128(reinterpret_cast<const __m128i *>(w + 4)));
		quotient = _mm256_broadcastsi128_si256(_mm_loadu_si128(reinterpret_cast<const __m128i *>(q + 4)));
	}
	if constexpr (Half == 2) {
		factor = _mm256_broadcastq_epi64(_mm_loadl_epi64(reinterpret_cast<const __m128i *>(w + 2)));
		quotient = _mm256_broadcastq_epi64(_mm_loadl_epi64(reinterpret_cast<const __m128i *>(q + 2)));
	}
	if constexpr (Inverse && Half > 1) x = _mm256_blend_epi32(x, fixed_product(x, factor, quotient), mask);
	__m256i y;
	if constexpr (Half == 4) y = _mm256_permute2x128_si256(x, x, 1);
	if constexpr (Half == 2) y = _mm256_shuffle_epi32(x, 0x4e);
	if constexpr (Half == 1) y = _mm256_shuffle_epi32(x, 0xb1);
	auto high = diff_vec(y, x);
	if constexpr (!Inverse && Half > 1) high = fixed_product(high, factor, quotient);
	return _mm256_blend_epi32(sum_vec(x, y), high, mask);
}

template<bool Inverse>
__attribute__((target("avx2")))
void leaf8(mint *a, size_t n, const mint *roots) {
	alignas(32) unsigned values[8], quotients[8];
	for (int i = 0; i < 8; ++i) {
		values[i] = roots[i].val();
		quotients[i] = (static_cast<unsigned long long>(values[i]) << 32) / mint::mod();
	}
	for (size_t i = 0; i < n; i += 8) {
		auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
		x = leaf_stage<Inverse ? 1 : 4, Inverse>(x, values, quotients);
		x = leaf_stage<2, Inverse>(x, values, quotients);
		x = leaf_stage<Inverse ? 4 : 1, Inverse>(x, values, quotients);
		_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), x);
	}
}

__attribute__((target("avx2")))
inline void expand_roots(mint *out, const mint *previous, size_t n, mint step) {
	for (size_t i = 0; i < n; ++i) {
		out[2 * i].v = previous[i].v;
		out[2 * i + 1].v = mint::reduce(static_cast<unsigned long long>(previous[i].v) * step.v);
	}
}

template<bool Inverse>
__attribute__((target("avx2")))
void vector_stage(mint *a, size_t n, size_t h, const mint *roots) {
	for (size_t start = 0; start < n; start += h * 2)
		for (size_t j = 0; j < h; j += 8) {
			auto *first = reinterpret_cast<__m256i *>(a + start + j);
			auto *last = reinterpret_cast<__m256i *>(a + start + j + h);
			auto x = _mm256_loadu_si256(first), y = _mm256_loadu_si256(last);
			auto w = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + j));
			if constexpr (Inverse) y = product(y, w);
			auto sum = sum_vec(x, y), difference = diff_vec(x, y);
			if constexpr (!Inverse) difference = product(difference, w);
			_mm256_storeu_si256(first, sum);
			_mm256_storeu_si256(last, difference);
		}
}
#endif

struct Roots {
	Series forward{0, 1}, inverse{0, 1};
	void prepare(size_t n) {
		size_t begin = forward.size();
		if (begin >= n) return;
		forward.resize(n), inverse.resize(n);
		for (size_t h = begin; h < n; h *= 2) {
			mint step = mint(3).pow((mint::mod() - 1) / (h * 2));
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
			if (simd_available() && h >= 16) expand_roots(forward.data() + h, forward.data() + h / 2, h / 2, step);
			else
#endif
			for (size_t j = 0; j < h / 2; ++j) {
				forward[h + 2 * j] = forward[h / 2 + j];
				forward[h + 2 * j + 1] = forward[h / 2 + j] * step;
			}
			inverse[h] = 1;
			for (size_t j = 1; j < h; ++j) inverse[h + j] = -forward[2 * h - j];
		}
	}
};

inline void pointwise(Series &a, const Series &b, [[maybe_unused]] bool vectorized = simd_available()) {
	assert(a.size() <= b.size());
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
	if (vectorized) return pointwise_avx2(a.data(), b.data(), a.size());
#endif
	for (size_t i = 0; i < a.size(); ++i) a[i] *= b[i];
}

inline void scale(Series &a, mint factor, [[maybe_unused]] bool vectorized = simd_available()) {
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
	if (vectorized) return scale_avx2(a.data(), a.size(), factor);
#endif
	for (auto &x : a) x *= factor;
}

template<bool Inverse>
void stage(mint *a, size_t n, size_t h, const mint *roots, [[maybe_unused]] bool vectorized) {
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
	if (vectorized && h >= 8) return vector_stage<Inverse>(a, n, h, roots);
#endif
	scalar_stage<Inverse>(a, n, h, roots);
}

inline void transform(Series &a, bool inverse = false) {
	size_t n = a.size();
	assert(std::has_single_bit(n) && n <= (size_t(1) << 23));
	static Roots roots;
	roots.prepare(n);
	bool vectorized = simd_available();
	if (inverse) {
		size_t h = 1;
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
		if (vectorized && n >= 8) leaf8<true>(a.data(), n, roots.inverse.data()), h = 8;
#endif
		for (; h < n; h *= 2) stage<true>(a.data(), n, h, roots.inverse.data() + h, vectorized);
		scale(a, mint::raw(mint::mod() - (mint::mod() - 1) / n), vectorized);
	} else {
		size_t h = n / 2;
		for (; h >= 8; h /= 2) stage<false>(a.data(), n, h, roots.forward.data() + h, vectorized);
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
		if (vectorized && n >= 8) return leaf8<false>(a.data(), n, roots.forward.data());
#endif
		for (; h; h /= 2) stage<false>(a.data(), n, h, roots.forward.data() + h, vectorized);
	}
}

inline Series multiply(const Series &a, const Series &b) {
	if (a.empty() || b.empty()) return {};
	[[maybe_unused]] constexpr size_t limit = size_t(1) << 23;
	assert(a.size() <= limit && b.size() <= limit && a.size() + b.size() - 1 <= limit);
	size_t length = a.size() + b.size() - 1;
	if (std::min(a.size(), b.size()) <= 32) {
		Series result(length);
		for (size_t i = 0; i < a.size(); ++i)
			for (size_t j = 0; j < b.size(); ++j) result[i + j] += a[i] * b[j];
		return result;
	}
	size_t n = std::bit_ceil(length);
	Series x = a;
	x.resize(n);
	transform(x);
	if (&a == &b) {
		pointwise(x, x);
	} else {
		Series y = b;
		y.resize(n);
		transform(y);
		pointwise(x, y);
	}
	transform(x, true);
	x.resize(length);
	return x;
}
}

