//! https://gcc.gnu.org/onlinedocs/libquadmath/Math-Library-Routines.html

//! https://trap.jp/post/1224/

//! https://misawa.github.io/others/avoid_errors/techniques_to_avoid_errors.html

//! https://qiita.com/Chippppp/items/13150f5e0ea99f444d97#%E5%A4%9A%E6%AC%A1%E5%85%83vector%E7%94%9F%E6%88%90%E9%96%A2%E6%95%B0

//! https://judge.yosupo.jp/submission/170706 (maspy さん)

//! https://judge.yosupo.jp/submission/21623  (Nyaan さん)

//! https://github.com/philip82148/cpp-dump

//! https://www.mathenachia.blog/even-mod-montgomery-impl/

#define SINGLE_TESTCASE 
// #define MULTI_TESTCASE
// #define AOJ_TESTCASE

#define FAST_IO 
// #define FAST_CIO
// #define INTERACTIVE

#define INF 4'000'000'000'000'000'037LL
#define EPS 1e-11

// https://github.com/miscalculation53/library/tree/wip/template/template_all.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_all_but_modint.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_types.hpp

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

// https://github.com/miscalculation53/library/tree/wip/template/template_float128.hpp

using namespace std;

#if __cplusplus > 202002L && defined(__STDCPP_FLOAT128_T__)
#include <stdfloat>
using f128 = std::float128_t;
#elif defined(__SIZEOF_FLOAT128__)
using f128 = __float128;
#else
#error "f128 requires a compiler with IEEE binary128 support, such as GCC on x86_64."
#endif
#define LIBRARY_HAS_FLOAT128 1

#if __cplusplus > 202002L && defined(__STDCPP_FLOAT128_T__) && \
    (defined(_GLIBCXX_HAVE_FLOAT128_MATH) || defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128))
#define LIBRARY_USE_QUADMATH 0
#else
#include <quadmath.h>
#define LIBRARY_USE_QUADMATH 1

#define _p_F128_UNARY(name) \
  inline f128 name(f128 x) { return f128(name##q(__float128(x))); }
_p_F128_UNARY(acos)
_p_F128_UNARY(acosh)
_p_F128_UNARY(asin)
_p_F128_UNARY(asinh)
_p_F128_UNARY(atan)
_p_F128_UNARY(atanh)
_p_F128_UNARY(cbrt)
_p_F128_UNARY(ceil)
_p_F128_UNARY(cos)
_p_F128_UNARY(cosh)
_p_F128_UNARY(erf)
_p_F128_UNARY(erfc)
_p_F128_UNARY(exp)
_p_F128_UNARY(exp2)
_p_F128_UNARY(expm1)
_p_F128_UNARY(fabs)
_p_F128_UNARY(floor)
_p_F128_UNARY(lgamma)
_p_F128_UNARY(log)
_p_F128_UNARY(log10)
_p_F128_UNARY(log1p)
_p_F128_UNARY(log2)
_p_F128_UNARY(logb)
_p_F128_UNARY(nearbyint)
_p_F128_UNARY(rint)
_p_F128_UNARY(round)
_p_F128_UNARY(sin)
_p_F128_UNARY(sinh)
_p_F128_UNARY(sqrt)
_p_F128_UNARY(tan)
_p_F128_UNARY(tanh)
_p_F128_UNARY(tgamma)
_p_F128_UNARY(trunc)
#undef _p_F128_UNARY

#define _p_F128_BINARY(name) \
  inline f128 name(f128 x, f128 y) { return f128(name##q(__float128(x), __float128(y))); } \
  template <class T, enable_if_t<is_arithmetic_v<T>, int> = 0> \
  inline f128 name(f128 x, T y) { return name(x, f128(y)); } \
  template <class T, enable_if_t<is_arithmetic_v<T>, int> = 0> \
  inline f128 name(T x, f128 y) { return name(f128(x), y); }
_p_F128_BINARY(atan2)
_p_F128_BINARY(copysign)
_p_F128_BINARY(fdim)
_p_F128_BINARY(fmax)
_p_F128_BINARY(fmin)
_p_F128_BINARY(fmod)
_p_F128_BINARY(hypot)
_p_F128_BINARY(nextafter)
_p_F128_BINARY(pow)
_p_F128_BINARY(remainder)
#undef _p_F128_BINARY

