#line 1 "No_142_\u5358\u306a\u308b\u914d\u5217\u306e\u64cd\u4f5c\u306b\u95a2\u3059\u308b\u5b9f\u88c5\u554f\u984c.cpp"
#define YRSD
#line 1 "YRS/aa/fast.hpp"
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")
#line 2 "YRS/all.hpp"

#line 2 "YRS/aa/head.hpp"

#include <iostream>
#include <algorithm>

#include <array>
#include <bitset>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <tuple>

#include <bit>
#include <chrono>
#include <functional>
#include <iomanip>
#include <utility>
#include <type_traits>
#include <cassert>
#include <cctype>
#include <cmath>
#include <cstring>
#include <ctime>
#include <limits>
#include <ranges>
#include <concepts>

#define TE template <typename T>
#define TES template <typename T, typename ...S>
#define Z auto
#define ep emplace_back
#define eb emplace
#define fi first
#define se second
#define all(x) (x).begin(), (x).end()

#define OV4(a, b, c, d, e, ...) e
#define FOR1(a) for (int _ = 0; _ < (a); ++_)
#define FOR2(i, a) for (int i = 0; i < (a); ++i)
#define FOR3(i, a, b) for (int i = (a); i < (b); ++i)
#define FOR4(i, a, b, c) for (int i = (a); i < (b); i += (c))
#define FOR(...) OV4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR1_R(a) for (int _ = (a) - 1; _ >= 0; --_)
#define FOR2_R(i, a) for (int i = (a) - 1; i >= 0; --i)
#define FOR3_R(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define FOR4_R(i, a, b, c) for (int i = (b) - 1; i >= (a); i -= (c))
#define FOR_R(...) OV4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) for (int t = (s); t > -1; t = (t == 0 ? -1 : (t - 1) & s))

#define sort ranges::sort

using namespace std;

TE using vc = vector<T>;
TE using vvc = vc<vc<T>>;
TE using T1 = tuple<T>;
TE using T2 = tuple<T, T>;
TE using T3 = tuple<T, T, T>;
TE using T4 = tuple<T, T, T, T>;
TE using max_heap = priority_queue<T>;
TE using min_heap = priority_queue<T, vc<T>, greater<T>>;
using u8 = unsigned char; using uint = unsigned int; using ll = long long;      using ull = unsigned long long;
using ld = long double;   using i128 = __int128;     using u128 = __uint128_t;  using f128 = __float128;
using u16 = uint16_t;
using PII = pair<int, int>;   using PLL = pair<ll, ll>;

#ifdef YRSD
constexpr bool dbg = 1;
#else
constexpr bool dbg = 0;
#endif
#line 2 "YRS/IO/IO.hpp"

istream &operator>>(istream &I, i128 &x) {
  static string s;
  I >> s;
  int f = s[0] == '-';
  x = 0;
  const int N = (int)s.size();
  FOR(i, f, N) x = x * 10 + s[i] - '0';
  if (f) x = -x;
  return I;
}
ostream &operator<<(ostream &O, i128 x) {
  static string s;
  s.clear();
  bool f = x < 0;
  if (f) x = -x;
  while (x) s += '0' + x % 10, x /= 10;
  if (s.empty()) s += '0';
  if (f) s += '-';
  reverse(all(s));
  return O << s;
}
istream &operator>>(istream &I, f128 &x) {
  static string s;
  I >> s, x = stold(s);
  return I;
}
ostream &operator<<(ostream &O, const f128 x) { return O << ld(x); }
template <typename... S>
istream &operator>>(istream &I, tuple<S...> &t) {
  return apply([&I](Z &...s) { ((I >> s), ...); }, t), I;
}
template <typename T, typename U>
istream &operator>>(istream &I, pair<T, U> &x) {
  return I >> x.fi >> x.se;
}
template <typename T, typename U>
ostream &operator<<(ostream &O, const pair<T, U> &x) {
  return O << x.fi << ' ' << x.se;
}
TE requires requires(T &c) { begin(c); end(c); } and 
                          (not is_same_v<decay_t<T>, string>)
istream &operator>>(istream &I, T &c) {
  for (Z &e : c) I >> e;
  return I;
}
TE requires requires(const T &c) { begin(c); end(c); } and 
  (not is_same_v<decay_t<T>, const char*>) and 
  (not is_same_v<decay_t<T>, string>) and 
  (not is_array_v<remove_reference_t<T>> or 
   not is_same_v<remove_extent_t<remove_reference_t<T>>, char>)
ostream &operator<<(ostream &O, const T &a) {
  if (a.empty()) return O;
  Z i = a.begin();
  O << *i++;
  for (; i != a.end(); ++i) O << ' ' << *i;
  return O;
}
void IN() {}
TE void IN(T &x, Z &...s) { cin >> x, IN(s...); }
void print() { cout << '\n'; }
TES void print(T &&x, S &&...y) {
  cout << x;
  if constexpr (sizeof...(S)) cout << ' ';
  print(forward<S>(y)...);
}
void put() { cout << ' '; }
TES void put(T &&x, S &&...y) {
  cout << x;
  if constexpr (sizeof...(S)) cout << ' ';
  put(forward<S>(y)...);
}

