結果
| 問題 | No.2164 Equal Balls |
| ユーザー |
👑  Nachia
|
| 提出日時 | 2022-12-15 10:39:38 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2,105 ms / 5,000 ms |
| コード長 | 23,004 bytes |
| コンパイル時間 | 2,303 ms |
| コンパイル使用メモリ | 122,764 KB |
| 実行使用メモリ | 12,432 KB |
| 最終ジャッジ日時 | 2024-04-27 04:24:46 |
| 合計ジャッジ時間 | 50,877 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 2 ms
6,940 KB |
| testcase_02 | AC | 2 ms
6,940 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | AC | 2 ms
6,944 KB |
| testcase_05 | AC | 4 ms
6,944 KB |
| testcase_06 | AC | 3 ms
6,940 KB |
| testcase_07 | AC | 3 ms
6,944 KB |
| testcase_08 | AC | 50 ms
6,944 KB |
| testcase_09 | AC | 39 ms
6,940 KB |
| testcase_10 | AC | 22 ms
6,940 KB |
| testcase_11 | AC | 103 ms
6,940 KB |
| testcase_12 | AC | 52 ms
6,944 KB |
| testcase_13 | AC | 38 ms
6,940 KB |
| testcase_14 | AC | 45 ms
6,940 KB |
| testcase_15 | AC | 99 ms
7,112 KB |
| testcase_16 | AC | 48 ms
6,944 KB |
| testcase_17 | AC | 12 ms
6,944 KB |
| testcase_18 | AC | 64 ms
6,940 KB |
| testcase_19 | AC | 111 ms
7,048 KB |
| testcase_20 | AC | 55 ms
6,940 KB |
| testcase_21 | AC | 10 ms
6,944 KB |
| testcase_22 | AC | 11 ms
6,944 KB |
| testcase_23 | AC | 1,125 ms
6,940 KB |
| testcase_24 | AC | 645 ms
7,640 KB |
| testcase_25 | AC | 1,029 ms
6,944 KB |
| testcase_26 | AC | 266 ms
7,012 KB |
| testcase_27 | AC | 779 ms
8,376 KB |
| testcase_28 | AC | 796 ms
8,552 KB |
| testcase_29 | AC | 369 ms
6,940 KB |
| testcase_30 | AC | 784 ms
7,268 KB |
| testcase_31 | AC | 1,402 ms
6,944 KB |
| testcase_32 | AC | 882 ms
8,112 KB |
| testcase_33 | AC | 717 ms
6,940 KB |
| testcase_34 | AC | 945 ms
6,944 KB |
| testcase_35 | AC | 198 ms
6,944 KB |
| testcase_36 | AC | 1,743 ms
9,344 KB |
| testcase_37 | AC | 1,638 ms
6,940 KB |
| testcase_38 | AC | 2,098 ms
12,304 KB |
| testcase_39 | AC | 2,103 ms
12,304 KB |
| testcase_40 | AC | 2,099 ms
12,428 KB |
| testcase_41 | AC | 2,099 ms
12,304 KB |
| testcase_42 | AC | 2,098 ms
12,432 KB |
| testcase_43 | AC | 2,101 ms
12,304 KB |
| testcase_44 | AC | 2,099 ms
12,432 KB |
| testcase_45 | AC | 2,098 ms
12,428 KB |
| testcase_46 | AC | 2,100 ms
12,432 KB |
| testcase_47 | AC | 2,102 ms
12,432 KB |
| testcase_48 | AC | 2,105 ms
12,308 KB |
| testcase_49 | AC | 1,921 ms
6,940 KB |
| testcase_50 | AC | 1,951 ms
6,940 KB |
| testcase_51 | AC | 1,917 ms
6,940 KB |
| testcase_52 | AC | 1,920 ms
6,940 KB |
| testcase_53 | AC | 1,918 ms
6,944 KB |
ソースコード
#line 1 "Main.cpp"
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#line 1 "nachia\\atcoder\\convolution.hpp"
#line 4 "nachia\\atcoder\\convolution.hpp"
#include <array>
#include <cassert>
#include <type_traits>
#line 1 "nachia\\atcoder\\internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#line 1 "nachia\\atcoder\\static_modint.hpp"
#line 1 "nachia\\atcoder\\internal_modint_base.hpp"
#line 1 "nachia\\atcoder\\internal_type_traits.hpp"
#line 5 "nachia\\atcoder\\internal_type_traits.hpp"
#include <numeric>
#line 7 "nachia\\atcoder\\internal_type_traits.hpp"
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<
std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<
std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<
std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<
std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<
(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<
(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<
std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<
is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<
is_integral<T>::value && std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#line 7 "nachia\\atcoder\\internal_modint_base.hpp"
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#line 1 "nachia\\atcoder\\internal_math.hpp"
#line 5 "nachia\\atcoder\\internal_math.hpp"