inline f128 fma(f128 x, f128 y, f128 z)
{ return f128(fmaq(__float128(x), __float128(y), __float128(z))); }
inline f128 hypot(f128 x, f128 y, f128 z)
{ return hypot(hypot(x, y), z); }
namespace template_float128_detail
{
template <class T>
constexpr bool arithmetic = is_arithmetic_v<T> || is_same_v<T, f128>;
}
#define _p_F128_TERNARY_MIXED(name) \
  template <class T, class U, enable_if_t<template_float128_detail::arithmetic<T> && template_float128_detail::arithmetic<U>, int> = 0> \
  inline f128 name(f128 x, T y, U z) { return name(x, f128(y), f128(z)); } \
  template <class T, class U, enable_if_t<template_float128_detail::arithmetic<T> && !is_same_v<T, f128> && template_float128_detail::arithmetic<U>, int> = 0> \
  inline f128 name(T x, f128 y, U z) { return name(f128(x), y, f128(z)); } \
  template <class T, class U, enable_if_t<template_float128_detail::arithmetic<T> && !is_same_v<T, f128> && template_float128_detail::arithmetic<U> && !is_same_v<U, f128>, int> = 0> \
  inline f128 name(T x, U y, f128 z) { return name(f128(x), f128(y), z); }
inline f128 frexp(f128 x, int *exponent)
{ return f128(frexpq(__float128(x), exponent)); }
inline f128 ldexp(f128 x, int exponent)
{ return f128(ldexpq(__float128(x), exponent)); }
inline f128 scalbn(f128 x, int exponent)
{ return f128(scalbnq(__float128(x), exponent)); }
inline f128 scalbln(f128 x, long exponent)
{ return f128(scalblnq(__float128(x), exponent)); }
inline f128 modf(f128 x, f128 *integer)
{
  __float128 value;
  const auto fraction = modfq(__float128(x), &value);
  *integer = f128(value);
  return f128(fraction);
}
inline f128 remquo(f128 x, f128 y, int *quotient)
{ return f128(remquoq(__float128(x), __float128(y), quotient)); }
inline long lrint(f128 x) { return lrintq(__float128(x)); }
inline long lround(f128 x) { return lroundq(__float128(x)); }
inline long long llrint(f128 x) { return llrintq(__float128(x)); }
inline long long llround(f128 x) { return llroundq(__float128(x)); }
inline int ilogb(f128 x) { return ilogbq(__float128(x)); }
#endif

namespace template_float128_detail
{
inline bool parse(string_view s, f128 &x)
{
  if (!s.empty() && s.front() == '+')
  {
    s.remove_prefix(1);
    if (s.empty() || s.front() == '-') return false;
  }
#if LIBRARY_USE_QUADMATH
  string token(s);
  char *end;
  errno = 0;
  const __float128 value = strtoflt128(token.c_str(), &end);
  if (end == token.data() || end != token.data() + token.size()) return false;
  if (errno == ERANGE && (value == 0 || isinfq(value))) return false;
  x = f128(value);
  return true;
#else
  auto [p, ec] = from_chars(s.data(), s.data() + s.size(), x);
  return ec == errc{} && p == s.data() + s.size();
#endif
}

inline string format(f128 x, chars_format style, int precision)
{
  string s(128, '\0');
  while (true)
  {
#if LIBRARY_USE_QUADMATH
    const char *spec = style == chars_format::fixed ? "%.*Qf" :
                       style == chars_format::scientific ? "%.*Qe" : "%.*Qg";
    const int n = quadmath_snprintf(s.data(), s.size(), spec, precision, __float128(x));
    if (n < 0) abort();
    if (size_t(n) < s.size())
    {
      s.resize(size_t(n));
      return s;
    }
    s.resize(size_t(n) + 1);
#else
    auto [p, ec] = to_chars(s.data(), s.data() + s.size(), x, style, precision);
    if (ec == errc{})
    {
      s.resize(size_t(p - s.data()));
      return s;
    }
    s.resize(s.size() * 2);
#endif
  }
}
} 

using ld = decltype(EPS);

using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
using tllll = tuple<ll, ll, ll, ll>;

#define vc vector
template <class T>
using vvc = vc<vc<T>>;
template <class T>
using vvvc = vc<vc<vc<T>>>;

using vb = vc<bool>;
using vl = vc<ll>;
using vpll = vc<pll>;
using vtlll = vc<tlll>;
using vtllll = vc<tllll>;
using vstr = vc<string>;
using vvb = vvc<bool>;
using vvl = vvc<ll>;

template <class T>
using pql = priority_queue<T, vc<T>, greater<T>>;
template <class T>
using pqg = priority_queue<T>;

using i128 = __int128_t;
using u128 = __uint128_t;
i128 stoi128(const string &s)
{
  const bool neg = s.front() == '-';
  u128 res = 0;
  for (size_t i = size_t(neg); i < s.size(); i++)
    res = 10 * res + unsigned(s[i] - '0');
  if (neg)
    return -i128(res - 1) - 1;
  return i128(res);
}
string i128tos(i128 x)
{
  if (x == 0) return "0";
  string sign = "", res = "";
  u128 ux;
  if (x < 0)
    ux = u128(-(x + 1)) + 1, sign = "-";
  else
    ux = u128(x);
  while (ux > 0)
  {
    res += char('0' + ux % 10);
    ux /= 10;
  }
  reverse(res.begin(), res.end());
  return sign + res;
}
istream &operator>>(istream &is, i128 &a)
{
  string s;
  if (!(is >> s)) return is;
  a = stoi128(s);
  return is;
}
ostream &operator<<(ostream &os, const i128 &a)
{
  os << i128tos(a);
  return os;
}