#define INT(...)  int    __VA_ARGS__; IN(__VA_ARGS__)
#define UINT(...) uint   __VA_ARGS__; IN(__VA_ARGS__)
#define LL(...)   ll     __VA_ARGS__; IN(__VA_ARGS__)
#define ULL(...)  ull    __VA_ARGS__; IN(__VA_ARGS__)
#define I128(...) i128   __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...)  string __VA_ARGS__; IN(__VA_ARGS__)
#define CH(...)   char   __VA_ARGS__; IN(__VA_ARGS__)
#define REAL(...) re     __VA_ARGS__; IN(__VA_ARGS__)
#define VEC(T, a, n) vc<T> a(n); IN(a)

void YES(bool o = 1) { print(o ? "YES" : "NO"); }
void Yes(bool o = 1) { print(o ? "Yes" : "No"); }
void yes(bool o = 1) { print(o ? "yes" : "no"); }
void NO(bool o = 1) { YES(not o); }
void No(bool o = 1) { Yes(not o); }
void no(bool o = 1) { yes(not o); }
void ALICE(bool o = 1) { print(o ? "ALICE" : "BOB"); }
void Alice(bool o = 1) { print(o ? "Alice" : "Bob"); }
void alice(bool o = 1) { print(o ? "alice" : "bob"); }
void BOB(bool o = 1) { ALICE(not o); }
void Bob(bool o = 1) { Alice(not o); }
void bob(bool o = 1) { alice(not o); }
void POSSIBLE(bool o = 1) { print(o ? "POSSIBLE" : "IMPOSSIBLE"); }
void Possible(bool o = 1) { print(o ? "Possible" : "Impossible"); }
void possible(bool o = 1) { print(o ? "possible" : "impossible"); }
void IMPOSSIBLE(bool o = 1) { POSSIBLE(not o); }
void Impossible(bool o = 1) { Possible(not o); }
void impossible(bool o = 1) { possible(not o); }
void TAK(bool o = 1) { print(o ? "TAK" : "NIE"); }
void NIE(bool o = 1) { TAK(not o); }
#line 5 "YRS/all.hpp"

#if (__cplusplus >= 202002L)
#include <numbers>
constexpr ld pi = numbers::pi;
#endif
TE constexpr T inf = numeric_limits<T>::max();
template <> constexpr i128 inf<i128> = i128(inf<ll>) * 2'000'000'000'000'000'000;
template <typename T, typename U>
constexpr pair<T, U> inf<pair<T, U>> = {inf<T>, inf<U>};

TE constexpr static inline int pc(T x) { return popcount(make_unsigned_t<T>(x)); }
constexpr static inline ll len(const Z &a) { return a.size(); }

void reverse(Z &a) { reverse(all(a)); }

void unique(Z &a) {
  sort(a);
  a.erase(unique(all(a)), a.end());
}
TE vc<int> inverse(const vc<T> &a) {
  int N = len(a);
  vc<int> b(N, -1);
  FOR(i, N) if (a[i] != -1) b[a[i]] = i;
  return b;
}

Z QMAX(const Z &a) { return *max_element(all(a)); }
Z QMIN(const Z &a) { return *min_element(all(a)); }
TE Z QMAX(T l, T r) { return *max_element(l, r); }
TE Z QMIN(T l, T r) { return *min_element(l, r); }
constexpr bool chmax(Z &a, const Z &b) { return (a < b ? a = b, 1 : 0); }
constexpr bool chmin(Z &a, const Z &b) { return (a > b ? a = b, 1 : 0); }

vc<int> argsort(const Z &a) {
  vc<int> I(len(a));
  iota(all(I), 0);
  sort(I, [&](int i, int k) { return a[i] < a[k] or (a[i] == a[k] and i < k); });
  return I;
}
TE vc<T> rearrange(const vc<T> &a, const vc<int> &I) {
  int N = len(I);
  vc<T> b(N);
  FOR(i, N) b[i] = a[I[i]];
  return b;
}
template <int of = 1, typename T> 
vc<T> pre_sum(const vc<T> &a) {
  int N = len(a);
  vc<T> c(N + 1);
  FOR(i, N) c[i + 1] = c[i] + a[i];
  if (of == 0) c.erase(c.begin());
  return c;
}

TE constexpr static int topbit(T x) {
  if (x == 0) return - 1;
  if constexpr (sizeof(T) <= 4) return 31 - __builtin_clz(x);
  else return 63 - __builtin_clzll(x);
}
TE constexpr static int lowbit(T x) {
  if (x == 0) return -1;
  if constexpr (sizeof(T) <= 4) return __builtin_ctz(x);
  else return __builtin_ctzll(x);
}

TE constexpr T floor(T x, T y) { return x / y - (x % y and (x ^ y) < 0); }
TE constexpr T ceil(T x, T y) { return floor(x + y - 1, y); }
TE constexpr T bmod(T x, T y) { return x - floor(x, y) * y; }
TE constexpr pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return pair{q, x - q * y};
}
template <typename T = ll>
T SUM(const Z &v) {
  return accumulate(all(v), T(0));
}
int lb(const Z &a, Z x) { return lower_bound(all(a), x) - a.begin(); }
TE int lb(T l, T r, Z x) { return lower_bound(l, r, x) - l; }
int ub(const Z &a, Z x) { return upper_bound(all(a), x) - a.begin(); }
TE int ub(T l, T r, Z x) { return upper_bound(l, r, x) - l; }

template <bool ck = 1>
ll bina(Z f, ll l, ll r) {
  if constexpr (ck) assert(f(l));
  while (abs(l - r) > 1) {
    ll x = (r + l) >> 1;
    (f(x) ? l : r) = x;
  }
  return l;
}
TE T bina_real(Z f, T l, T r, int c = 100) {
  while (c--) {
    T x = (l + r) / 2;
    (f(x) ? l : r) = x;
  }
  return (l + r) / 2;
}