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m){
x %= m;
if(x < 0) x += m;
return x;
}
// Fast moduler by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
using u64 = unsigned long long;
unsigned int _m;
u64 im;
// @param m `1 <= m`
barrett(unsigned int m) : _m(m), im((u64)(-1) / m + 1){}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
u64 z = a;
z *= b;
#ifdef _MSC_VER
u64 x;
_umul128(z, im, &x);
#else
u64 x = (u64)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if(_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m){
if(m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1, y = safe_mod(x, m);
while(n){
if(n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n){
if(n <= 1) return false;
if(n == 2 || n == 7 || n == 61) return true;
if(n % 2 == 0) return false;
long long d = n - 1;
while(d % 2 == 0) d /= 2;
for(long long a : {2, 7, 61}){
long long t = d, y = pow_mod_constexpr(a, t, n);
while(t != n - 1 && y != 1 && y != n - 1){
y = y * y % n;
t <<= 1;
}
if(y != n - 1 && t % 2 == 0) return false;
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b){
a = safe_mod(a, b);
if(a == 0) return {b, 0};
long long s = b, t = a, m0 = 0, m1 = 1;
while(t){
long long u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if(m0 < 0) m0 += b / s;
return {s, m0};
}
// @param m must be prime
constexpr int primitive_root_constexpr(int m){
if(m == 2) return 1;
if(m == 167772161) return 3;
if(m == 469762049) return 3;
if(m == 754974721) return 11;
if(m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m-1) / 2;
while(x%2 == 0) x /= 2;
for(int i=3; (long long)(i)*i <= x; i += 2){
if(x % i == 0){
divs[cnt++] = i;
while(x % i == 0) x /= i;
}
}
if(x>1) divs[cnt++] = x;
for(int g=2; ; g++){
bool ok = true;
for(int i=0; i<cnt; i++){
if(pow_mod_constexpr(g, (m-1) / divs[i], m) == 1){
ok = false;
break;
}
}
if(ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#line 10 "nachia\\atcoder\\static_modint.hpp"
namespace atcoder {
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod(){ return m; }
static mint raw(int v){
mint x;
x.w = v;
return x;
}
static_modint() : w(0){}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v){
long long x = (long long)(v % (long long)(umod()));
if(x < 0) x += umod();
w = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v){
w = (unsigned int)(v % umod());
}
static_modint(bool v){ w = ((unsigned int)(v) % umod()); }
unsigned int val() const { return w; }
mint& operator++(){
w++;
if(w == umod()) w = 0;
return *this;
}
mint& operator--(){
if(w == 0) w = umod();
w--;
return *this;
}
mint operator++(int){
mint result = *this;
++*this;
return result;
}
mint operator--(int){
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs){
w += rhs.w;
if(w >= umod()) w -= umod();
return *this;
}
mint& operator-=(const mint& rhs){
w -= rhs.w;
if(w >= umod()) w += umod();
return *this;
}
mint& operator*=(const mint& rhs){
unsigned long long z = w;
z *= rhs.w;
w = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs){ return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while(n){
if(n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if(prime){
assert(w);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(w, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs){ return mint(lhs) += rhs; }
friend mint operator-(const mint& lhs, const mint& rhs){ return mint(lhs) -= rhs; }
friend mint operator*(const mint& lhs, const mint& rhs){ return mint(lhs) *= rhs; }
friend mint operator/(const mint& lhs, const mint& rhs){ return mint(lhs) /= rhs; }
friend bool operator==(const mint& lhs, const mint& rhs){ return lhs.w == rhs.w; }
friend bool operator!=(const mint& lhs, const mint& rhs){ return lhs.w != rhs.w; }
private:
unsigned int w;
static constexpr unsigned int umod(){ return m; }
static constexpr bool prime = internal::is_prime<m>;
};