#define cauto const auto

// https://github.com/miscalculation53/library/tree/wip/template/template_rep.hpp

#define overload4(_1,_2,_3,_4,name,...) name
#define rep1(i,n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++)
#define rep2(i,l,r) for (ll i = ll(l), rrrrr = ll(r); i < rrrrr; i++)
#define rep3(i,l,r,d) for (ll i = ll(l), rrrrr = ll(r), ddddd = ll(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repi1(i,n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi2(i,l,r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)
#define repi3(i,l,r,d) for (int i = int(l), rrrrr = int(r), ddddd = int(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)

#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
#define fem(...) for (auto &__VA_ARGS__)

// https://github.com/miscalculation53/library/tree/wip/template/template_math.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/is_integral_ext.hpp

template <class T>
constexpr bool is_integral_ext = is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>;

template <class T>
constexpr bool is_signed_ext = is_signed_v<T> || is_same_v<T, i128>;

template <class T>
constexpr bool is_unsigned_ext = is_unsigned_v<T> || is_same_v<T, u128>;
// https://github.com/miscalculation53/library/tree/wip/utils/integer_arithmetic.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/make_unsigned_ext.hpp

template <class T>
struct make_unsigned_ext
{
  using type = make_unsigned_t<T>;
};
template <>
struct make_unsigned_ext<i128>
{
  using type = u128;
};
template <>
struct make_unsigned_ext<u128>
{
  using type = u128;
};
template <class T>
using make_unsigned_ext_t = typename make_unsigned_ext<T>::type;

template <class T>
struct make_signed_ext
{
  using type = make_signed_t<T>;
};
template <>
struct make_signed_ext<u128>
{
  using type = i128;
};
template <class T>
using make_signed_ext_t = typename make_signed_ext<T>::type;

template <class T>
constexpr bool is_negative(T x)
{
  static_assert(is_integral_ext<T>);
  if constexpr (is_signed_ext<T>) return x < 0;
  return false;
}

template <class T, bool = is_integral_ext<T>>
struct unsigned_arithmetic { using type = T; };

template <class T>
struct unsigned_arithmetic<T, true>
{
  static_assert(!is_same_v<T, bool>);
  using type = common_type_t<unsigned int, make_unsigned_ext_t<T>>;
};

template <class T>
using unsigned_arithmetic_t = typename unsigned_arithmetic<T>::type;

// https://github.com/miscalculation53/library/tree/wip/utils/default_infty.hpp

namespace default_infty_detail
{
  template <class T, class = void>
  struct has_infty : false_type {};

  template <class T>
  struct has_infty<T, void_t<decltype(T::infty())>> : true_type {};

  template <class T>
  inline constexpr bool unsupported = false;
}

namespace template_math_detail
{

} 

template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T safemod(U a, V b)
{
  const T x = T(a), y = T(b);
  if constexpr (is_signed_ext<T>)
    if (y == T(-1)) return T(0);
  const T r = x % y;
  return r != T(0) && is_negative(x) != is_negative(y) ? T(r + y) : r;
}

// https://github.com/miscalculation53/library/tree/wip/template/template_vector.hpp

#define ALL(a) (a).begin(), (a).end()
template <class T = ll, class V>
inline T SZ(const V &x) { return x.size(); }
#define eb emplace_back

#define LMD(x,fx) ([&](const auto &x) { return fx; })
#define GEN_VEC(n,i,fi) (gen_vec(n, LMD(i, fi)))

template <class T>
string vtos(const vc<T> &v, char first)
{
  string res = "";
  fe(vi : v) res += vi + first;
  return res;
}

// https://github.com/miscalculation53/library/tree/wip/template/template_algo.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/resolved_infty.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/resolved_value.hpp

template <class T>
vvc<T> top(const vvc<T> &a)
{
  if (a.empty())
    return {};
  const int n = a.size(), m = a[0].size();
  vvc<T> b(m, vc<T>(n));
  repi(i, n)
  {
    assert(SZ<int>(a[i]) == m);
    repi(j, m) b[j][i] = a[i][j];
  }
  return b;
}
vstr top(const vstr &a)
{
  vvc<char> a_(a.size());
  repi(i, SZ<int>(a)) a_[i] = {ALL(a[i])};
  vvc<char> b_ = top(a_);
  vstr b(b_.size());
  repi(i, SZ<int>(b)) b[i] = {ALL(b_[i])};
  return b;
}

template <class T, class = void>
struct has_e0 : false_type {};
template <class T>
struct has_e0<T, void_t<decltype(T::e0())>> : true_type {};
template <class T>
inline constexpr bool has_e0_v = has_e0<T>::value;

template <class T>
struct MonoidAdd
{
  using S = T;
};
template <class T, auto infty = nullptr>
struct MonoidMin
{
  using S = T;
};
template <class T, auto infty = nullptr>
struct MonoidMax
{
  using S = T;
};