Z pop(Z &s) {
  if constexpr (requires { s.pop_back(); }) {
    Z x = s.back();
    return s.pop_back(), x;
  } else if constexpr (requires { s.top(); }) {
    Z x = s.top();
    return s.pop(), x;
  } else {
    Z x = s.front();
    return s.pop(), x;
  }
}
void setp(int x) { cout << fixed << setprecision(x); }

TE inline void sh(vc<T> &a, int N, T b = {}) {
  a.resize(N, b);
}
#line 1 "YRS/debug.hpp"
#ifdef YRSD
void DBG() { cerr << "]" << endl; }
TES void DBG(T &&x, S &&...y) {
  cerr << x;
  if constexpr (sizeof...(S)) cerr << ", ";
  DBG(forward<S>(y)...);
}
#define debug(...) cerr << "[" << __LINE__ << "]: [" #__VA_ARGS__ "] = [", DBG(__VA_ARGS__)
void ERR() { cerr << endl; }
TES void ERR(T &&x, S &&...y) {
  cerr << x;
  if constexpr (sizeof...(S)) cerr << ", ";
  ERR(forward<S>(y)...);
}
#define err(...) cerr << "[" << __LINE__ << "]: ", ERR(__VA_ARGS__)
#define asser assert
#else
#define debug(...) void(0721)
#define err(...)   void(0721)
#define asser(...) void(0721)
#endif
#line 2 "YRS/IO/fast_io.hpp"

#define FIO

static constexpr uint SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint 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] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}
inline void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

inline void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

TE inline void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

TE inline void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') {
      minus = 1, c = ibuf[pil++];
    }
  }
  x = 0;
  while ('0' <= c) {
    x = x * 10 + (c & 15), c = ibuf[pil++];
  }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

inline void rd(int16_t &x) { rd_integer(x); }
inline void rd(uint16_t &x) { rd_integer(x); }
inline void rd(int &x) { rd_integer(x); }
inline void rd(long &x) { rd_integer(x); }
inline void rd(ll &x) { rd_integer(x); }
inline void rd(i128 &x) { rd_integer(x); }
inline void rd(uint &x) { rd_integer(x); }
inline void rd(ull &x) { rd_integer(x); }
inline void rd(u128 &x) { rd_integer(x); }
inline void rd(double &x) { rd_real(x); }
inline void rd(long double &x) { rd_real(x); }
inline void rd(f128 &x) { rd_real(x); }

template <typename T, typename U>
inline void rd(pair<T, U> &p) {
  return rd(p.fi), rd(p.se);
}
template <size_t N = 0, typename T>
inline void rd_tuple(T &t) {
  if constexpr (N < tuple_size<T>::value) {
    Z &x = get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <typename... T>
inline void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
inline void rd(array<T, N> &x) {
  for (Z &e : x) rd(e);
}
TE inline void rd(vc<T> &x) {
  for (Z &e : x) rd(e);
}

inline void read() {}
template <typename H, typename... T>
inline void read(H &h, T &...t) {
  rd(h), read(t...);
}

inline void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
inline void wt(const string s) {
  for (char c : s) wt(c);
}
inline void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

TE inline void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) {
    obuf[por++] = '-', x = -x;
  }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

TE inline void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(10) << double(x);
  string s = oss.str();
  wt(s);
}

inline void wt(int x) { wt_integer(x); }
inline void wt(long x) { wt_integer(x); }
inline void wt(ll x) { wt_integer(x); }
inline void wt(i128 x) { wt_integer(x); }
inline void wt(uint x) { wt_integer(x); }
inline void wt(ull x) { wt_integer(x); }
inline void wt(u128 x) { wt_integer(x); }
inline void wt(double x) { wt_real(x); }
inline void wt(long double x) { wt_real(x); }
inline void wt(f128 x) { wt_real(x); }

template <typename T, typename U>
inline void wt(const pair<T, U> &val) {
  wt(val.fi);
  wt(' ');
  wt(val.se);
}
template <size_t N = 0, typename T>
inline void wt_tuple(const T &t) {
  if constexpr (N < tuple_size<T>::value) {
    if constexpr (N > 0) {
      wt(' ');
    }
    const Z x = get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <typename... T>
inline void wt(tuple<T...> &tpl) {
  wt_tuple(tpl);
}
template <typename T, size_t S>
inline void wt(const array<T, S> &val) {
  Z n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
TE inline void wt(const vc<T> &a) {
  int N = len(a);
  FOR(i, N) {
    if (i) wt(' ');
    wt(a[i]);
  }
}
TE inline void wt(const vc<vc<T>> &v) {
  int N = len(v);
  FOR(i, N) {
    wt(v[i]);
    if (i + 1 != N) wt('\n');
  }
}
template <typename T, const size_t s>
inline void wt(const vc<array<T, s>> &v) {
  int N = len(v);
  FOR(i, N) {
    wt(v[i]);
    if (i + 1 != N) wt('\n');
  }
}

// gcc expansion. called automaticall after main.
inline void __attribute__((destructor)) _d() { flush(); }

inline void println() { wt('\n'); }
template <typename Head, typename... Tail>
inline void println(Head &&head, Tail &&...tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  println(forward<Tail>(tail)...);
}

#define IN(...) read(__VA_ARGS__)
#define print(...) println(__VA_ARGS__)
#define FLUSH() flush()
#line 6 "No_142_\u5358\u306a\u308b\u914d\u5217\u306e\u64cd\u4f5c\u306b\u95a2\u3059\u308b\u5b9f\u88c5\u554f\u984c.cpp"
// #include "YRS/random/rng.hpp"
// #include "YRS/ds/basic/retsu.hpp"
// #include "YRS/mod/mint.hpp"
#line 2 "YRS/mod/modint_d.hpp"