#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC pop_options
#endif


#line 1 "convolution/convolution_fft.hpp"



#line 1 "components/fft.hpp"



#line 7 "components/fft.hpp"
#include <cmath>
#include <complex>
#line 10 "components/fft.hpp"
#include <numbers>
#line 12 "components/fft.hpp"

template <class Real>
void fft(std::vector<std::complex<Real>> &a, bool inverse = false) {
	std::size_t n = a.size();
	assert(!n || std::has_single_bit(n));
	for (std::size_t i = 1, j = 0; i < n; ++i) {
		std::size_t bit = n >> 1;
		for (; j & bit; bit >>= 1) j ^= bit;
		j ^= bit;
		if (i < j) std::swap(a[i], a[j]);
	}
	for (std::size_t width = 2; width <= n; width *= 2) {
		Real angle = (inverse ? -2 : 2) * std::numbers::pi_v<Real> / Real(width);
		std::complex<Real> step(std::cos(angle), std::sin(angle));
		for (std::size_t start = 0; start < n; start += width) {
			std::complex<Real> w(1);
			for (std::size_t j = 0; j < width / 2; ++j, w *= step) {
				auto x = a[start + j], y = a[start + j + width / 2] * w;
				a[start + j] = x + y;
				a[start + j + width / 2] = x - y;
			}
		}
	}
	if (inverse)
		for (auto &x : a) x /= Real(n);
}


#line 11 "convolution/convolution_fft.hpp"

template <class Real>
std::vector<std::complex<Real>> convolution_fft(const std::vector<std::complex<Real>> &a, const std::vector<std::complex<Real>> &b) {
	if (a.empty() || b.empty()) return {};
	std::size_t length = a.size() + b.size() - 1, n = std::bit_ceil(length);
	std::vector<std::complex<Real>> x(a.begin(), a.end()), y(b.begin(), b.end());
	x.resize(n);
	y.resize(n);
	fft(x, false);
	if (&a == &b) y = x;
	else fft(y, false);
	for (std::size_t i = 0; i < n; ++i) x[i] *= y[i];
	fft(x, true);
	x.resize(length);
	return x;
}
template <class Real>
	requires std::is_floating_point_v<Real>
std::vector<Real> convolution_fft(const std::vector<Real> &a, const std::vector<Real> &b) {
	std::vector<std::complex<Real>> x(a.begin(), a.end()), y(b.begin(), b.end());
	auto values = &a == &b ? convolution_fft(x, x) : convolution_fft(x, y);
	std::vector<Real> result;
	result.reserve(values.size());
	for (const auto &x : values) result.push_back(x.real());
	return result;
}


#line 1 "convolution/convolution_mod.hpp"



#line 1 "components/ntt_mod.hpp"



#line 8 "components/ntt_mod.hpp"
#include <cstdint>
#line 10 "components/ntt_mod.hpp"
#if defined(__x86_64__) || defined(__i386__)
#include <immintrin.h>
#endif

namespace ntt_mod_detail {
template <std::uint32_t mod> struct Vector;

template <std::uint32_t mod>
std::uint32_t power(std::uint32_t a, std::uint32_t k) {
	std::uint32_t result = 1;
	for (; k; k >>= 1, a = std::uint64_t(a) * a % mod)
		if (k & 1) result = std::uint64_t(result) * a % mod;
	return result;
}

template <std::uint32_t mod>
void butterfly(std::uint32_t *a, std::size_t n, std::size_t half,
			   const std::uint32_t *roots, const std::uint32_t *quotients) {
	for (std::size_t start = 0; start < n; start += 2 * half)
		for (std::size_t j = 0; j < half; ++j) {
			std::uint32_t x = a[start + j], v = a[start + j + half];
			std::uint32_t q = std::uint64_t(v) * quotients[j] >> 32;
			std::uint32_t y = v * roots[j] - q * mod;
			if (y >= mod) y -= mod;
			a[start + j] = x + y < mod ? x + y : x + y - mod;
			a[start + j + half] = x >= y ? x - y : x + mod - y;
		}
}

#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
__attribute__((target("avx2")))
void butterfly_avx2(std::uint32_t *a, std::size_t n, std::size_t half,
					const std::uint32_t *roots, const std::uint32_t *quotients) {
	using V = Vector<mod>;
	for (std::size_t start = 0; start < n; start += 2 * half)
		for (std::size_t j = 0; j < half; j += 8) {
			auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j));
			auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j + half));
			auto r = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + j));
			auto q = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(quotients + j));
			y = V::multiply(y, r, q);
			_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j), V::add(x, y));
			_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j + half), V::subtract(x, y));
		}
}
#endif

template <std::uint32_t mod>
std::uint32_t shoup(std::uint32_t value, std::uint32_t factor, std::uint32_t quotient) {
	std::uint32_t q = std::uint64_t(value) * quotient >> 32;
	std::uint32_t result = value * factor - q * mod;
	return result < mod ? result : result - mod;
}


template <std::uint32_t mod>
void forward_stage(std::uint32_t *a, std::size_t n, std::size_t half,
		const std::uint32_t *roots, const std::uint32_t *quotients) {
	for (std::size_t start = 0; start < n; start += 2 * half)
		for (std::size_t j = 0; j < half; ++j) {
			std::uint32_t x = a[start + j], y = a[start + j + half];
			a[start + j] = x + y < mod ? x + y : x + y - mod;
			std::uint32_t difference = x >= y ? x - y : x + mod - y;
			a[start + j + half] = shoup<mod>(difference, roots[j], quotients[j]);
		}
}