namespace internal
{
  template <class M, class I, class = void>
  struct HasMonoidPow : false_type
  {
  };
  template <class M, class I>
  struct HasMonoidPow<M, I, void_t<decltype(M::pow(declval<const typename M::S &>(), declval<I>()))>> : true_type
  {
  };
}

constexpr array<pll, 4> DRULgrid = {{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}};
constexpr array<pll, 4> DRULplane = {{{0, -1}, {1, 0}, {0, 1}, {-1, 0}}};
// https://github.com/miscalculation53/library/tree/wip/template/template_binsearch.hpp

template <class T>
struct is_random_access_iterator
{
  static constexpr bool value = is_same_v<
    typename iterator_traits<T>::iterator_category,
    random_access_iterator_tag
  >;
};
template <class T>
constexpr bool is_random_access_iterator_v = is_random_access_iterator<T>::value;

#define DEFAULT_COMP ranges::less

namespace internal
{
};

// https://github.com/miscalculation53/library/tree/wip/template/template_bit.hpp

template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }

inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); }

inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); }

inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); }
inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); }
inline constexpr ll popcount(ll x) { return std::popcount((ull)x); }
inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); }

inline constexpr ull lsb_pos(ull x) { assert(x != 0); return countr_zero(x); }
inline constexpr ull msb_pos(ull x) { assert(x != 0); return bit_width(x) - 1; }
inline constexpr ull lsb_mask(ull x) { assert(x != 0); return x & -x; }
inline constexpr ull msb_mask(ull x) { assert(x != 0); return bit_floor(x); }

inline constexpr bool btest(ull x, uint k) { return (x >> k) & 1; }
inline constexpr bool bsubset(ull x, ull y) { return (x & y) == x; }
inline constexpr bool bsupset(ull x, ull y) { return (x & y) == y; }
inline constexpr ull bsetminus(ull x, ull y) { return x & ~y; }

// https://github.com/miscalculation53/library/tree/wip/template/template_inout.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_dump.hpp

#if defined(LOCAL) && LIBRARY_HAS_FLOAT128
namespace cpp_dump::_detail
{
  struct export_command;
  inline string export_var(const f128 &, const string &, size_t,
                           size_t, bool, const export_command &);
}
#endif

// https://github.com/miscalculation53/library/tree/wip/template/template_dump_map.hpp

#define CPP_DUMP_DEFINE_DATA(...) 
#define dump(...) ((void)0)
#define local(...) 
#define oj(...) __VA_ARGS__
#define local_oj(a,b) (b)

#if LIBRARY_HAS_FLOAT128
inline istream &operator>>(istream &is, f128 &x)
{
  string s;
  if (is >> s)
  {
    f128 value;
    if (template_float128_detail::parse(s, value)) x = value;
    else is.setstate(ios::failbit);
  }
  return is;
}

inline ostream &operator<<(ostream &os, f128 x)
{
  const auto field = os.flags() & ios::floatfield;
  const auto format = field == ios::fixed ? chars_format::fixed :
                      field == ios::scientific ? chars_format::scientific : chars_format::general;
  string s = template_float128_detail::format(x, format, int(os.precision()));
  if ((os.flags() & ios::showpos) && !signbit(x)) s.insert(s.begin(), '+');
  if (os.flags() & ios::uppercase)
    for (char &c : s) c = char(toupper(static_cast<unsigned char>(c)));
  return os << s;
}
#endif

namespace fastio {
template <class T>
struct unsigned_integer
{
  using type = make_unsigned_t<T>;
};
template <>
struct unsigned_integer<bool>
{
  using type = uint;
};
template <>
struct unsigned_integer<i128>
{
  using type = u128;
};
template <>
struct unsigned_integer<u128>
{
  using type = u128;
};
template <class T>
using unsigned_integer_t = typename unsigned_integer<T>::type;

static constexpr uint32_t SIZ = 1 << 17;

char ibuf[SIZ + 1] = {'\x7f'};
char obuf[SIZ];
char out[100];

uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = char(n % 10 | '0');
        n /= 10;
      }
    }
  }
} constexpr pre;

[[gnu::noinline]] inline void load() {
  const uint32_t rest = pir - pil;
  if (rest && pil) memmove(ibuf, ibuf + pil, rest);
  pir = rest + uint32_t(fread(ibuf + rest, 1, SIZ - rest, stdin));
  pil = 0;
  ibuf[pir] = '\x7f';
}

inline void flush() {
  uint32_t written = 0;
  while (written < por) {
    const auto n = fwrite(obuf + written, 1, por - written, stdout);
    if (n == 0) abort();
    written += uint32_t(n);
  }
  por = 0;
}

inline void skip_space() {
  while (true) {
    while (static_cast<unsigned char>(ibuf[pil]) <= ' ') ++pil;
    if (pil < pir) return;
    load();
    if (pir == 0) abort();
  }
}

