#line 1 "/home/maspy/compro/library/my_template.hpp"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) \
  overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sum = 0;
  for (auto &&a: A) sum += a;
  return sum;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T pick(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}

template <typename T>
T pick(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}

template <typename T>
T pick(pqg<T> &que) {
  assert(que.size());
  T a = que.top();
  que.pop();
  return a;
}

template <typename T>
T pick(vc<T> &que) {
  assert(que.size());
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}

template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}

template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename F>
ll binary_search(F check, ll ok, ll ng) {
  assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return ok;
}

template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = S[i] - first_char; }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

template <typename CNT, typename T>
vc<CNT> bincount(const vc<T> &A, int size) {
  vc<CNT> C(size);
  for (auto &&x: A) { ++C[x]; }
  return C;
}

// stable
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(A.size());
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
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;
}
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace detail {
template <typename T, decltype(&T::is_modint) = &T::is_modint>
std::true_type check_value(int);
template <typename T>
std::false_type check_value(long);
} // namespace detail

template <typename T>
struct is_modint : decltype(detail::check_value<T>(0)) {};
template <typename T>
using is_modint_t = enable_if_t<is_modint<T>::value>;
template <typename T>
using is_not_modint_t = enable_if_t<!is_modint<T>::value>;

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <class T, is_modint_t<T> * = nullptr>
  bool read_single(T &ref) {
    long long val = 0;
    bool f = read_single(val);
    ref = T(val);
    return f;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <class A, class B, class C>
  bool read_single(tuple<A, B, C> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)));
  }
  template <class A, class B, class C, class D>
  bool read_single(tuple<A, B, C, D> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)) && read_single(get<3>(p)));
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char &val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string &s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double &x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double &x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <class T, is_modint_t<T> * = nullptr>
  void write(T &ref) {
    write(ref.val);
  }
  template <class T>
  void write(const vector<T> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> &val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <class A, class B, class C>
  void write(const tuple<A, B, C> &val) {
    auto &[a, b, c] = val;
    write(a), write(' '), write(b), write(' '), write(c);
  }
  template <class A, class B, class C, class D>
  void write(const tuple<A, B, C, D> &val) {
    auto &[a, b, c, d] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d);
  }
  template <class A, class B, class C, class D, class E>
  void write(const tuple<A, B, C, D, E> &val) {
    auto &[a, b, c, d, e] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);
  }
  template <class A, class B, class C, class D, class E, class F>
  void write(const tuple<A, B, C, D, E, F> &val) {
    auto &[a, b, c, d, e, f] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);
  }
  template <class T, size_t S>
  void write(const array<T, S> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if(val < 0){
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if(negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};

Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);

