#line 1 "test/yj_convolution_mod_raw.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod"
/**
* @see http://wwwa.pikara.ne.jp/okojisan/stockham/
*/
#include <cstdio>
#include <utility>
#include <vector>
#line 1 "ModularArithmetic/modint.cpp"
/**
* @brief 合同算術用クラス
* @author えびちゃん
*/
#include <cstdint>
#include <limits>
#include <type_traits>
#line 13 "ModularArithmetic/modint.cpp"
template <intmax_t Modulo>
class modint {
public:
using value_type = typename std::conditional<
(0 < Modulo && Modulo < std::numeric_limits<int>::max() / 2), int, intmax_t
>::type;
private:
static constexpr value_type S_cmod = Modulo; // compile-time
static value_type S_rmod; // runtime
value_type M_value = 0;
static constexpr value_type S_inv(value_type n, value_type m) {
value_type x = 0;
value_type y = 1;
value_type a = n;
value_type b = m;
for (value_type u = y, v = x; a;) {
value_type q = b / a;
std::swap(x -= q*u, u);
std::swap(y -= q*v, v);
std::swap(b -= q*a, a);
}
if ((x %= m) < 0) x += m;
return x;
}
static value_type S_normalize(intmax_t n, value_type m) {
if (n >= m) {
n %= m;
} else if (n < 0) {
if ((n %= m) < 0) n += m;
}
return n;
}
public:
modint() = default;
modint(intmax_t n): M_value(S_normalize(n, get_modulo())) {}
modint& operator =(intmax_t n) {
M_value = S_normalize(n, get_modulo());
return *this;
}
modint& operator +=(modint const& that) {
if ((M_value += that.M_value) >= get_modulo()) M_value -= get_modulo();
return *this;
}
modint& operator -=(modint const& that) {
if ((M_value -= that.M_value) < 0) M_value += get_modulo();
return *this;
}
modint& operator *=(modint const& that) {
intmax_t tmp = M_value;
tmp *= that.M_value;
M_value = tmp % get_modulo();
return *this;
}
modint& operator /=(modint const& that) {
intmax_t tmp = M_value;
tmp *= S_inv(that.M_value, get_modulo());
M_value = tmp % get_modulo();
return *this;
}
modint& operator ++() {
if (++M_value == get_modulo()) M_value = 0;
return *this;
}
modint& operator --() {
if (M_value-- == 0) M_value = get_modulo()-1;
return *this;
}
modint operator ++(int) { modint tmp(*this); ++*this; return tmp; }
modint operator --(int) { modint tmp(*this); --*this; return tmp; }
friend modint operator +(modint lhs, modint const& rhs) { return lhs += rhs; }
friend modint operator -(modint lhs, modint const& rhs) { return lhs -= rhs; }
friend modint operator *(modint lhs, modint const& rhs) { return lhs *= rhs; }
friend modint operator /(modint lhs, modint const& rhs) { return lhs /= rhs; }
modint operator +() const { return *this; }
modint operator -() const {
if (M_value == 0) return *this;
return modint(get_modulo() - M_value);
}
friend bool operator ==(modint const& lhs, modint const& rhs) {
return lhs.M_value == rhs.M_value;
}
friend bool operator !=(modint const& lhs, modint const& rhs) {
return !(lhs == rhs);
}
value_type get() const { return M_value; }
static value_type get_modulo() { return ((S_cmod > 0)? S_cmod: S_rmod); }
template <int M = Modulo, typename Tp = typename std::enable_if<(M <= 0)>::type>
static Tp set_modulo(value_type m) { S_rmod = m; }
};
template <intmax_t N>
constexpr typename modint<N>::value_type modint<N>::S_cmod;
template <intmax_t N>
typename modint<N>::value_type modint<N>::S_rmod;
#line 1 "integer/bit.cpp"
/**
* @brief ビット演算
* @author えびちゃん
*/
// XXX integral promotion 関連の注意をあまりしていません
#include <climits>
#include <type_traits>
template <typename Tp>
constexpr auto countl_zero(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
int bits = (sizeof(value_type) * CHAR_BIT);
if (n == 0) return bits;