#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
__attribute__((target("avx2")))
void forward_stage_avx2(std::uint32_t *a, std::size_t n, std::size_t half,
		const std::uint32_t *roots, const std::uint32_t *quotients) {
	using V = Vector<mod>;
	for (std::size_t start = 0; start < n; start += 2 * half)
		for (std::size_t j = 0; j < half; j += 8) {
			auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j));
			auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j + half));
			auto r = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + j));
			auto q = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(quotients + j));
			auto difference = V::multiply(V::subtract(x, y), r, q);
			_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j), V::add(x, y));
			_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j + half), difference);
		}
}
#endif

#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
struct Vector {
	static constexpr std::uint32_t range = mod < (std::uint32_t(1) << 30) ? 2 * mod : mod;
	__attribute__((target("avx2"), always_inline))
	static inline __m256i add(__m256i x, __m256i y) {
		auto sum = _mm256_add_epi32(x, y);
		return _mm256_min_epu32(sum, _mm256_sub_epi32(sum, _mm256_set1_epi32(range)));
	}
	__attribute__((target("avx2"), always_inline))
	static inline __m256i subtract(__m256i x, __m256i y) {
		auto difference = _mm256_sub_epi32(x, y);
		return _mm256_min_epu32(difference, _mm256_add_epi32(difference, _mm256_set1_epi32(range)));
	}
	__attribute__((target("avx2"), always_inline))
	static inline __m256i multiply(__m256i x, __m256i factor, __m256i quotient) {
		auto even = _mm256_mul_epu32(x, quotient);
		auto odd = _mm256_mul_epu32(_mm256_srli_epi64(x, 32), _mm256_srli_epi64(quotient, 32));
		auto q = _mm256_blend_epi32(_mm256_srli_epi64(even, 32), odd, 0xaa);
		auto result = _mm256_sub_epi32(_mm256_mullo_epi32(x, factor), _mm256_mullo_epi32(q, _mm256_set1_epi32(mod)));
		if constexpr (range == 2 * mod) return result;
		return _mm256_min_epu32(result, _mm256_sub_epi32(result, _mm256_set1_epi32(mod)));
	}
};

template <std::uint32_t mod, bool inverse>
__attribute__((target("avx2")))
void leaf_avx2(std::uint32_t *a, std::size_t n, const std::uint32_t *roots, const std::uint32_t *quotients) {
	using V = Vector<mod>;
	auto r4 = _mm256_broadcastsi128_si256(_mm_loadu_si128(reinterpret_cast<const __m128i *>(roots + 4)));
	auto q4 = _mm256_broadcastsi128_si256(_mm_loadu_si128(reinterpret_cast<const __m128i *>(quotients + 4)));
	auto r2 = _mm256_setr_epi32(roots[2], roots[3], roots[2], roots[3], roots[2], roots[3], roots[2], roots[3]);
	auto q2 = _mm256_setr_epi32(quotients[2], quotients[3], quotients[2], quotients[3], quotients[2], quotients[3], quotients[2], quotients[3]);
	for (std::size_t i = 0; i < n; i += 8) {
		auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
		if constexpr (!inverse) {
			auto y = _mm256_permute2x128_si256(x, x, 1);
			x = _mm256_blend_epi32(V::add(x, y), V::multiply(V::subtract(y, x), r4, q4), 0xf0);
			y = _mm256_shuffle_epi32(x, 0x4e);
			x = _mm256_blend_epi32(V::add(x, y), V::multiply(V::subtract(y, x), r2, q2), 0xcc);
			y = _mm256_shuffle_epi32(x, 0xb1);
			x = _mm256_blend_epi32(V::add(x, y), V::subtract(y, x), 0xaa);
		} else {
			auto y = _mm256_shuffle_epi32(x, 0xb1);
			x = _mm256_blend_epi32(V::add(x, y), V::subtract(y, x), 0xaa);
			x = _mm256_blend_epi32(x, V::multiply(x, r2, q2), 0xcc);
			y = _mm256_shuffle_epi32(x, 0x4e);
			x = _mm256_blend_epi32(V::add(x, y), V::subtract(y, x), 0xcc);
			x = _mm256_blend_epi32(x, V::multiply(x, r4, q4), 0xf0);
			y = _mm256_permute2x128_si256(x, x, 1);
			x = _mm256_blend_epi32(V::add(x, y), V::subtract(y, x), 0xf0);
		}
		_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), x);
	}
}

template <std::uint32_t mod, bool inverse>
__attribute__((target("avx2")))
void pair_avx2(std::uint32_t *a, std::size_t n, std::size_t h, const std::uint32_t *roots, const std::uint32_t *quotients) {
	using V = Vector<mod>;
	for (std::size_t start = 0; start < n; start += 4 * h)
		for (std::size_t j = 0; j < h; j += 8) {
			auto x0 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j));
			auto x1 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j + h));
			auto x2 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j + 2 * h));
			auto x3 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j + 3 * h));
			auto r0 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + 2 * h + j));
			auto q0 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(quotients + 2 * h + j));
			auto r1 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + 3 * h + j));
			auto q1 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(quotients + 3 * h + j));
			auto r2 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + h + j));
			auto q2 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(quotients + h + j));
			if constexpr (!inverse) {
				auto y0 = V::add(x0, x2), y1 = V::add(x1, x3);
				auto y2 = V::multiply(V::subtract(x0, x2), r0, q0);
				auto y3 = V::multiply(V::subtract(x1, x3), r1, q1);
				x0 = V::add(y0, y1); x1 = V::multiply(V::subtract(y0, y1), r2, q2);
				x2 = V::add(y2, y3); x3 = V::multiply(V::subtract(y2, y3), r2, q2);
			} else {
				x1 = V::multiply(x1, r2, q2); x3 = V::multiply(x3, r2, q2);
				auto y0 = V::add(x0, x1), y1 = V::subtract(x0, x1);
				auto y2 = V::multiply(V::add(x2, x3), r0, q0);
				auto y3 = V::multiply(V::subtract(x2, x3), r1, q1);
				x0 = V::add(y0, y2); x2 = V::subtract(y0, y2);
				x1 = V::add(y1, y3); x3 = V::subtract(y1, y3);
			}
			_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j), x0);
			_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j + h), x1);
			_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j + 2 * h), x2);
			_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j + 3 * h), x3);
		}
}