void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)      \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 1 "/home/maspy/compro/library/mod/factorial107.hpp"
// 1<<20
int factorial107table[1024] = {1,55098162,799018112,644524227,804570289,699421653,999080403,347644092,298264049,547915206,68604898,242165296,99769214,860919687,695517422,304751648,800304985,404296372,345504787,346396697,661521818,811907079,150066936,379369971,383295467,935785718,884263687,185573413,564595064,703180737,200891912,45268585,361946029,862561983,555223579,717470752,742784681,818749011,825255985,753131797,774984247,244818236,509057662,323909107,486700580,791867040,303567866,976227856,944323045,513842788,567328309,686789145,441779759,195814622,2372115,135277835,294954750,723496015,119271996,986547466,717213282,842873786,234208469,864111391,117175975,118474328,890000195,504224423,508111147,725796711,802878396,246336953,468479803,310148765,702396285,576460826,175957429,883569154,610938868,287010876,212131504,438039362,359800384,432795594,633410554,155137408,314936343,179257123,943713322,673162662,422288605,545194215,158939936,115503469,689488055,401702717,532814826,592763273,773200138,474494844,496413916,528795782,353056535,193856493,974131920,921613963,393169150,830738748,837700032,174096350,803328680,434966400,698398808,589644499,669724987,860591235,921625212,16363628,511768062,515388641,946983274,375285964,288822198,841563728,550332445,512378200,723231171,688050346,638916270,303773384,338440254,794857710,983752474,388318097,628785057,576616801,25029917,915971206,534292228,562759338,78040824,844961917,391581518,37735563,166114276,533068572,866703952,971782310,839681504,713554826,626185157,514984174,485251798,656102354,587843669,710027943,85325823,3718675,780721779,888259006,709912685,458901728,526677538,873562554,28552679,273046452,694930680,19258350,633408320,497294065,699279305,863781574,941853248,754504516,567820050,153017173,309672260,864251395,999648212,504204977,139941702,735693996,475650352,751284240,61380201,358232497,650878822,427480644,552589593,7500105,216677699,848980694,565479858,273508588,466692797,613411243,300912167,686394608,943827276,838125279,585515687,370926564,947737740,905550006,780384258,985335993,380437817,436417804,952004841,168955240,310513812,254079069,734838326,209059985,189848103,178192696,239063132,724829800,471021218,22656326,940110791,670514782,160800189,60164301,534784668,623973502,444037086,781751482,292944263,109226380,542920902,293050078,501265668,293547492,678045668,870103700,199000138,973807329,712358272,567141781,667220314,930560330,520238050,188798676,915219645,875218552,107463226,924068096,373354885,161687663,742633209,899649882,172223561,490032230,532248036,733461058,864357307,39004186,666796032,19300991,866949601,152723250,632980031,28154382,812475803,342290061,378814433,311792214,811932026,628385664,925729472,483891986,104909388,838245993,226415225,80497756,905742254,760776367,59951296,502463774,432422968,529614143,987845867,941009243,680208181,129640287,135701022,93697263,580002085,736790935,647149348,963929930,456358064,393498474,345303775,836988638,663009951,688270876,821556726,61653598,10436780,40516807,602622268,365808294,624854174,764883550,133418712,979879958,883675628,802594907,960259381,657818185,789571797,869941376,925271608,584915231,373203547,780879573,162303580,219381059,988122582,809692587,524697206,890686281,255441194,208655553,818176738,234316848,355059206,328134956,168206574,937157388,816978580,176422569,755437061,653448585,104372309,277493780,817870252,509736736,467977765,33347068,537441964,30292019,828581950,303478168,255296787,226318316,205744264,27632923,92186650,148892391,626052914,122285044,885244951,369494295,227491286,978201674,280638485,366898179,400916139,936093782,457514504,799178457,77262843,887662440,311502312,433979195,62200437,841399346,399849157,55933275,269778121,314076684,346937429,587781485,403077288,120051495,341462465,804288108,354008902,773347166,273225862,977284051,711403642,332515431,72546287,70463395,383292501,583203296,58684392,59801553,934861184,123659858,172225366,16490486,640104831,651484064,414057597,912563140,516388569,982284977,354948305,845441532,249139343,112170128,852836789,363141564,95948290,593351477,538225430,684921161,437291872,753187673,197482933,175217286,930569788,733325632,206283594,860092876,264612104,375479413,433058282,824726232,663285168,610355794,410260572,141034667,801620565,280447634,539012567,582334448,117111267,192909957,901437820,242191138,473245986,119617826,582524622,27271548,763258578,517785257,740102975,807353604,677357433,502074113,763360936,37227708,928062158,453067630,416392863,403468924,390966467,90780688,97580941,397618185,444801884,718494493,905625902,439144581,809645601,571259258,311262977,379698006,619843354,42160512,709478648,139908674,884941258,7778675,277356393,574397869,64807900,568439116,884254362,793527033,634827367,242270229,166836929,699666005,782871805,430576594,69423864,551852289,854389404,33130302,690600649,389114637,594444305,378027483,501