int res = 0;
for (int i = bits / 2; i > 0; i /= 2) {
value_type mask = ((static_cast<value_type>(1) << i) - 1) << i;
if (n & mask) n >>= i;
else res += i;
}
return res;
}
template <typename Tp>
constexpr auto countl_one(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
return countl_zero(static_cast<value_type>(~n));
}
template <typename Tp>
constexpr auto countr_zero(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
int bits = (sizeof(value_type) * CHAR_BIT);
if (n == 0) return bits;
int res = 0;
for (int i = bits / 2; i > 0; i /= 2) {
value_type mask = ((static_cast<value_type>(1) << i) - 1);
if (!(n & mask)) res += i, n >>= i;
}
return res;
}
template <typename Tp>
constexpr auto countr_one(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
return countr_zero(static_cast<value_type>(~n));
}
constexpr unsigned long long half_mask[] = {
0x5555555555555555uLL, 0x3333333333333333uLL, 0x0F0F0F0F0F0F0F0FuLL,
0x00FF00FF00FF00FFuLL, 0x0000FFFF0000FFFFuLL, 0x00000000FFFFFFFFuLL
};
template <typename Tp>
constexpr auto popcount(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
int bits = static_cast<int>((sizeof n) * CHAR_BIT);
for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
if (j <= 8) n = (n & half_mask[i]) + ((n >> j) & half_mask[i]);
else n += n >> j;
}
return n & 0xFF;
}
template <typename Tp>
constexpr auto parity(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{ return popcount(n) & 1; }
template <typename Tp>
int clz(Tp n) { return countl_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }
template <typename Tp>
int ctz(Tp n) { return countr_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }
template <typename Tp>
int ilog2(Tp n) {
return (CHAR_BIT * sizeof(Tp) - 1) - clz(static_cast<typename std::make_unsigned<Tp>::type>(n));
}
template <typename Tp>
bool is_pow2(Tp n) { return (n > 0) && ((n & (n-1)) == 0); }
template <typename Tp>
Tp floor2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(1) << ilog2(n); }
template <typename Tp>
Tp ceil2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(2) << ilog2(n); }
template <typename Tp>
constexpr auto reverse(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, Tp>::type
{
int bits = static_cast<int>((sizeof n) * CHAR_BIT);
for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
n = ((n & half_mask[i]) << j) | ((n >> j) & half_mask[i]);
}
return n;
}
#line 13 "test/yj_convolution_mod_raw.test.cpp"
constexpr intmax_t mod = 998244353;
using mi = modint<mod>;
void fft4(std::vector<mi>& x, bool inv = false) {
size_t n = ceil2(x.size());
size_t s = 1;
x.resize(n, 0);
std::vector<mi> y(n);
mi omega = 15311432;
int nn = countr_zero<unsigned>(mi::get_modulo()-1);
for (int i = ilog2(n); i < nn; ++i) omega *= omega;
if (inv) omega = 1 / omega;
mi j = omega;
for (int i = 2; i < ilog2(n); ++i) j *= j;
for (size_t i = n; i > 1; i >>= 2) {
size_t n0 = 0;
size_t n1 = i / 4;
size_t n2 = i / 2;
size_t n3 = n1 + n2;
if (i == 2) {
for (size_t q = 0; q < s; ++q) {
mi a = x[q + 0];
mi b = x[q + s];
x[q + 0] = a + b;
x[q + s] = a - b;
}
break;
}
mi w1p = 1;
for (size_t p = 0; p < n1; ++p) {
mi w2p = w1p * w1p;
mi w3p = w1p * w2p;
for (size_t q = 0; q < s; ++q) {
mi a = x[q + s * (p + n0)];
mi b = x[q + s * (p + n1)];
mi c = x[q + s * (p + n2)];
mi d = x[q + s * (p + n3)];
mi apc = a + c;
mi amc = a - c;
mi bpd = b + d;
mi jbmd = j * (b - d);
y[q + s * (p << 2 | 0)] = apc + bpd;
y[q + s * (p << 2 | 1)] = w1p * (amc + jbmd);
y[q + s * (p << 2 | 2)] = w2p * (apc - bpd);
y[q + s * (p << 2 | 3)] = w3p * (amc - jbmd);