#endif

#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
__attribute__((target("avx2")))
void build_roots_avx2(std::uint32_t *roots, std::uint32_t *quotients, std::size_t half, std::uint32_t step) {
	std::uint32_t initial[8], w = 1;
	for (int i = 0; i < 8; ++i) {
		initial[i] = w;
		w = std::uint64_t(w) * step % mod;
	}
	auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(initial));
	auto factor = _mm256_set1_epi32(w), quotient = _mm256_set1_epi32((std::uint64_t(w) << 32) / mod);
	for (std::size_t j = 0; j < half; j += 8) {
		x = _mm256_min_epu32(x, _mm256_sub_epi32(x, _mm256_set1_epi32(mod)));
		_mm256_storeu_si256(reinterpret_cast<__m256i *>(roots + j), x);
		for (int k = 0; k < 8; ++k) quotients[j + k] = (std::uint64_t(roots[j + k]) << 32) / mod;
		x = Vector<mod>::multiply(x, factor, quotient);
	}
}
#endif

template <std::uint32_t mod, std::uint32_t root>
struct Plan {
	std::vector<std::uint32_t> roots, quotients;
	explicit Plan(std::size_t n, [[maybe_unused]] bool vectorized = false) : roots(n), quotients(n) {
		static_assert(mod > 2 && mod < (std::uint32_t(1) << 31));
		assert(std::has_single_bit(n) && (mod - 1) % n == 0);
		if (n == 1) return;
		std::size_t half = n / 2;
		std::uint32_t step = power<mod>(root, (mod - 1) / n), w = 1;
#if defined(__x86_64__) || defined(__i386__)
		if (vectorized && half >= 8) build_roots_avx2<mod>(roots.data() + half, quotients.data() + half, half, step);
		else
#endif
		for (std::size_t j = 0; j < half; ++j) {
			roots[half + j] = w;
			quotients[half + j] = (std::uint64_t(w) << 32) / mod;
			w = std::uint64_t(w) * step % mod;
		}
		for (half /= 2; half; half /= 2)
			for (std::size_t j = 0; j < half; ++j) {
				roots[half + j] = roots[2 * half + 2 * j];
				quotients[half + j] = quotients[2 * half + 2 * j];
			}
	}
};

template <std::uint32_t mod, std::uint32_t root>
void forward(std::vector<std::uint32_t> &a, const Plan<mod, root> &plan, [[maybe_unused]] bool vectorized) {
	std::size_t half = a.size() / 2;
#if defined(__x86_64__) || defined(__i386__)
	if (vectorized && a.size() >= 8) {
		for (; half >= 16; half /= 4) pair_avx2<mod, false>(a.data(), a.size(), half / 2, plan.roots.data(), plan.quotients.data());
		if (half == 8) forward_stage_avx2<mod>(a.data(), a.size(), half, plan.roots.data() + half, plan.quotients.data() + half);
		leaf_avx2<mod, false>(a.data(), a.size(), plan.roots.data(), plan.quotients.data());
		return;
	}
#endif
	for (; half; half /= 2) forward_stage<mod>(a.data(), a.size(), half, plan.roots.data() + half, plan.quotients.data() + half);
}

template <std::uint32_t mod, std::uint32_t root>
void backward(std::vector<std::uint32_t> &a, const Plan<mod, root> &plan, [[maybe_unused]] bool vectorized) {
	std::size_t half = 1;
#if defined(__x86_64__) || defined(__i386__)
	if (vectorized && a.size() >= 8) {
		leaf_avx2<mod, true>(a.data(), a.size(), plan.roots.data(), plan.quotients.data());
		half = 8;

		for (; 2 * half < a.size(); half *= 4) pair_avx2<mod, true>(a.data(), a.size(), half, plan.roots.data(), plan.quotients.data());
		if (half < a.size()) butterfly_avx2<mod>(a.data(), a.size(), half, plan.roots.data() + half, plan.quotients.data() + half);
		return;
	}
#endif
	for (; half < a.size(); half *= 2) butterfly<mod>(a.data(), a.size(), half, plan.roots.data() + half, plan.quotients.data() + half);
}

#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
__attribute__((target("avx2")))
void scale_avx2(std::uint32_t *a, std::size_t n, std::uint32_t factor, std::uint32_t quotient) {
	auto r = _mm256_set1_epi32(factor), q = _mm256_set1_epi32(quotient);
	for (std::size_t i = 0; i < n; i += 8) {
		auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
		auto y = Vector<mod>::multiply(x, r, q);
		_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), _mm256_min_epu32(y, _mm256_sub_epi32(y, _mm256_set1_epi32(mod))));
	}
}
#endif

template <std::uint32_t mod>
void scale(std::vector<std::uint32_t> &a, std::uint32_t factor, [[maybe_unused]] bool vectorized) {
	std::uint32_t quotient = (std::uint64_t(factor) << 32) / mod;
#if defined(__x86_64__) || defined(__i386__)
	if (vectorized && a.size() >= 8) {
		scale_avx2<mod>(a.data(), a.size(), factor, quotient);
		return;
	}
#endif
	for (auto &x : a) x = shoup<mod>(x, factor, quotient);
}