#line 2 "YRS/mod/barrett.hpp"

struct Barrett {
  uint m;
  ull im;
  explicit Barrett(uint m = 1) : m(m), im(ull(-1) / m + 1) {}
  uint modulo(ull z) const {
    if (m == 1) return 0;
    ull x = ull((u128(z) * im) >> 64);
    ull y = x * m;
    return (z - y + (z < y ? m : 0));
  }
  inline uint mul(uint a, uint b) const { return modulo(ull(a) * b); }
  uint pow(uint a, uint b) const {
    uint s = 1;
    for (; b; b >>= 1, a = mul(a, a)) {
      if (b & 1) s = mul(s, a);
    }
    return s - (s >= m ? m : 0);
  }
  ull floor(ull z) const {
    if (m == 1) return z;
    ull x = (ull)(((u128)z * im) >> 64);
    ull y = x * m;
    return (z < y ? x - 1 : x);
  }
  pair<ull, uint> divmod(ull z) const {
    if (m == 1) return {z, 0};
    ull x = ull((u128(z) * im) >> 64), y = x * m;
    if (z < y) return {x - 1, z - y + m};
    return {x, z - y};
  }
  uint umod() const { return m; }
};

struct Barrett_64 {
  u128 m, mh, ml;
  explicit Barrett_64(ull mod = 1) : m(mod) {
    u128 m = u128(-1) / mod;
    if (m * mod + mod == u128(0)) ++m;
    mh = m >> 64;
    ml = m & ull(-1);
  }
  ull modulo(u128 x) const {
    u128 z = (x & ull(-1)) * ml;
    z = (x & ull(-1)) * mh + (x >> 64) * ml + (z >> 64);
    z = (x >> 64) * mh + (z >> 64);
    x -= z * m;
    return x < m ? x : x - m;
  }
  ull mul(ull a, ull b) const { return modulo(u128(a) * b); }
  ull pow(ull a, ull b) const {
    ull s = 1;
    for (; b; b >>= 1, a = mul(a, a)) {
      if (b & 1) s = mul(s, a);
    }
    return s - (s >= m ? m : 0);
  }
  ull umod() const { return m; }
};
#line 2 "YRS/mod/modint_common.hpp"

TE concept is_mint = requires(T x) {
  { T::get_mod() };
  { T::gen(0ull) } -> same_as<T>;
  x.val;
};
TE concept has_const_mod =
    requires { integral_constant<int, (int)T::get_mod()> {}; };

TE static vc<T> &invs() {
  static vc<T> a{0, 1};
  return a;
}
TE static vc<T> &fac() {
  static vc<T> a{1, 1};
  return a;
}
TE static vc<T> &ifac() {
  static vc<T> a{1, 1};
  return a;
}

TE static int Set_inv(int N) {
  static vc<T> &inv = invs<T>();
  if (len(inv) >= N) return N;
  inv.resize(N + 1);
  inv[0] = 1, inv[1] = 1;
  FOR(i, 1, N) inv[i + 1] = inv[i] * i;
  T t = pop(inv).inv();
  FOR_R(i, N) inv[i] *= t, t *= i;
  return N;
}
TE static int Set_comb(int N) {
  static vc<T> &fa = fac<T>(), &ifa = ifac<T>();
  if (len(fa) >= N) return N;
  fa.resize(N);
  ifa.resize(N);
  FOR(i, 1, N) fa[i] = fa[i - 1] * i;
  ifa[N - 1] = fa[N - 1].inv();
  FOR_R(i, N - 1) ifa[i] = ifa[i + 1] * (i + 1);
  return N;
}

template <typename mint>
mint inv(int n) {
  static const int mod = mint::get_mod();
  static vc<mint> &a = invs<mint>();
  assert(0 <= n);
  while (len(a) <= n) {
    int k = len(a);
    int q = (mod + k - 1) / k;
    int r = k * q - mod;
    a.ep(a[r] * mint(q));
  }
  return a[n];
}
template <typename mint>
mint fact(int n) {
  static const int mod = mint::get_mod();
  static vc<mint> &a = fac<mint>();
  assert(0 <= n);
  if (n >= mod) return 0;
  while (len(a) <= n) {
    int k = len(a);
    a.ep(a[k - 1] * mint(k));
  }
  return a[n];
}

template <typename mint>
mint fact_inv(int n) {
  static vc<mint> &a = ifac<mint>();
  if (n < 0) return mint(0);
  while (len(a) <= n)
    a.ep(a[len(a) - 1] * inv<mint>(len(a)));
  return a[n];
}

template <typename mint, typename... Ts>
mint fact_invs(Ts... xs) {
  return (mint(1) * ... * fact_inv<mint>(xs));
}

template <typename mint, typename X, typename... S>
mint multinomial(X&& a, S&&... b) {
  return fact<mint>(a) * fact_invs<mint>(forward<S>(b)...);
}

template <typename mint>
mint C_dense(int n, int k) {
  assert(n >= 0);
  if (k < 0 or n < k) return 0;
  static vc<vc<mint>> C;
  static int H = 0, W = 0;
  Z calc = [&](int i, int j) -> mint {
    if (i == 0) return(j == 0 ? mint(1) : mint(0));
    return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
  };
  if (W <= k) {
    for (int i = 0; i < H; ++i) {
      C[i].resize(k + 1);
      for (int j = W; j < k + 1; ++j) {
        C[i][j] = calc(i, j);
      }
    }
    W = k + 1;
  }
  if (H <= n) {
    C.resize(n + 1);
    for (int i = H; i < n + 1; ++i) {
      C[i].resize(W);
      for (int j = 0; j < W; ++j) {
        C[i][j] = calc(i, j);
      }
    }
    H = n + 1;
  }
  return C[n][k];
}