void rd1(char &c) {
  skip_space();
  c = ibuf[pil++];
}

void rd1(string &x) {
  x.clear();
  skip_space();
  while (true) {
    uint32_t p = pil;
    while (pil < pir && static_cast<unsigned char>(ibuf[pil]) > ' ') ++pil;
    x.append(ibuf + p, pil - p);
    if (pil < pir) {
      ++pil;
      return;
    }
    load();
    if (pir == 0) return;
  }
}

template <typename T>
void rd1_real(T &x) {
  string s;
  rd1(s);

  if constexpr (!is_same_v<T, long double>)
  {
    auto [p, ec] = from_chars(s.data(), s.data() + s.size(), x);
    if (ec == errc{} && p == s.data() + s.size()) return;
  }

  if constexpr (is_same_v<T, long double>)
    x = stold(s);
  else
    x = T(stod(s));
}

template <typename T>
inline void rd1_integer(T &x) {
  using U = unsigned_integer_t<T>;
  bool minus = false;
  U val = 0;
  skip_space();
  uint32_t p = pil;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (ibuf[p] == '-') minus = true, ++p;
  }
  if (ibuf[p] == '+') ++p;
  while (true) {

    if constexpr (sizeof(T) >= 4) {
      while (p + 8 <= pir) {
        uint64_t digits;
        memcpy(&digits, ibuf + p, 8);
        digits ^= 0x3030303030303030ULL;
        if (digits & 0xf0f0f0f0f0f0f0f0ULL) break;
        if ((digits + 0x0606060606060606ULL) & 0x1010101010101010ULL) break;
        digits = (digits * 10 + (digits >> 8)) & 0x00ff00ff00ff00ffULL;
        digits = (digits * 100 + (digits >> 16)) & 0x0000ffff0000ffffULL;
        val = U(val * 100000000 + uint(digits * 10000 + (digits >> 32)));
        p += 8;
      }
    }

    while (uint(ibuf[p] - '0') < 10) val = U(val * 10 + uint(ibuf[p++] - '0'));
    if (p < pir) break;
    pil = p;
    load();
    p = 0;
    if (pir == 0) break;
  }
  pil = p;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>)
  {
    if (minus)
    {
      const U min_abs = U(numeric_limits<T>::max()) + 1;
      x = val == min_abs ? numeric_limits<T>::lowest() : -T(val);
    }
    else x = T(val);
  }
  else
    x = T(val);
}

template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void rd1(T &x) { rd1_integer(x); }
void rd1(i128 &x) { rd1_integer(x); }
void rd1(u128 &x) { rd1_integer(x); }
void rd1(float &x) { rd1_real(x); }
void rd1(double &x) { rd1_real(x); }
void rd1(long double &x) { rd1_real(x); }
#if LIBRARY_HAS_FLOAT128
inline void rd1(f128 &x) {
  string s;
  rd1(s);
  if (!template_float128_detail::parse(s, x)) abort();
}
#endif

template <class... T>
void read(T &...x) {
  (rd1(x), ...);
}

void wt1(const char c) {
  if (por == SIZ) flush();
  obuf[por++] = c;
}
void wt1(string_view s) {
  while (!s.empty()) {
    if (por == SIZ) flush();
    size_t n = min<size_t>(s.size(), SIZ - por);
    memcpy(obuf + por, s.data(), n);
    por += uint32_t(n);
    s.remove_prefix(n);
  }
}

template <typename T>
void wt1_integer(T x) {
  if (por > SIZ - 100) flush();
  using U = unsigned_integer_t<T>;
  U ux;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>)
  {
    if (x < 0)
      obuf[por++] = '-', ux = U(U(0) - U(x));
    else
      ux = U(x);
  }
  else
    ux = x;
  uint parts[numeric_limits<U>::digits10 / 4 + 1];
  uint n = 0;
  if constexpr (sizeof(U) > 8) {
    while (ux > numeric_limits<ull>::max()) {
      ull part = ull(ux % 10000000000000000ULL);
      ux /= 10000000000000000ULL;
      for (int i = 0; i < 4; ++i) {
        parts[n++] = uint(part % 10000);
        part /= 10000;
      }
    }
  }
  auto value = static_cast<conditional_t<(sizeof(U) > 4), ull, uint>>(ux);
  while (value >= 10000) {
    parts[n++] = uint(value % 10000);
    value /= 10000;
  }
  const uint v = uint(value);
  if (v >= 1000) {
    memcpy(obuf + por, pre.num[v], 4);
    por += 4;
  } else if (v >= 100) {
    memcpy(obuf + por, pre.num[v] + 1, 3);
    por += 3;
  } else if (v >= 10) {
    memcpy(obuf + por, pre.num[v] + 2, 2);
    por += 2;
  } else
    obuf[por++] = char(v | '0');
  while (n) {
    memcpy(obuf + por, pre.num[parts[--n]], 4);
    por += 4;
  }
}

template <typename T>
void wt1_real(T x) {

  if constexpr (!is_same_v<T, long double>)
  {
    auto [p, ec] = to_chars(out, out + sizeof(out), x, chars_format::fixed, 15);
    if (ec == errc{}) {
      wt1(string_view(out, p));
      return;
    }
  }