inline void bit_reverse(std::vector<std::uint32_t> &a) {
	for (std::size_t i = 1, j = 0; i < a.size(); ++i) {
		std::size_t bit = a.size() >> 1;
		for (; j & bit; bit >>= 1) j ^= bit;
		j ^= bit;
		if (i < j) std::swap(a[i], a[j]);
	}
}

template <std::uint32_t mod, std::uint32_t root>
void transform(std::vector<std::uint32_t> &a, bool inverse, bool vectorized) {
	Plan<mod, root> plan(a.size(), vectorized);
	if (inverse) {
		bit_reverse(a);
		backward(a, plan, vectorized);
		std::reverse(a.begin() + 1, a.end());
		scale<mod>(a, mod - (mod - 1) / a.size(), vectorized);
	} else {
		forward(a, plan, vectorized);
		if constexpr (mod < (std::uint32_t(1) << 30)) for (auto &x : a) if (x >= mod) x -= mod;
		bit_reverse(a);
	}
}

template <std::uint32_t mod>
constexpr std::uint32_t negative_inverse = [] {
	std::uint32_t value = mod;
	for (int i = 0; i < 5; ++i) value *= 2 - mod * value;
	return 0 - value;
}();

#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
__attribute__((target("avx2")))
void pointwise_avx2(std::uint32_t *a, const std::uint32_t *b, std::size_t n) {
	auto p = _mm256_set1_epi32(mod), inverse = _mm256_set1_epi32(negative_inverse<mod>);
	for (std::size_t i = 0; i < n; i += 8) {
		auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
		auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(b + i));
		auto even = _mm256_mul_epu32(x, y);
		auto odd = _mm256_mul_epu32(_mm256_srli_epi64(x, 32), _mm256_srli_epi64(y, 32));
		auto qe = _mm256_mul_epu32(even, inverse), qo = _mm256_mul_epu32(odd, inverse);
		even = _mm256_srli_epi64(_mm256_add_epi64(even, _mm256_mul_epu32(qe, p)), 32);
		odd = _mm256_add_epi64(odd, _mm256_mul_epu32(qo, p));
		x = _mm256_blend_epi32(even, odd, 0xaa);
		x = _mm256_min_epu32(x, _mm256_sub_epi32(x, p));
		_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), x);
	}
}
#endif

template <std::uint32_t mod>
void pointwise(std::vector<std::uint32_t> &a, const std::vector<std::uint32_t> &b, [[maybe_unused]] bool vectorized) {
#if defined(__x86_64__) || defined(__i386__)
	if (vectorized && a.size() >= 8) {
		pointwise_avx2<mod>(a.data(), b.data(), a.size());
		return;
	}
#endif
	for (std::size_t i = 0; i < a.size(); ++i) {
		std::uint64_t product = std::uint64_t(a[i]) * b[i];
		std::uint32_t q = std::uint32_t(product) * negative_inverse<mod>;
		std::uint32_t value = (product + std::uint64_t(q) * mod) >> 32;
		a[i] = value < mod ? value : value - mod;
	}
}

}

template <std::uint32_t mod, std::uint32_t root>
void ntt_mod(std::vector<std::uint32_t> &a, bool inverse = false) {
	bool vectorized = false;
#if defined(__x86_64__) || defined(__i386__)
	vectorized = __builtin_cpu_supports("avx2");
#endif
	ntt_mod_detail::transform<mod, root>(a, inverse, vectorized);
}


#line 9 "convolution/convolution_mod.hpp"
#include <limits>
#include <utility>
#line 12 "convolution/convolution_mod.hpp"