}
w1p *= omega;
}
std::swap(x, y);
omega *= omega;
omega *= omega;
s <<= 2;
}
if (inv) {
mi n_ = mi(1) / n;
for (auto& xi: x) xi *= n_;
}
}
#line 1 "utility/fast_io.cpp"
/**
* @brief 高速入出力
* @author えびちゃん
* @see https://qiita.com/rsk0315_h4x/items/17a9cb12e0de5fd918f4
*/
#include <cstddef>
#line 13 "utility/fast_io.cpp"
#include <cstring>
#line 15 "utility/fast_io.cpp"
#include <string>
#include <type_traits>
#line 18 "utility/fast_io.cpp"
#line 20 "utility/fast_io.cpp"
namespace fast {
static constexpr size_t buf_size = 1 << 17;
static constexpr size_t margin = 1;
static char inbuf[buf_size + margin] = {};
static __attribute__((aligned(8))) char outbuf[buf_size + margin] = {};
static __attribute__((aligned(8))) char minibuf[32];
static constexpr size_t int_digits = 20; // 18446744073709551615
static constexpr uintmax_t digit_mask = 0x3030303030303030;
static constexpr uintmax_t first_mask = 0x00FF00FF00FF00FF;
static constexpr uintmax_t second_mask = 0x0000FFFF0000FFFF;
static constexpr uintmax_t third_mask = 0x00000000FFFFFFFF;
static constexpr uintmax_t tenpow[] = {
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000,
1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000,
100000000000000, 1000000000000000, 10000000000000000, 100000000000000000,
1000000000000000000, 10000000000000000000u,
};
static __attribute__((aligned(8))) char inttab[40000] = {}; // 4-digit integers (10000 many)
static char S_sep = ' ', S_end = '\n';
template <typename Tp>
using enable_if_integral = std::enable_if<std::is_integral<Tp>::value, Tp>;
class scanner {
char* pos = inbuf;
char* endpos = inbuf + buf_size;
void M_read_from_stdin() {
endpos = inbuf + fread(pos, 1, buf_size, stdin);
}
void M_reread_from_stdin() {
ptrdiff_t len = endpos - pos;
if (!(inbuf + len <= pos)) return;
memcpy(inbuf, pos, len);
char* tmp = inbuf + len;
endpos = tmp + fread(tmp, 1, buf_size-len, stdin);
*endpos = 0;
pos = inbuf;
}
public:
scanner() { M_read_from_stdin(); }
template <typename Integral,
typename enable_if_integral<Integral>::type* = nullptr>
void scan_parallel(Integral& x) {
if (__builtin_expect(endpos <= pos + int_digits, 0))
M_reread_from_stdin();
bool ends = false;
typename std::make_unsigned<Integral>::type y = 0;
bool neg = false;
if (std::is_signed<Integral>::value && *pos == '-') {
neg = true;
++pos;
}
do {
memcpy(minibuf, pos, 8);
intmax_t c = *(intmax_t*)minibuf;
intmax_t d = (c & digit_mask) ^ digit_mask;
int skip = 8;
int shift = 8;
if (d) {
int ctz = countr_zero<uintmax_t>(d);
if (ctz == 4) break;
c &= (1L << (ctz-5)) - 1;
int discarded = (68-ctz) / 8;
shift -= discarded;
c <<= discarded * 8;
skip -= discarded;
ends = true;
}
c |= digit_mask;
c ^= digit_mask;
c = ((c >> 8) + c*10) & first_mask;
c = ((c >> 16) + c*100) & second_mask;
c = ((c >> 32) + c*10000) & third_mask;
y = y*tenpow[shift] + c;
pos += skip;
} while (!ends);
x = (neg? -y: y);
++pos;
}
template <typename Integral,
typename enable_if_integral<Integral>::type* = nullptr>
void scan_serial(Integral& x) {
if (__builtin_expect(endpos <= pos + int_digits, 0))
M_reread_from_stdin();
bool neg = false;
if (std::is_signed<Integral>::value && *pos == '-') {
neg = true;
++pos;
}
typename std::make_unsigned<Integral>::type y = *pos-'0';
while (*++pos >= '0') y = 10*y + *pos-'0';
x = (neg? -y: y);
++pos;
}
template <typename Integral,
typename enable_if_integral<Integral>::type* = nullptr>
// Use scan_parallel(x) only when x may be too large (about 10^12).
// Otherwise, even when x <= 10^9, scan_serial(x) may be faster.