  ostringstream oss;
  oss << fixed << setprecision(15) << x;
  wt1(oss.str());
}

void wt1(int x) { wt1_integer(x); }
template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void wt1(T x);
void wt1(i128 x) { wt1_integer(x); }
void wt1(u128 x) { wt1_integer(x); }
void wt1(double x) { wt1_real(x); }
void wt1(long double x) { wt1_real(x); }
#if LIBRARY_HAS_FLOAT128
inline void wt1(f128 x) {
  wt1(template_float128_detail::format(x, chars_format::fixed, 35));
}
#endif

template <class T, class U>
void wt1(const pair<T, U> &val);
template <class... T>
void wt1(const tuple<T...> &tpl);
template <class T, size_t S>
void wt1(const array<T, S> &val);
template <class T>
void wt1(const vector<T> &val);

template <class... T>
void write(T &&...x) {
  (wt1(std::forward<T>(x)), ...);
}

template <class... T>
void print(T &&...x) {
  if constexpr (sizeof...(T))
  {
    int i = 0;
    ((i++ ? wt1(' ') : void(), wt1(std::forward<T>(x))), ...);
  }
  wt1('\n');
}

} 

struct Dummy {
  Dummy() { atexit(fastio::flush); }
} dummy;

namespace internal
{

template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }

}; 

#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)

#define IN(T,...) T __VA_ARGS__; READ(__VA_ARGS__)

#define CHAR(...) IN(char, __VA_ARGS__)
#define INT(...) IN(int, __VA_ARGS__)
#define LL(...) IN(ll, __VA_ARGS__)
#define STR(...) IN(string, __VA_ARGS__)
#define ARR(T,n,...) array<T, n> __VA_ARGS__; READ(__VA_ARGS__)

#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define READVEC2(...) internal::READVEC2nodump(__VA_ARGS__); dump(__VA_ARGS__)

#define VEC(T,n,...) vc<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define VEC2(T,n,m,...) vvc<T> __VA_ARGS__; READVEC2(n, m, __VA_ARGS__)

#define READJAG(...) internal::READJAGnodump(__VA_ARGS__); dump(__VA_ARGS__)

#define JAG(T,n,...) vvc<T> __VA_ARGS__; READJAG(n, __VA_ARGS__)

#define ENDL '\n'

#define WRITE fastio::write
#define PRINT fastio::print

#define PRINTEXIT(...) do { PRINT(__VA_ARGS__); exit(0); } while (false)
#define PRINTRETURN(...) do { PRINT(__VA_ARGS__); return; } while (false)

#define PRINTVEXIT(...) do { PRINTV(__VA_ARGS__); exit(0); } while (false)
#define PRINTVRETURN(...) do { PRINTV(__VA_ARGS__); return; } while (false)

namespace internal
{

}; 

namespace internal
{

};

namespace internal
{

};

#define UNZIP(vt,...) auto [__VA_ARGS__] = unzip(vt)
#define ZIP(vt,...) auto vt = internal::zip_vectors(__VA_ARGS__)

// https://github.com/miscalculation53/library/tree/wip/template/template_random.hpp

mt19937_64 mt;

bool randbool(double p)
{
  assert(0 <= p && p <= 1);
  return bernoulli_distribution(p)(mt);
}

namespace internal
{
}; 

// https://github.com/miscalculation53/library/tree/wip/math/modint/template_modint.hpp

// https://github.com/miscalculation53/library/tree/wip/math/modint/modint.hpp

// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_static.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/larger_int.hpp

namespace larger_int_detail
{
}

template <class T>
struct larger_int
{
private:
  static constexpr bool check();
  static_assert(check());

public:
  using type = T;
};

#define LARGER_INT(T,U) template <> struct larger_int<T> { using type = U; };

LARGER_INT(signed char, short)
LARGER_INT(short, int)
LARGER_INT(int, long long)
LARGER_INT(long, __int128_t)
LARGER_INT(long long, __int128_t)

LARGER_INT(unsigned char, unsigned short)
LARGER_INT(unsigned short, unsigned int)
LARGER_INT(unsigned int, unsigned long long)
LARGER_INT(unsigned long, __uint128_t)
LARGER_INT(unsigned long long, __uint128_t)

#undef LARGER_INT

template <class T>
struct Rational;

template <class T>
struct larger_int<Rational<T>>
{
  using type = Rational<typename larger_int<T>::type>;
};

template <class T>
using larger_int_t = typename larger_int<T>::type;
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_isprime.hpp

namespace internal
{

template <class T>
constexpr ll powmod_constexpr(ll x, ll n, T m)
{
  if (m == 1)
    return 0;
  using U = make_unsigned_t<T>;
  using L = larger_int_t<U>;

  U r = 1, y = safemod(x, m);
  while (n)
  {
    if (n & 1)
      r = L(r) * y % m;
    y = L(y) * y % m;
    n >>= 1;
  }
  return r;
}

template <auto n>
constexpr bool isprime = isprime_constexpr(n);