template <typename mint>
mint C(int N, int K) {
  assert(N >= 0);
  if (K < 0 or N < K) return 0;
  return fact<mint>(N) * fact_inv<mint>(K) * fact_inv<mint>(N - K);
}

template <typename mint>
mint lucas(ll N, ll K) {
  static constexpr int P = mint::get_mod();
  if (K > N) return 0;
  if (K == 0) return 1;
  return C<mint>(N % P, K % P) * lucas<mint>(N / P, K / P);
}

template <typename mint, bool large = false, bool dense = false>
mint binom(ll n, ll k) {
  assert(n >= 0);
  if (k < 0 or n < k) return 0;
  if constexpr (dense) return C_dense<mint>(n, k);
  if constexpr (not large) return multinomial<mint>(n, k, n - k);
  k = min(k, n - k);
  mint x(1);
  FOR(i, k) x *= mint(n - i);
  return x * fact_inv<mint>(k);
}

template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
  assert(n >= 0);
  assert(0 <= k and k <= n);
  if (not large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
  return mint(1) / binom<mint, 1>(n, k);
}

// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
  assert(n >= 0);
  if (d < 0) return mint(0);
  if (n == 0) return (d == 0 ? mint(1) : mint(0));
  return binom<mint, large, dense>(n + d - 1, d);
}

#define CC C<mint>
#define fac fact<mint>
#define ifac fact_inv<mint>
#define set_comb Set_comb<mint>
#define set_inv Set_inv<mint>
#line 2 "YRS/mod/primitive_root.hpp"

#line 2 "YRS/random/rng.hpp"

#include <random>

#ifdef MeIoN
std::mt19937 rg(0);
std::mt19937_64 rd_64(0);
#else
std::mt19937 rg(std::chrono::steady_clock::now().time_since_epoch().count());
std::mt19937_64 rd_64(std::chrono::steady_clock::now().time_since_epoch().count());
#endif

uint rng() { return rg(); }
uint rng(uint lim) { return rg() % lim; }
int rng(int l, int r) { return l + rg() % (r - l); }
ull rng_64() { return rd_64(); }
ull rng_64(ull lim) { return rd_64() % lim; }
ll rng_64(ll l, ll r) { return l + rd_64() % (r - l); }

template <typename T>
void shuffle(vector<T> &v) {
  const int N = len(v);
  FOR(i, 1, N) {
    int k = rng(0, i + 1);
    if (i != k) swap(v[i], v[k]);
  }
}
#line 2 "YRS/pr/factors.hpp"

#line 2 "YRS/pr/ptest.hpp"

struct MM {
  using uu = unsigned __int128;
  inline static ull m, r, nn;
  static void set_mod(ull m) {
    MM::m = m;
    nn = -uu(m) % m;
    r = m;
    FOR(5) r *= 2 - m * r;
    r = -r;
  }
  static ull reduce(uu x) { return (x + uu(ull(x) * r) * m) >> 64; }

  ull x;
  MM() : x(0) {}
  MM(ull x) : x(reduce(uu(x) * nn)) {}
  ull val() const {
    ull y = reduce(x);
    return y >= m ? y - m : y;
  }
  MM &operator+=(MM y) {
    x += y.x - (m << 1);
    x = (ll(x) < 0 ? x + (m << 1) : x);
    return *this;
  }
  MM &operator-=(MM y) {
    x -= y.x;
    x = (ll(x) < 0 ? x + (m << 1) : x);
    return *this;
  }
  MM &operator*=(MM y) {
    x = reduce(uu(x) * y.x);
    return *this;
  }
  MM operator+(MM y) const { return MM(*this) += y; }
  MM operator-(MM y) const { return MM(*this) -= y; }
  MM operator*(MM y) const { return MM(*this) *= y; }
  bool operator==(MM y) const {
    return (x >= m ? x - m : x) == (y.x >= m ? y.x - m : y.x);
  }
  bool operator!=(MM y) const { return not operator==(y); }
  MM pow(ull k) const {
    MM r = 1, a = *this;
    for (; k; k >>= 1, a *= a) if (k & 1) r *= a;
    return r;
  }
};

bool ptest(const ull x) {
  if (x == 2 or x == 3 or x == 5 or x == 7) return 1;
  if (x % 2 == 0 or x % 3 == 0 or x % 5 == 0 or x % 7 == 0) return 0;
  if (x < 121) return x > 1;
  const ull d = (x - 1) >> __builtin_ctzll(x - 1);
  MM::set_mod(x);
  const MM o(1), mo(x - 1);
  Z f = [&](ull a) -> bool {
    MM y = MM(a).pow(d);
    ull t = d;
    while (y != o and y != mo and t != x - 1) y *= y, t <<= 1;
    if (y != mo and t % 2 == 0) return 1;
    return 0;
  };
  if (x < (1ull << 32)) {
    for (ull a : {2, 7, 61}) if (f(a)) return 0;
  } else {
    for (ull a : {2, 325, 9'375, 281'78, 450'775, 978'050'4, 179'526'502'2}) {
      if (x <= a) return 1;
      if (f(a)) return 0;
    }
  }
  return 1;
}
ll rho(ll n, ll c) {
  MM::set_mod(n);
  const MM cc(c);
  Z f = [&](MM x) { return x * x + cc; };
  MM x = 1, y = 2, z = 1, q = 1;
  ll g = 1;
  const ll m = 1ll << (__lg(n) / 5);
  for (ll r = 1; g == 1; r <<= 1) {
    x = y;
    FOR(r) y = f(y);
    for (ll k = 0; k < r and g == 1; k += m) {
      z = y;
      FOR(i, min(m, r - k)) y = f(y), q *= x - y;
      g = gcd(q.val(), n);
    }
  }
  if (g == n) do {
    z = f(z);
    g = gcd((x - z).val(), n);
  } while (g == 1);
  return g;
}
#line 5 "YRS/pr/factors.hpp"