void scan(Integral& x) { scan_serial(x); }
void scan_serial(std::string& s) {
// until first whitespace
s = "";
do {
char* startpos = pos;
while (*pos > ' ') ++pos;
s += std::string(startpos, pos);
if (*pos != 0) {
++pos; // skip the space
break;
}
M_reread_from_stdin();
} while (true);
}
void scan(std::string& s) { scan_serial(s); }
template <typename Tp, typename... Args>
void scan(Tp& x, Args&&... xs) {
scan(x);
scan(std::forward<Args>(xs)...);
}
};
class printer {
char* pos = outbuf;
void M_flush_stdout() {
fwrite(outbuf, 1, pos-outbuf, stdout);
pos = outbuf;
}
static int S_int_digits(uintmax_t n) {
if (n < tenpow[16]) { // 1
if (n < tenpow[8]) { // 2
if (n < tenpow[4]) { // 3
if (n < tenpow[2]) { // 4
if (n < tenpow[1]) return 1; // 5
return 2; // 5
}
if (n < tenpow[3]) return 3; // 4
return 4; // 4
}
if (n < tenpow[6]) { // 4
if (n < tenpow[5]) return 5; // 5
return 6; // 5
}
if (n < tenpow[7]) return 7; // 5
return 8; // 5
}
if (n < tenpow[12]) { // 3
if (n < tenpow[10]) { // 4
if (n < tenpow[9]) return 9; // 5
return 10; // 5
}
if (n < tenpow[11]) return 11; // 5
return 12; // 5
}
if (n < tenpow[14]) { // 4
if (n < tenpow[13]) return 13; // 5
return 14; // 5
}
if (n < tenpow[15]) return 15; // 5
return 16; // 5
}
if (n < tenpow[18]) { // 2
if (n < tenpow[17]) return 17; // 3
return 18; // 3
}
return 19; // 2
if (n < tenpow[19]) return 19; // 3
return 20; // 3
}
void M_precompute() {
uintmax_t const digit1 = 0x0200000002000000;
uintmax_t const digit2 = 0xf600fffff6010000;
uintmax_t const digit3 = 0xfff600fffff60100;
uintmax_t const digit4 = 0xfffff600fffff601;
uintmax_t counter = 0x3130303030303030;
for (int i = 0, i4 = 0; i4 < 10; ++i4, counter += digit4)
for (int i3 = 0; i3 < 10; ++i3, counter += digit3)
for (int i2 = 0; i2 < 10; ++i2, counter += digit2)
for (int i1 = 0; i1 < 5; ++i1, ++i, counter += digit1)
*((uintmax_t*)inttab + i) = counter;
}
public:
printer() { M_precompute(); }
~printer() { M_flush_stdout(); }
void print(char c) {
if (__builtin_expect(pos + 1 >= outbuf + buf_size, 0)) M_flush_stdout();
*pos++ = c;
}
template <size_t N>
void print(char const(&s)[N]) {
if (__builtin_expect(pos + N >= outbuf + buf_size, 0)) M_flush_stdout();
memcpy(pos, s, N-1);
pos += N-1;
}
void print(char const* s) {
// FIXME: strlen や memcpy などで定数倍高速化したい
while (*s != 0) {
*pos++ = *s++;
if (pos == outbuf + buf_size) M_flush_stdout();
}
}
void print(std::string const& s) { print(s.data()); }
template <typename Integral,
typename enable_if_integral<Integral>::type* = nullptr>
void print(Integral x) {
if (__builtin_expect(pos + int_digits >= outbuf + buf_size, 0))
M_flush_stdout();
if (x == 0) {
*pos++ = '0';
return;
}
if (x < 0) {
*pos++ = '-';
if (__builtin_expect(x == std::numeric_limits<Integral>::min(), 0)) {
switch (sizeof x) {
case 2: print("32768"); return;
case 4: print("2147483648"); return;
case 8: print("9223372036854775808"); return;
}
}
x = -x;
}
typename std::make_unsigned<Integral>::type y = x;
int len = S_int_digits(y);
pos += len;
char* tmp = pos;
int w = (pos - outbuf) & 3;
if (w > len) w = len;
for (int i = w; i > 0; --i) {
*--tmp = y % 10 + '0';
y /= 10;
}
len -= w;
while (len >= 4) {
tmp -= 4;
*(unsigned*)tmp = *((unsigned*)inttab + (y % 10000));
len -= 4;
if (len) y /= 10000;
}
while (len-- > 0) {
*--tmp = y % 10 + '0';
y /= 10;
}
}
template <typename Tp, typename... Args>
void print(Tp const& x, Args&&... xs) {
if (sizeof...(Args) > 0) {
print(x);
print(S_sep);
print(std::forward<Args>(xs)...);
}
}
template <typename Tp>
void println(Tp const& x) { print(x), print(S_end); }
template <typename Tp, typename... Args>
void println(Tp const& x, Args&&... xs) {
print(x, std::forward<Args>(xs)...);
print(S_end);
}
static void set_sep(char c) { S_sep = c; }
static void set_end(char c) { S_end = c; }
};
} // fast::
fast::scanner cin;
fast::printer cout;
#line 78 "test/yj_convolution_mod_raw.test.cpp"
int main() {
size_t n, m;
cin.scan(n, m);
std::vector<int> a(n), b(m);
for (auto& ai: a) cin.scan(ai);
for (auto& bi: b) cin.scan(bi);
std::vector<mi> f(a.begin(), a.end());
std::vector<mi> g(b.begin(), b.end());
size_t n2 = ceil2(n+m-1);
f.resize(n2, 0);
g.resize(n2, 0);
fft4(f);
fft4(g);
for (size_t i = 0; i < n2; ++i) f[i] *= g[i];
fft4(f, true);
for (size_t i = 0; i+1 < n+m; ++i) {
cout.print<unsigned>(f[i].get());
cout.print(i+2<n+m? ' ': '\n');
}
}
test/yj_convolution_mod_raw.test.cpp