namespace convolution_mod_detail {
using Word = std::uint32_t;
template <Word mod, Word root, class T>
std::vector<Word> multiply(const std::vector<T> &a, const std::vector<T> &b, Word factor = 1) {
	const auto &small = a.size() <= b.size() ? a : b;
	const auto &large = a.size() <= b.size() ? b : a;
	std::size_t length = a.size() + b.size() - 1;
	bool blocked = small.size() > 32 && large.size() / small.size() >= 8, square = &a == &b;
	std::size_t n = std::bit_ceil(blocked ? 2 * small.size() - 1 : length), block = n - small.size() + 1;
	std::vector<Word> x(n), y(square ? 0 : n);
	auto reduce = [](T value) {
		__int128_t r = __int128_t(value) % mod;
		return Word(r < 0 ? r + mod : r);
	};
	for (std::size_t i = 0; i < small.size(); ++i) x[i] = reduce(small[i]);
	if (small.size() <= 32) {
		if (!square) for (std::size_t i = 0; i < large.size(); ++i) y[i] = reduce(large[i]);
		const auto &other = square ? x : y;
		std::vector<Word> result(length);
		for (std::size_t i = 0; i < small.size(); ++i)
			for (std::size_t j = 0; j < large.size(); ++j) result[i + j] = (result[i + j] + std::uint64_t(x[i]) * other[j]) % mod;
		if (factor != 1) for (auto &v : result) v = std::uint64_t(v) * factor % mod;
		return result;
	}
	bool vectorized = false;
#if defined(__x86_64__) || defined(__i386__)
	vectorized = __builtin_cpu_supports("avx2");
#endif
	ntt_mod_detail::Plan<mod, root> plan(n, vectorized);
	ntt_mod_detail::forward(x, plan, vectorized);
	Word scale = (std::uint64_t(1) << 32) % mod * (mod - (mod - 1) / n) % mod * factor % mod;
	std::vector<Word> result(blocked ? length : 0);
	auto &work = square ? x : y;
	for (std::size_t start = 0; start < large.size(); start += block) {
		std::size_t size = std::min(block, large.size() - start);
		if (!square) {
			for (std::size_t i = 0; i < size; ++i) y[i] = reduce(large[start + i]);
			std::fill(y.begin() + size, y.end(), 0);
			ntt_mod_detail::forward(y, plan, vectorized);
		}
		ntt_mod_detail::pointwise<mod>(work, x, vectorized);
		ntt_mod_detail::backward(work, plan, vectorized);
		std::reverse(work.begin() + 1, work.end());
		ntt_mod_detail::scale<mod>(work, scale, vectorized);
		if (!blocked) {
			work.resize(length);
			return std::move(work);
		}
		for (std::size_t i = 0; i < size + small.size() - 1; ++i) {
			Word sum = result[start + i] + work[i];
			result[start + i] = sum < mod ? sum : sum - mod;
		}
	}
	return result;
}
inline constexpr Word p = 754974721, q = 1224736769, r = 2013265921;
inline constexpr __uint128_t modulus = __uint128_t(p) * q * r;
struct Reconstruction { std::uint64_t low; Word high; };
template <Word P = p, Word Q = q, Word R = r>
inline Reconstruction reconstruct(Word a, Word b, Word c) {
	static const Word inverse_p = ntt_mod_detail::power<Q>(P, Q - 2);
	static const Word inverse_pq = ntt_mod_detail::power<R>(std::uint64_t(P) * Q % R, R - 2);
	std::uint64_t x = std::uint64_t(b + Q - a) * inverse_p % Q;
	std::uint64_t low = a + std::uint64_t(P) * x;
	std::uint64_t y = std::uint64_t(c + R - low % R) * inverse_pq % R;
	return {low, Word(y)};
}
inline __uint128_t restore(Word a, Word b, Word c) {
	auto [low, high] = reconstruct(a, b, c);
	return low + __uint128_t(p) * q * high;
}
#if defined(__x86_64__) || defined(__i386__)
template <Word P, Word Q, Word R>
__attribute__((target("avx2")))
void combine(Word *a, const Word *b, const Word *c, std::size_t n) {
	static_assert(P > 256 && Q > 256 && R > 256 && P + std::uint64_t(Q) + R < (std::uint64_t(1) << 32));
	constexpr Word mod = 1000000007;
	constexpr auto form = [](std::uint64_t x) { return Word(x % mod * ((std::uint64_t(1) << 32) % mod) % mod); };
	constexpr Word place[3] = {form(std::uint64_t(Q) * R), form(std::uint64_t(P) * R), form(std::uint64_t(P) * Q)};
	constexpr Word wrap = form(mod - std::uint64_t(P) * Q % mod * R % mod);
	const auto p = _mm256_set1_epi32(mod), inverse = _mm256_set1_epi32(ntt_mod_detail::negative_inverse<mod>);
	std::size_t i = 0;
	for (; n - i >= 8; i += 8) {
		auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
		auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(b + i));
		auto z = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(c + i));
		auto quotient = [&](__m256i a, __m256i b, __m256i c) __attribute__((target("avx2"), always_inline)) {
			auto s = _mm256_mul_epu32(a, _mm256_set1_epi32((std::uint64_t(1) << 40) / P + 1));
			s = _mm256_add_epi64(s, _mm256_mul_epu32(b, _mm256_set1_epi32((std::uint64_t(1) << 40) / Q + 1)));
			s = _mm256_add_epi64(s, _mm256_mul_epu32(c, _mm256_set1_epi32((std::uint64_t(1) << 40) / R + 1)));
			return _mm256_srli_epi64(_mm256_add_epi64(s, _mm256_set1_epi64x(std::uint64_t(1) << 39)), 40);
		};
		auto reduce = [&](__m256i a, __m256i b, __m256i c, __m256i t) __attribute__((target("avx2"), always_inline)) {
			auto s = _mm256_add_epi64(_mm256_mul_epu32(a, _mm256_set1_epi32(place[0])), _mm256_mul_epu32(b, _mm256_set1_epi32(place[1])));
			s = _mm256_add_epi64(s, _mm256_mul_epu32(c, _mm256_set1_epi32(place[2])));
			s = _mm256_add_epi64(s, _mm256_mul_epu32(t, _mm256_set1_epi32(wrap)));
			return _mm256_add_epi64(s, _mm256_mul_epu32(_mm256_mul_epu32(s, inverse), p));
		};
		auto xo = _mm256_srli_epi64(x, 32), yo = _mm256_srli_epi64(y, 32), zo = _mm256_srli_epi64(z, 32);
		auto even = reduce(x, y, z, quotient(x, y, z)), odd = reduce(xo, yo, zo, quotient(xo, yo, zo));
		x = _mm256_blend_epi32(_mm256_srli_epi64(even, 32), odd, 0xaa);
		x = _mm256_min_epu32(x, _mm256_sub_epi32(x, p));
		_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), x);
	}
	for (; i < n; ++i) {
		std::uint64_t t = (std::uint64_t(a[i]) * ((std::uint64_t(1) << 40) / P + 1) + std::uint64_t(b[i]) * ((std::uint64_t(1) << 40) / Q + 1) + std::uint64_t(c[i]) * ((std::uint64_t(1) << 40) / R + 1) + (std::uint64_t(1) << 39)) >> 40;
		std::uint64_t sum = std::uint64_t(a[i]) * place[0] + std::uint64_t(b[i]) * place[1] + std::uint64_t(c[i]) * place[2] + std::uint64_t(t) * wrap;
		auto q = Word(sum) * ntt_mod_detail::negative_inverse<mod>;
		Word value = (sum + std::uint64_t(q) * mod) >> 32;
		a[i] = value < mod ? value : value - mod;
	}
}
#endif
template <Word P, Word PR, Word Q, Word QR, Word R, Word RR>
std::vector<Word> modular(const std::vector<Word> &a, const std::vector<Word> &b, Word mod) {
#if defined(__x86_64__) || defined(__i386__)
	if constexpr (P + std::uint64_t(Q) + R < (std::uint64_t(1) << 32)) {
		if (mod == 1000000007 && __uint128_t(std::min(a.size(), b.size())) * (mod - 1) * (mod - 1) * 4 < __uint128_t(P) * Q * R && __builtin_cpu_supports("avx2")) {
			auto x = multiply<P, PR>(a, b, ntt_mod_detail::power<P>(std::uint64_t(Q) * R % P, P - 2));
			auto y = multiply<Q, QR>(a, b, ntt_mod_detail::power<Q>(std::uint64_t(P) * R % Q, Q - 2));
			auto z = multiply<R, RR>(a, b, ntt_mod_detail::power<R>(std::uint64_t(P) * Q % R, R - 2));
			combine<P, Q, R>(x.data(), y.data(), z.data(), x.size());
			return x;
		}
	}
#endif
	auto x = multiply<P, PR>(a, b);
	auto y = multiply<Q, QR>(a, b);
	auto z = multiply<R, RR>(a, b);
	std::uint64_t pq_mod = std::uint64_t(P) * Q % mod;
	for (std::size_t i = 0; i < x.size(); ++i) {
		auto [low, high] = reconstruct<P, Q, R>(x[i], y[i], z[i]);
		x[i] = (low % mod + pq_mod * high) % mod;
	}
	return x;
}