// https://yukicoder.me/problems/no/36 => factor();

ll find_pr_e(ll x) {
  assert(x > 1);
  if (ptest(x)) return x;
  FOR(100) {
    ll e = rho(x, rng_64(x));
    if (ptest(e)) return e;
    x = e;
  }
  err("failed");
  assert(0);
}

vc<pair<ll, int>> factor(ll x) {
  assert(x >= 1);
  vc<pair<ll, int>> r;
  for (int e = 2; e < 100; ++e) {
    if (e * e > x) break;
    if (x % e == 0) {
      int c = 0;
      do {
        x /= e, c += 1;
      } while (x % e == 0);
      r.ep(e, c);
    }
  }
  while (x > 1) {
    ll e = find_pr_e(x);
    int c = 0;
    do {
      x /= e, c += 1;
    } while (x % e == 0);
    r.ep(e, c);
  }
  return sort(r), r;
}
vc<pair<ll, int>> factor_by_lpf(ll n, vc<int> &lpf) {
  vc<pair<ll, int>> s;
  while (n > 1) {
    int p = lpf[n], e = 0;
    while (n % p == 0) n /= p, ++e;
    s.ep(p, e);
  }
  return s;
}
#line 2 "YRS/mod/mod_pow.hpp"

#line 4 "YRS/mod/mod_pow.hpp"

uint mod_pow(int a, ll k, uint mod) {
  a %= mod;
  uint s = 1;
  Barrett X(mod);
  for (; k; k >>= 1, a = X.mul(a, a)) 
    if (k & 1) s = X.mul(s, a);
  return s;
}
template <uint mod>
uint mod_pow(ull a, ull k) {
  a %= mod;
  ull s = 1;
  for (; k; k >>= 1, a = a * a % mod)
    if (k & 1) s = s * a % mod;
  return s;
}
// a ^ (b ^ c) % mod
template <uint mod>
uint mod_pow_tri(ull a, ll b, ull c) {
  return a % mod == 0 ? 0 : mod_pow<mod>(a, mod_pow<mod - 1>(b, c));
}
ull mod_pow_64(ll a, ll k, ull mod) {
  a %= mod;
  ll s = 1;
  for (; k; k >>= 1, a = u128(a) * a % mod) 
    if (k & 1) s = u128(s) * a % mod;
  return s;
}
#line 6 "YRS/mod/primitive_root.hpp"

int primitive_root(int p) {
  Z pf = factor(p - 1);
  Z is_ok = [&](int g) -> bool {
    for (Z [q, e] : pf)
      if (mod_pow(g, (p - 1) / q, p) == 1) return 0;
    return 1;
  };
  while (1) {
    int x = rng(1, p);
    if (is_ok(x)) return x;
  }
  return -1;
}

ll primitive_root_64(ll p) {
  Z pf = factor(p - 1);
  Z is_ok = [&](ll g) -> bool {
    for (Z [q, e]: pf)
      if (mod_pow_64(g, (p - 1) / q, p) == 1) return 0;
    return 1;
  };
  while (1) {
    ll x = rng_64(1, p);
    if (is_ok(x)) return x;
  }
  return -1;
}
#line 6 "YRS/mod/modint_d.hpp"

template <int id>
struct dynamic_mint {
  static constexpr bool is_modint = true;
  using mint = dynamic_mint;
  uint x;
  static Barrett bt;
  static uint umod() { return bt.umod(); }

  static int get_mod() { return (int)bt.umod(); }
  static void set_mod(int m) {
    assert(1 <= m);
    bt = Barrett(m);
  }

  static mint gen(uint v) {
    mint x;
    x.x = v;
    return x;
  }
  dynamic_mint() : x(0) {}
  dynamic_mint(uint x) : x(bt.modulo(x)) {}
  dynamic_mint(ull x) : x(bt.modulo(x)) {}
  dynamic_mint(int x) : x((x %= get_mod()) < 0 ? x + get_mod() : x) {}
  dynamic_mint(ll x) : x((x %= get_mod()) < 0 ? x + get_mod() : x) {}
  dynamic_mint(i128 x) : x((x %= get_mod()) < 0 ? x + get_mod() : x) {};

  mint &operator+=(const mint &rhs) {
    x = (x += rhs.x) < umod() ? x : x - umod();
    return *this;
  }
  mint &operator-=(const mint &rhs) {
    x = (x += umod() - rhs.x) < umod() ? x : x - umod();
    return *this;
  }
  mint &operator*=(const mint &rhs) {
    x = bt.mul(x, rhs.x);
    return *this;
  }
  mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
  mint operator-() const { return mint() - *this; }
  friend istream& operator>>(istream& is, mint &p) {
    ll x;
    return is >> x, p = x, is;
  }
  friend ostream& operator<<(ostream& os, mint p) {
    return os << p.x;
  }
  uint val() const { return x; }
  mint pow(ll k) const {
    assert(0 <= k);
    mint x = *this, r = 1;
    while (k) {
      if (k & 1) r *= x;
      x *= x, k >>= 1;
    }
    return r;
  }
  mint inv() const {
    int x = val(), mod = get_mod(), a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return u < 0 ? u + mod : u;
  }