626534,769371462,565727105,185366687,760889594,622679145,531967768,895838088,631099033,636979633,966288648,722632929,487185734,674289231,978197320,42219437,631006005,62801370,477869560,150370443,708309474,569052485,373979365,110651678,526192057,1187964,604094093,92402540,199407377,263950464,85094825,143055746,488295779,242448163,271952450,88191394,640214992,291887361,38760888,143069496,957354294,970267065,791944735,188497194,644438434,778147734,540003575,909162269,307294631,117326469,318009725,133188612,150701170,968756181,75908005,226593925,597645956,881933480,899459287,455981899,229221768,807672432,414097149,643328910,465859747,254429407,523184583,71216457,323329780,538880177,339599190,794248796,185173563,244936068,257855397,449978612,725702638,935779255,177430235,442849413,379319626,300751979,635487273,183449414,5934499,378785317,861919911,678817974,268409923,203403445,572871951,443809175,295389783,505988742,840133940,846932417,746139508,669216033,75861584,858480227,466369788,200782437,410124462,398817445,968382032,980738344,56008451,983178362,179562483,823724361,469703761,906401712,312400795,531915860,313966891,499155799,188116091,542673699,973727253,756116696,555496689,953139148,664729273,301347505,874894370,769419863,39619555,844221994,437468538,567165362,826223750,237919972,889742229,340395341,391452566,470281592,861327653,391319516,846903225,165819062,626164401,316709929,521538790,990712756,973874818,890738343,563978092,109958482,828180512,763297389,963971145,754096813,773609544,459522164,8038398,631562195,353217532,305814226,567542439,895416683,84833664,222068809,137353990,316612885,847273944,686340505,587953096,891163150,312873714,170456823,499030076,552288670,984000707,296655021,907848089,795824037,868241961,731318793,613986016,504817890,831254264,714194680,892153437,432990870,213690618,820549872,68492073,905288570,828076972,100771571,701929895,429147966,855717720,702005759,834355402,271364955,808645569,975796499,767810085,630847407,570582799,453848037,305413582,658578009,72025782,432456806,679768447,209753914,642309814,367985447,648596045,662634665,934081491,20395923,976333508,947778280,290901114,683388002,527020810,977326275,488693383,189698098,419374780,110616851,127872982,575257710,581134348,809887616,616715986,785224788,330000241,549806410,300312979,453241111,120873512,806993146,171910094,251834489,979979771,418698259,752813751,394025833,29105970,80840916,796020902,589114561,204474745,376387134,234987470,80775688,766942711,782094550,251204403,958598099,73582601,425563446,280068465,830973501,760007127,289646156,209940903,843351800,279527279,738627148,205145989,347868746,12854961,648847391,11192482,203518335,83599363,614624895,760355983,241204239,725553388,423530890,233709513,129164025,183143523,474024463,587482677,262947835,830758485,490545965,42715938,774365958,917430364,848838405,184884783,363325662,815621393,13287526,130498889,568838029,994918408,689158356,514272481,755554988,448513470,717322665,827827457,350229871,213613603,814952584,154931117,596054309,996378663,464177580,523761543,498980428,224645330,774166263,755880313,389249660,81743329,776397644,662396499,223245698,916069463,500419874,906869272,990436276,83413835,861165195,955992714,931625913,809913797,990584878,385913422,976567861,988873023,385236984,677028085,265052939,959365279,418677004,258798519,676383755,636025853,270238386,206316099,239739022,885152995,473139022,930824994,355594287,876223850,584874216,450993348,250278273,66731334,677818083,932165316,513087030,595832582,266493735,941688056,358758739,118809938,109331276,935297327,907221850,844856226,966689708,153251680,426805713,872205902,228749156,852770211,253065643,265234802,21716397,785998921,576621647,514060757,602374495,488838351,959753273,105481283,471659303,687019929,675067970,650147251,384820796,572532868,616933893,598368862,955007801,991174700,162133698,58160791,148888347,464964795,922938492,89012579,110574373,388391339,378503165,317247776,8038731,656691478,44251737,780947050,9218625,591467905,660897916,894672548,927151139,575483441,12732642,292282890,535590986,602061256,105810330,549519899,900104648,428472182,404847041,747230327,464453245,284822208,7040213,767161925,268629370,892069143,822121223,971455916,221846561,64553306,769796929,675275231,652246661,449517151,975374186,994429602,299117212,782066823,100306236,683957845,778001329,951091055,742690935,735367617,614080637,290990048,34499833,990980489,559407811,525864614,317820378,806036323,701425752,761690151,688462290,373529632,32050577,719463331,118313951,999322637,97750199,523426443,819087263,545301062,488598090,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};

int factorial107(ll n) {
  constexpr int mod = 1000000007;
  if (n >= mod) return 0;
  auto [q, r] = divmod(n, 1 << 20);
  ll x = factorial107table[q];
  int s = q << 20;
  FOR(i, r) x = x * (s + i + 1) % mod;
  return x;
}
#line 4 "main.cpp"

void solve() {
  LL(N);
  print(1);
  print(factorial107(N));
  print(N);
}

signed main() {
  cout << fixed << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}