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#line 11 "nachia\\atcoder\\convolution.hpp"
namespace atcoder {
namespace internal {
template <class mint,
int g = internal::primitive_root<mint::mod()>,
internal::is_static_modint_t<mint>* = nullptr>
struct fft_info {
static constexpr int rank2 = bsf_constexpr(mint::mod()-1);
std::array<mint, rank2+1> root;
std::array<mint, rank2+1> iroot;
std::array<mint, std::max(0, rank2-1)> rate2;
std::array<mint, std::max(0, rank2-1)> irate2;
std::array<mint, std::max(0, rank2-2)> rate3;
std::array<mint, std::max(0, rank2-2)> irate3;
fft_info(){
root[rank2] = mint(g).pow((mint::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];
}
mint 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];
}
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];
}
}
};
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a){
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
int len = 0;
while(len < h){
if(h-len == 1){
int p = 1 << (h-len-1);
mint 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 *= info.rate2[bsf(~(unsigned int)(s))];
}
len++;
} else {
int p = 1 << (h-len-2);
mint rot = 1, imag = info.root[2];
for(int s=0; s<(1<<len); s++){
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h-len);
for(int i=0; i<p; i++){
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i+offset].val();
auto a1 = 1ULL * a[i+offset+p].val() * rot.val();
auto a2 = 1ULL * a[i+offset+2*p].val() * rot2.val();
auto a3 = 1ULL * a[i+offset+3*p].val() * rot3.val();
auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val();
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 *= info.rate3[bsf(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a){
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
constexpr int MOD = mint::mod();
int len = h;
while(len){
if(len == 1){
int p = 1 << (h-len);
mint 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)(MOD + l.val() - r.val()) * irot.val();
}
if(s+1 != (1<<(len-1))) irot *= info.irate2[bsf(~(unsigned int)(s))];
}
len--;
} else {
int p = 1 << (h-len);
mint irot = 1, iimag = info.iroot[2];
for(int s=0; s<(1<<(len-2)); s++){
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h-len+2);
for(int i=0; i<p; i++){
auto a0 = 1ULL * a[i+offset+0*p].val();
auto a1 = 1ULL * a[i+offset+1*p].val();
auto a2 = 1ULL * a[i+offset+2*p].val();
auto a3 = 1ULL * a[i+offset+3*p].val();
auto a2na3iimag = 1ULL * mint((MOD + a2 - a3) * iimag.val()).val();
a[i+offset] = a0 + a1 + a2 + a3;
a[i+offset+1*p] = (a0 + (MOD - a1) + a2na3iimag) * irot.val();
a[i+offset+2*p] = (a0 + a1 + (MOD - a2) + (MOD - a3)) * irot2.val();
a[i+offset+3*p] = (a0 + (MOD - a1) + (MOD - a2na3iimag)) * irot3.val();
}
if(s+1 != (1<<(len-2))) irot *= info.irate3[bsf(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <class Elem>
std::vector<Elem> convolution_naive(const std::vector<Elem>& a, const std::vector<Elem>& b){
int n = int(a.size()), m = int(b.size());
std::vector<Elem> ans(n+m-1);
if(n < m){
for(int j=0; j<m; j++) for(int i=0; i<n; i++) ans[i+j] += a[i] * b[j];
} else {
for(int i=0; i<n; i++) for(int j=0; j<m; j++) ans[i+j] += a[i] * b[j];
}
return ans;
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b){
int n = int(a.size()), m = int(b.size());
int z = 1 << internal::ceil_pow2(n+m-1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for(int i=0; i<z; i++) a[i] *= b[i];
internal::butterfly_inv(a);
a.resize(n+m-1);
mint iz = mint(z).inv();
for(int i=0; i<n+m-1; i++) a[i] *= iz;
return a;
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b){
int n = int(a.size()), m = int(b.size());
if(!n || !m) return {};
if(std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(const std::vector<mint>& a, const std::vector<mint>& b){
int n = int(a.size()), m = int(b.size());
if(!n || !m) return {};
if(std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b){