}

template <class T>
std::vector<T> convolution_integer(const std::vector<T> &a, const std::vector<T> &b) {
	static_assert(std::numeric_limits<T>::is_integer && sizeof(T) <= 8);
	if (a.empty() || b.empty()) return {};
	assert(a.size() + b.size() - 1 <= std::size_t(1) << 24);
	auto x = convolution_mod_detail::multiply<convolution_mod_detail::p, 11>(a, b);
	auto y = convolution_mod_detail::multiply<convolution_mod_detail::q, 3>(a, b);
	auto z = convolution_mod_detail::multiply<convolution_mod_detail::r, 31>(a, b);
	std::vector<T> result(x.size());
	for (std::size_t i = 0; i < x.size(); ++i) {
		auto value = convolution_mod_detail::restore(x[i], y[i], z[i]);
		if constexpr (std::numeric_limits<T>::is_signed) {
			__int128_t v = value > convolution_mod_detail::modulus / 2 ? __int128_t(value) - __int128_t(convolution_mod_detail::modulus) : __int128_t(value);
			assert(std::numeric_limits<T>::lowest() <= v && v <= std::numeric_limits<T>::max());
			result[i] = T(v);
		} else {
			assert(value <= std::numeric_limits<T>::max());
			result[i] = T(value);
		}
	}
	return result;
}

template <class T>
std::vector<std::uint32_t> convolution_mod(const std::vector<T> &a, const std::vector<T> &b, std::uint32_t mod) {
	static_assert(std::numeric_limits<T>::is_integer && sizeof(T) <= 8);
	assert(mod > 0);
	if (a.empty() || b.empty()) return {};
	assert(a.size() + b.size() - 1 <= std::size_t(1) << 24);
	if (mod == 1) return std::vector<std::uint32_t>(a.size() + b.size() - 1);
	std::vector<std::uint32_t> x(a.size()), y(&a == &b ? 0 : b.size());
	auto reduce = [=](T value) {
		__int128_t r = __int128_t(value) % mod;
		return std::uint32_t(r < 0 ? r + mod : r);
	};
	std::transform(a.begin(), a.end(), x.begin(), reduce);
	if (&a != &b) std::transform(b.begin(), b.end(), y.begin(), reduce);
	const auto &other = &a == &b ? x : y;

	if (std::min(x.size(), other.size()) <= 32) {
		std::vector<std::uint32_t> result(x.size() + other.size() - 1);
		for (std::size_t i = 0; i < x.size(); ++i)
			for (std::size_t j = 0; j < other.size(); ++j) result[i + j] = (result[i + j] + std::uint64_t(x[i]) * other[j]) % mod;
		return result;
	}
	if (mod == 998244353 && x.size() + other.size() - 1 <= std::size_t(1) << 23) return convolution_mod_detail::multiply<998244353, 3>(x, other);
	constexpr std::uint32_t P = 167772161, Q = 469762049, R = 754974721;
	if (__uint128_t(std::min(x.size(), other.size())) * (mod - 1) * (mod - 1) < __uint128_t(P) * Q * R)
		return convolution_mod_detail::modular<P, 3, Q, 3, R, 11>(x, other, mod);
	return convolution_mod_detail::modular<convolution_mod_detail::p, 11, convolution_mod_detail::q, 3, convolution_mod_detail::r, 31>(x, other, mod);
}


#line 1 "convolution/convolution_ring.hpp"



#line 6 "convolution/convolution_ring.hpp"
#include <span>
#line 8 "convolution/convolution_ring.hpp"

namespace convolution_ring_detail {
template <class T>
std::vector<T> multiply(std::span<const T> a, std::span<const T> b) {
	if (a.empty() || b.empty()) return {};
	std::vector<T> result(a.size() + b.size() - 1, T(0));
	if (std::min(a.size(), b.size()) <= 32) {
		for (std::size_t i = 0; i < a.size(); ++i)
			for (std::size_t j = 0; j < b.size(); ++j) result[i + j] += a[i] * b[j];
		return result;
	}
	std::size_t half = std::max(a.size(), b.size()) / 2;
	auto al = a.first(std::min(a.size(), half)), ar = a.subspan(al.size());
	auto bl = b.first(std::min(b.size(), half)), br = b.subspan(bl.size());
	auto low = multiply(al, bl), high = multiply(ar, br);
	std::vector<T> x(std::max(al.size(), ar.size()), T(0)), y(std::max(bl.size(), br.size()), T(0));
	for (std::size_t i = 0; i < al.size(); ++i) x[i] += al[i];
	for (std::size_t i = 0; i < ar.size(); ++i) x[i] += ar[i];
	for (std::size_t i = 0; i < bl.size(); ++i) y[i] += bl[i];
	for (std::size_t i = 0; i < br.size(); ++i) y[i] += br[i];
	auto middle = multiply<T>(x, y);
	for (std::size_t i = 0; i < low.size(); ++i) result[i] += low[i], middle[i] -= low[i];
	for (std::size_t i = 0; i < high.size(); ++i) result[i + 2 * half] += high[i], middle[i] -= high[i];
	for (std::size_t i = 0; i < middle.size() && i + half < result.size(); ++i) result[i + half] += middle[i];
	return result;
}
}

template <class T>
std::vector<T> convolution_ring(const std::vector<T> &a, const std::vector<T> &b) {
	return convolution_ring_detail::multiply<T>(a, b);
}