  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.val == rhs.val; }
  friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs.val != rhs.val; }
  static PII get_ntt() {
    static PII p = {-1, -1};
    return p;
  }
  static PII ntt_info() { return get_ntt(); }
  static constexpr bool can_ntt() { return 0; }
};

using dmint = dynamic_mint<-1>;
template <int id>
Barrett dynamic_mint<id>::bt;

#ifdef FIO
void rd(dmint &x) {
  LL(t);
  x = t;
}
void wt(dmint x) { wt(x.val()); }
#endif
#line 2 "YRS/ds/basic/bs.hpp"

// range xor (ofast 50% faster) https://yukicoder.me/problems/no/142

struct bs {
  int N;
  vc<ull> a;

  bs(int N = 0) : N(N), a((N + 63) >> 6) {};

  void set(int x, bool f) {
    if (f) set(x);
    else reset(x);
  }
  void set(int x) { a[x / 64] |= 1ull << (x & 63); }
  void set() { fill(all(a), -1ull); }
  void reset(int x) { a[x / 64] &= ~(1ull << (x & 63)); }
  void reset() { fill(all(a), 0); }
  void flip(int x) { a[x / 64] ^= 1ull << (x & 63); }
  void flip() {
    int sz = len(a) - 1;
    FOR(i, sz) a[i] = ~a[i];
    FOR(i, sz << 6, N) flip(i);
  }

  inline bool get(int x) const { return a[x / 64] >> (x & 63) & 1; }
  inline bool operator[](int x) const { return get(x); }

  int prev(int i) const {
    int k = i >> 6;
    if ((i & 63) < 63) {
      ull x = a[k];
      x &= (1ull << ((i & 63) + 1)) - 1;
      if (x) return k << 6 | topbit(x);
      --k;
    }
    FOR_R(i, k + 1) if (a[i]) return i << 6 | topbit(a[i]);
    return -1;
  }
  int next(int i) const {
    int k = i >> 6, s = i & 63;
    ull x = (a[k] >> s) << s;
    if (x) return k << 6 | lowbit(x);
    FOR(i, k + 1, (N + 63) >> 6) if (a[i]) return i << 6 | lowbit(a[i]);
    return N;
  }

  int _Find_first() const { return next(0); }
  int _Find_next(int i) const { return next(i + 1); } 

  void resize(int sz) {
    a.resize((sz + 63) >> 6);
    int r = sz & 63;
    if (r) a.back() &= (1ull << r) - 1;
    N = sz;
  }

  void range_set(int l, int r) {
    while (l < r and (l & 63)) set(l++);
    while (l < r and (r & 63)) set(--r);
    FOR(i, l >> 6, r >> 6) a[i] = -1ull;
  }
  void range_reset(int l, int r) {
    while (l < r and (l & 63)) reset(l++);
    while (l < r and (r & 63)) reset(--r);
    FOR(i, l >> 6, r >> 6) a[i] = 0;
  }
  void range_flip(int l, int r) {
    while (l < r and (l & 63)) flip(l++);
    while (l < r and (r & 63)) flip(--r);
    FOR(i, l >> 6, r >> 6) a[i] = ~a[i];
  }
  int range_count(int l, int r) const {
    int s = 0;
    while (l < r and (l & 63)) s += get(l++);
    while (l < r and (r & 63)) s += get(--r);
    FOR(i, l >> 6, r >> 6) s += pc(a[i]);
    return s;
  }

  void range_assign(int l, int r, bs p) {
    assert(p.N == r - l);
    int f = 0, t = r - l;
    while (l < r and (l & 63)) set(l++, p.get(f++));
    while (l < r and (r & 63)) set(--r, p.get(--t));
    l >>= 6, r >>= 6;
    int s = f >> 6, N = r - l, hi = f & 63, lo = 64 - hi;
    if (not(f & 63)) FOR(i, N) a[l + i] = p.a[s + i];
    else FOR(i, N) a[l + i] = (p.a[s + i] >> hi) | (p.a[s + i + 1] << lo);
  }
  void range_xor(int l, int r, bs p) {
    assert(p.N == r - l);
    int f = 0, t = r - l;
    while (l < r and (l & 63)) a[l >> 6] ^= ull(p.get(f)) << (l & 63), ++f, ++l;
    while (l < r and (r & 63)) --t, --r, a[r >> 6] ^= ull(p.get(t)) << (r & 63);
    l >>= 6, r >>= 6;
    int s = f >> 6, N = r - l, hi = f & 63, lo = 64 - hi;
    if (not(f & 63)) FOR(i, N) a[l + i] ^= p.a[s + i];
    else FOR(i, N) a[l + i] ^= (p.a[s + i] >> hi) | (p.a[s + i + 1] << lo);
  }
  void range_and(int l, int r, bs p) {
    assert(p.N == r - l);
    int f = 0, t = r - l;
    while (l < r and (l & 63)) {
      if (!p.get(f)) a[l >> 6] &= ~(1ull << (l & 63));
      ++f, ++l;
    }
    while (l < r and (r & 63)) {
      --t, --r;
      if (!p.get(t)) a[r >> 6] &= ~(1ull << (r & 63));
    }
    l >>= 6, r >>= 6;
    int s = f >> 6, N = r - l, hi = f & 63, lo = 64 - hi;
    if (not(f & 63)) FOR(i, N) a[l + i] &= p.a[s + i];
    else FOR(i, N) a[l + i] &= (p.a[s + i] >> hi) | (p.a[s + i + 1] << lo);
  }
  void range_or(int l, int r, bs p) {
    assert(p.N == r - l);
    int f = 0, t = r - l;
    while (l < r and (l & 63)) a[l >> 6] |= ull(p.get(f)) << (l & 63), ++f, ++l;
    while (l < r and (r & 63)) --t, --r, a[r >> 6] |= ull(p.get(t)) << (r & 63);
    l >>= 6, r >>= 6;
    int s = f >> 6, N = r - l, hi = f & 63, lo = 64 - hi;
    if (not(f & 63)) FOR(i, N) a[l + i] |= p.a[s + i];
    else FOR(i, N) a[l + i] |= (p.a[s + i] >> hi) | (p.a[s + i + 1] << lo);
  }