int n = int(a.size()), m = int(b.size());
if(!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for(int i=0; i<n; i++) a2[i] = mint(a[i]);
for(int i=0; i<m; i++) b2[i] = mint(b[i]);
auto c2 = convolution(std::move(a2), std::move(b2));
std::vector<T> c(n+m-1);
for(int i=0; i<n+m-1; i++) c[i] = c2[i].val();
return c;
}
std::vector<long long> convolution_ll(
const std::vector<long long>& a,
const std::vector<long long>& b)
{
int n = int(a.size()), m = int(b.size());
if(!n || !m) return {};
using u64 = unsigned long long;
static constexpr u64 MOD1 = 754974721, MOD2 = 167772161, MOD3 = 469762049;
static constexpr u64 M2M3 = MOD2 * MOD3, M1M3 = MOD1 * MOD3, M1M2 = MOD1 * MOD2;
static constexpr u64 M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr u64 i1 = internal::inv_gcd(M2M3, MOD1).second;
static constexpr u64 i2 = internal::inv_gcd(M1M3, MOD2).second;
static constexpr u64 i3 = internal::inv_gcd(M1M2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n+m-1);
for(int i=0; i<n+m-1; i++){
u64 x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
long long diff = c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if(diff < 0) diff += MOD1;
static constexpr u64 offset[5] = { 0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
} // namespace atcoder
#line 3 "nachia\\fps\\many-polynomial-product.hpp"
namespace nachia{
template<class Modint>
std::vector<Modint> ProductOfManyPolynomials(std::vector<std::vector<Modint>> poly){
if(poly.empty()) return {Modint(1)};
for(auto& p : poly) while(!p.empty() && p.back().val() == 0) p.pop_back();
for(auto& p : poly) if(p.size() == 0) return {Modint(0)};
for(size_t K=16; poly.size() != 1; K*=2){
size_t pos = poly.size();
for(size_t i=0; i<poly.size(); i++){
if(pos == poly.size() || poly[pos].size() + poly[i].size() - 1 > K){ pos = i; continue; }
poly[pos] = atcoder::convolution(poly[pos], poly[i]);
std::swap(poly[i--], poly.back());
poly.pop_back();
}
}
return std::move(poly[0]);
}
} // namespace nachia
#line 3 "nachia\\math\\combination.hpp"
namespace nachia{
template<class Modint>
class Comb{
private:
std::vector<Modint> F;
std::vector<Modint> iF;
public:
void extend(int newN){
int prevN = (int)F.size() - 1;
if(prevN >= newN) return;
F.resize(newN+1);
iF.resize(newN+1);
for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i);
iF[newN] = F[newN].inv();
for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i);
}
Comb(int n = 1){
F.assign(2, Modint(1));
iF.assign(2, Modint(1));
extend(n);
}
Modint factorial(int n) const { return F[n]; }
Modint invFactorial(int n) const { return iF[n]; }
Modint invOf(int n) const { return iF[n] * F[n-1]; }
Modint comb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[r] * iF[n-r];
}
Modint invComb(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[r] * F[n-r];
}
Modint perm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return F[n] * iF[n-r];
}
Modint invPerm(int n, int r) const {
if(n < 0 || n < r || r < 0) return Modint(0);
return iF[n] * F[n-r];
}
Modint operator()(int n, int r) const { return comb(n,r); }
};
} // namespace nachia
#line 8 "Main.cpp"
using namespace std;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;
using Modint = atcoder::static_modint<998244353>;
int main(){
const int Z = 700;
nachia::Comb<Modint> comb(Z);
int n, m; cin >> n >> m;
vector<int> A(n), B(n);
rep(i,n) cin >> A[i];
rep(i,n) cin >> B[i];
vector<vector<Modint>> Comb(m, vector<Modint>(2*Z+1, 1));
auto Diff = [&](int a, int b, int d) -> Modint { return comb.comb(a+b, a+d); };
rep(i,n) rep(d,2*Z+1) Comb[i%m][d] *= Diff(A[i], B[i], d-Z);
auto anss = nachia::ProductOfManyPolynomials(std::move(Comb));
auto ans = anss[Z * m];
cout << ans.val() << '\n';
return 0;
}
struct ios_do_not_sync{
ios_do_not_sync(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
}
} ios_do_not_sync_instance;