#line 12 "convolution/convolution_light.hpp"

namespace light_convolution {
namespace detail {
template<class T> struct IsComplex : std::false_type {};
template<class T> struct IsComplex<std::complex<T>> : std::true_type {};
}

template<class T>
std::vector<T> convolution(const std::vector<T> &a, const std::vector<T> &b) {
	if constexpr (requires { T::mod(); T::raw(0); a[0].val(); }) {
		if constexpr (std::is_same_v<T, mint>) return fps_light_detail::multiply(a, b);
		using M = std::conditional_t<T::mod() == 998244353, mint, std::uint32_t>;
		auto convert = [](const std::vector<T> &input) {
			std::vector<M> result;
			result.reserve(input.size());
			for (auto x : input) {
				if constexpr (std::is_same_v<M, mint>) result.push_back(mint::raw(x.val()));
				else result.push_back(x.val());
			}
			return result;
		};
		auto x = convert(a), y = &a == &b ? std::vector<M>{} : convert(b);
		const auto &other = &a == &b ? x : y;
		auto values = [&] {
			if constexpr (std::is_same_v<M, mint>) return fps_light_detail::multiply(x, other);
			else return convolution_mod(x, other, T::mod());
		}();
		std::vector<T> result;
		result.reserve(values.size());
		for (auto value : values) {
			if constexpr (std::is_same_v<M, mint>) result.push_back(T::raw(value.val()));
			else result.push_back(T::raw(value));
		}
		return result;
	} else if constexpr (std::numeric_limits<T>::is_integer && sizeof(T) <= 8) return convolution_integer(a, b);
	else if constexpr (std::is_floating_point_v<T> || detail::IsComplex<T>::value) return convolution_fft(a, b);
	else return convolution_ring(a, b);
}
}






vector<mint> fact,invf;
void init_modfact(ll sz){
    fact.resize(sz);
    invf.resize(sz);
    fact[0]=1;
    rep(i,sz-1){
        fact[i+1]=fact[i]*(i+1);
    }
    invf[sz-1]=1/fact[sz-1];
    for(ll i=sz-2; i>=0; i--){
        invf[i]=invf[i+1]*(i+1);
    }
}
mint choose(ll n,ll r){
    if(n<r || r<0 || n<0)return 0;
    return fact[n]*invf[r]*invf[n-r];
}

using fps=vector<mint>;

void solve(){
    ll n,m;
    cin >> n >> m;
    unordered_map<ll,ll> a,b;
    rep(i,n){
        ll p,e;
        cin>> p >> e;
        a[p]=e;
    }
    rep(i,m){
        ll p,e;
        cin >> p >> e;
        b[p]=e;
    }

    priority_queue<pair<ll,ll>,vector<pair<ll,ll>>,greater<pair<ll,ll>>> pq;
    unordered_map<ll,pair<fps,fps>> v;
    for(auto [p,e]:a){
        if(!b.count(p))continue;
        fps f(min(a[p],b[p])+1,0),g(min(a[p],b[p])+1,0);
        f[0]=1;
        g[1]=a[p]*b[p]*(p-1);
        for(ll i=1;i<f.size();i++){
            f[i]=f[i-1]*(a[p]+1-i)*(b[p]+1-i)*p/i;
        }
        for(ll i=2;i<g.size();i++){
            g[i]=g[i-1]*(a[p]+1-i)*(b[p]+1-i)*p/(i-1);
        }
        v[p]={f,g};
        pq.push({f.size(),p});
    }

    while(pq.size()>1){
        auto [_1,p]=pq.top();
        pq.pop();
        auto [_2,q]=pq.top();
        pq.pop();
        
        fps nf=light_convolution::convolution(v[p].first,v[q].first);
        fps g1=light_convolution::convolution(v[p].first,v[q].second);
        fps g2=light_convolution::convolution(v[p].second,v[q].first);
        fps ng(max(g1.size(),g2.size()),0);
        rep(i,g1.size())ng[i]+=g1[i];
        rep(i,g2.size())ng[i]+=g2[i];
        v[p]={nf,ng};
        pq.push({nf.size(),p});
    }

    init_modfact(121212);
    mint C=1;
    ll asz=0,bsz=0;
    fps g;
    if(pq.empty()){
        {
            for(auto [p,e]:a){
                C*=invf[e];
                asz+=e;
            }
            for(auto [p,e]:b){
                C*=invf[e];
                bsz+=e;
            }
            C*=fact[asz]*fact[bsz];
        }
        cout << C.val() << endl;
        return;
    }
    else{
        auto [_1,p]=pq.top();
        g=v[p].second;
    }
    mint ans=1;
    {
        for(auto [p,e]:a){
            C*=invf[e];
            asz+=e;
        }
        for(auto [p,e]:b){
            C*=invf[e];
            bsz+=e;
        }
        C*=fact[asz]*fact[bsz];
    }
    for(ll k=1;k<g.size();k++){
        ans+=g[k]*fact[k-1]*invf[asz]*fact[asz-k]*invf[bsz]*fact[bsz-k];
    }
    ans*=C;
    cout << ans.val() << endl;
}



int main(){
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);


    // ll mx=12345678;
    // vc fl(mx+1,0);
    // for(ll d=2;d<=mx;d++){
    //     if(fl[d])continue;
    //     ll x=d;
    //     ps.push_back(x);
    //     while(x<=mx){
    //         fl[x]=1;
    //         x+=d;
    //     }
    // }


    ll t = 1;
    // cin >> t;
    while (t--){
        solve();
        cout << flush;
    }
}