};

namespace internal
{

template <auto M>
struct policy_static
{
  using mod_type = decltype(M);
  using value_type = make_unsigned_t<mod_type>;
  using calc_type = conditional_t<(M <= UINT_MAX), ull, larger_int_t<value_type>>;

  static constexpr bool is_prime = isprime_constexpr(M);

  static constexpr value_type init(value_type v) { return v; }
  static constexpr mod_type val(value_type v);
};

};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_barrett32.hpp

namespace internal
{

struct barrett32
{
  uint m = 0;
  ull im = 0;
  barrett32() = default;
  explicit barrett32(uint m) : m(m), im((ull)(-1) / m + 1) {}
  uint umod() const { return m; }
  uint mul(uint a, uint b) const
  {
    ull z = a;
    z *= b;
    ull x = ull((u128(z) * im) >> 64);
    ull y = x * m;
    return uint(z - y + (z < y ? m : 0));
  }
};

template <int id>
struct policy_barrett32
{
  using value_type = uint;
  using calc_type = ull;
  using mod_type = int;
  
  static constexpr bool is_prime = false;
  static inline barrett32 reducer{};
  static value_type init(value_type v) { return v; }
  static mod_type val(value_type v);
};

};

// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_montgomery64.hpp

namespace internal
{

inline constexpr ull inv64(ull a)
{
  ull x = a;
  while (a * x != 1) x *= 2 - a * x;
  return x;
}

struct montgomery64odd
{
  ull m = 0, im = 0, sq = 0;
  montgomery64odd() = default;
  explicit montgomery64odd(ull m) : m(m), im(inv64(m)), sq(-u128(m) % m) {}
  ull umod() const { return m; }
  ull reduce(u128 x) const
  {
    auto t = (x + u128(m) * (-im * ull(x))) >> 64;
    if (t >= m) t -= m;
    return (ull)t;
  }
  ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * sq); }
};

struct montgomery64
{
  ull m = 0, mx = 0, imx = 0, d = 0, q = 0;
  uint b = 0;
  montgomery64() = default;
  explicit montgomery64(ull m) : m(m)
  {
    b = countr_zero(m), mx = m >> b; 
    imx = inv64(mx);
    d = powmod_constexpr((mx + 1) / 2, b, mx); 
    u128 sq = -u128(mx) % mx; 
    q = (1 + (((sq - 1) * d) << b)) % m;
  }
  ull umod() const { return m; }
  ull reduce(u128 x) const
  {
    if (b == 0)
    {
      auto t = (x + u128(mx) * (-imx * ull(x))) >> 64;
      if (t >= m) t -= m;
      return (ull)t;
    }
    ull p = x & MASK(b); 
    x = (x >> b) + p * d;
    ull y = p << (64 - b);
    auto t = (x + u128(mx) * (imx * (y - ull(x)))) >> (64 - b);
    if (t >= m) { t -= m; if (t >= m) t -= m; }
    return (ull)t;
  }
  ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * q); }
};

template <int id>
struct policy_montgomery64_odd
{
  using value_type = ull;
  using calc_type = u128;
  using mod_type = ll;

  static constexpr bool is_prime = false;
  static inline montgomery64odd reducer{};
  static value_type init(value_type v) { return reducer.inv_reduce(v); }
  static mod_type val(value_type v);
};

template <int id>
struct policy_montgomery64
{
  using value_type = ull;
  using calc_type = u128;
  using mod_type = ll;

  static constexpr bool is_prime = false;
  static inline montgomery64 reducer{};
  static value_type init(value_type v) { return reducer.inv_reduce(v); }
  static mod_type val(value_type v);
};

};
// https://github.com/miscalculation53/library/tree/wip/math/extgcd.hpp

namespace internal
{

  template <class Policy, class PowInv = void>
  struct modint_impl
  {
    using V = typename Policy::value_type;
    using M = typename Policy::mod_type;
    using mint = modint_impl;

  private:
    V _v;

  public:

    modint_impl();

    template <class T, typename = enable_if_t<is_integral_ext<T>>>
    modint_impl(T v);

    M val() const;

    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._v == rhs._v; }
    friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
    friend M safe_hash_key(const mint &x) { return x.val(); }
  
    friend void rd1(mint &x)
    {
      long long a;
      fastio::rd1(a);
      x = a;
    }
    friend void wt1(const mint &x)
    {
      fastio::wt1(x.val());
    }

  };