  int count() const {
    int N = len(a), s = 0;
    FOR(i, N) s += pc(a[i]);
    return s;
  }

  bs range(int l, int r) const {
    bs s(r - l);
    int rm = (r - l) & 63;
    while (rm--) s.set(r - l - 1, get(r - 1)), --r;
    int N = (r - l) >> 6, hi = l & 63, lo = 64 - hi, t = l >> 6;
    if (hi == 0) FOR(i, N) s.a[i] ^= a[t + i];
    else FOR(i, N) s.a[i] ^= (a[t + i] >> hi) ^ (a[t + i + 1] << lo);
    return s;
  }

  void moveL(int x) {
    if (not x) return;
    int sz = (N + 63) >> 6;
    FOR(i, sz - x) a[i] = a[i + x];
    FOR(i, max(0, sz - x), sz) a[i] = 0;
  }
  void moveR(int x) {
    if (not x) return;
    int sz = (N + 63) >> 6;
    FOR_R(i, x, sz) a[i] = a[i - x];
    FOR(i, min(x, sz)) a[i] = 0;
  }
  bs &operator<<=(int x) {
    if (x < 0) return *this >>= -x;
    moveR(x >> 6);
    x &= 63;
    ull s = 0, ls = 0, ps = 64 - x;
    FOR(i, 1, x + 1) s |= 1ull << (64 - i);
    int sz = (N + 63) >> 6;
    FOR(i, sz) {
      ull c = (a[i] & s) >> ps;
      a[i] <<= x, a[i] |= ls, ls = c;
    }
    return resize(N), *this;
  }
  bs &operator>>=(int x) {
    if (x < 0) return *this <<= -x;
    moveL(x >> 6);
    x &= 63;
    ull s = (1ull << x) - 1, ls = 0, ps = 64 - x;
    int sz = (N + 63) >> 6;
    FOR_R(i, sz) {
      ull ss = (a[i] & s) << ps;
      a[i] >>= x, a[i] |= ls, ls = ss;
    }
    return *this;
  }
  bs operator<<(int x) const { return bs(*this) <<= x; };
  bs operator>>(int x) const { return bs(*this) >>= x; };

  void AND(const bs &p) {
    int sz = (N + 63) >> 6;
    FOR(i, sz) a[i] &= p.a[i];
  }
  void OR(const bs &p) {
    int sz = (N + 63) >> 6;
    FOR(i, sz) a[i] |= p.a[i];
  }
  void XOR(const bs &p) {
    int sz = (N + 63) >> 6;
    FOR(i, sz) a[i] ^= p.a[i];
  }
  bs operator&=(const bs &p) { return AND(p), *this; }
  bs operator&(const bs &p) { return bs(*this) &= p; }
  bs operator|=(const bs &p) { return OR(p), *this; }
  bs operator|(const bs &p) { return bs(*this) |= p; }
  bs operator^=(const bs &p) { return XOR(p), *this; }
  bs operator^(const bs &p) { return bs(*this) ^= p; }
  bs operator~() const {
    bs r = *this;
    return r.flip(), r;
  }

  string to_s() const {
    string s;
    FOR(i, N) s += '0' + get(i);
    return s;
  }
};
#line 11 "No_142_\u5358\u306a\u308b\u914d\u5217\u306e\u64cd\u4f5c\u306b\u95a2\u3059\u308b\u5b9f\u88c5\u554f\u984c.cpp"

using mint = dmint;
void Yorisou() {
  INT(N, s, x, y, z);
  dmint::set_mod(z);
  bs bit(N);
  if (s & 1) bit.set(0);
  mint g = s;
  FOR(i, 1, N) {
    g = g * x + y;
    if (g.val() & 1) bit.set(i);
  }
  
  INT(Q);
  FOR(Q) {
    INT(a, b, c, d);
    --a, --c;
    bit.range_xor(c, d, bit.range(a, b));
  }
  string ans = bit.to_s();
  for (char &c : ans) c = c == '0' ? 'E' : 'O';
  print(ans);
}
constexpr int tests = 0, fl = 0, DB = 10;
#line 1 "YRS/aa/main.hpp"
int main() {
  cin.tie(nullptr)->sync_with_stdio(0);
  int T = 1;
  if (fl) cerr.tie(0);
  if (tests and not fl) IN(T);
  for (int i = 0; i < T or fl; ++i) {
    Yorisou();
    if (fl and i % DB == 0) cerr << "Case: " << i << '\n';
  }
  return 0;
}
#line 36 "No_142_\u5358\u306a\u308b\u914d\u5217\u306e\u64cd\u4f5c\u306b\u95a2\u3059\u308b\u5b9f\u88c5\u554f\u984c.cpp"