};

template <int mod>
using static_modint32 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint32 = internal::modint_impl<internal::policy_barrett32<id>>;
template <ll mod>
using static_modint64 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint64_odd = internal::modint_impl<internal::policy_montgomery64_odd<id>>;
template <int id>
using dynamic_modint64 = internal::modint_impl<internal::policy_montgomery64<id>>;

using modint998244353 = static_modint32<998244353>;
using modint1000000007 = static_modint32<1000000007>;
using modint = dynamic_modint32<-1>;
using modint61 = static_modint64<(1LL << 61) - 1>;
using modint64 = dynamic_modint64<-1>;

template <class T>
struct is_modint : std::false_type
{
};
template <class Policy, class PowInv>
struct is_modint<internal::modint_impl<Policy, PowInv>> : std::true_type
{
};
template <class T>
inline constexpr bool is_modint_v = is_modint<T>::value;

template <class T>
struct is_static_modint : false_type {};
template <int m, class PowInv>
struct is_static_modint<internal::modint_impl<internal::policy_static<m>, PowInv>> : true_type {};
template <ll m, class PowInv>
struct is_static_modint<internal::modint_impl<internal::policy_static<m>, PowInv>> : true_type {};
template <class T>
inline constexpr bool is_static_modint_v = is_static_modint<T>::value;

template <class T>
struct is_dynamic_modint : false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint32<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64_odd<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64<id>> : true_type {};
template <class T>
inline constexpr bool is_dynamic_modint_v = is_dynamic_modint<T>::value;

template <typename, typename = void>
struct has_mod : std::false_type
{
};
template <typename T>
struct has_mod<T, std::void_t<decltype(T::mod())>> : std::true_type
{
};

template <class mint>
struct modint_less
{
};

template <class mint>
struct modint_hash
{
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/power_table.hpp

template <class mint>
struct PowerTable
{
private:
  decltype(mint::mod()) mod;
  mint base;
  vc<mint> pw;

public:

};
// https://github.com/miscalculation53/library/tree/wip/math/modint/binomial.hpp

template <class T>
struct Binomial
{
private:
  inline static decltype(T::mod()) mod;
  
public:
  inline static vc<T> fac_, finv_, inv_;

};
// https://github.com/miscalculation53/library/tree/wip/math/modint/stom.hpp

// https://github.com/miscalculation53/library/tree/wip/math/modint/to_rational.hpp

// https://github.com/miscalculation53/library/tree/wip/math/svp2d.hpp

namespace cpp_dump
{
  template <class T>
  struct rat_value
  {
    T p, q;

    friend ostream &operator<<(ostream &os, const rat_value &x)
    {
      os << x.p;
      if (x.q != 1)
        os << '/' << x.q;
      return os;
    }
  };

  struct mint_to_rat_fn
  {
  };

  template <class T>
  struct rat_object
  {
    T value;
  };

  template <class T>
  inline constexpr bool rat_is_map = false;
  template <class... Args>
  inline constexpr bool rat_is_map<std::map<Args...>> = true;
  template <class... Args>
  inline constexpr bool rat_is_map<std::multimap<Args...>> = true;
  template <class... Args>
  inline constexpr bool rat_is_map<std::unordered_map<Args...>> = true;
  template <class... Args>
  inline constexpr bool rat_is_map<std::unordered_multimap<Args...>> = true;

  struct rat_closure : std::ranges::range_adaptor_closure<rat_closure>
  {

  };

  constexpr rat_closure rat()
  {
    return rat_closure{};
  }
}

using mint = modint998244353;
// using mint = modint1000000007;
// using mint = static_modint<1000000000>;
// using mint = modint;
using bi = Binomial<mint>;

void init()
{
  oj(mt.seed(random_device()()));
}

void main2()
{
  LL(N, A, B, C);
  vvl ans(N, vl(N, -1));
  rep(i, N) rep(j, N)
  {
    if (ans[i][j] != -1)
      continue;

    if (B)
    {
      ans[i][j] = 2;
      B--;
      if (B == 0 && i != N - 1 && j != N - 1)
      {
        if (A >= 2)
        {
          ans[i + 1][j] = 1;
          ans[i][j + 1] = 1;
          A -= 2;
        }
        else
        {
          assert(C >= 2);
          ans[i + 1][j] = 3;
          ans[i][j + 1] = 3;
          C -= 2;
        }
      }
    }
    else
    {
      if (A)
        ans[i][j] = 1, A--;
      else
        ans[i][j] = 3, C--;
    }
  }
  fec(ansi : ans) PRINT(vtos(ansi, '0'));
}

void test()
{

}

// https://github.com/miscalculation53/library/tree/wip/template/template_main.hpp

template <auto init, auto main2, auto test>
struct Main
{
  Main()
  {
    cauto CERR = [](string val, string color)
    {
      string s = "\033[" + color + "m" + val + "\033[m";
      
    };
  
    CERR("\n[FAST_IO]\n\n", "32");
    
    cout << fixed << setprecision(20);
  
    init();
    
    CERR("\n[SINGLE_TESTCASE]\n\n", "36");
    main2();
  }
};
Main<init, main2, test> main_dummy;
int main() {}


// submit-code: hash=b93325e37421 source=b93325e37421a81050c671f4f06fc5b8073988b6e8aa004dafd5d8fe6d42a51f input=77e8317195bde342a9938cee3ccd4c0f58e64d04ad6ace1086719d620d58d8f1 body=416d1172d5116ee35607e7875efb94a5755141f47ee32088e5c634c0a872d478