#line 1 "/opt/library/template.hpp"
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using i64 = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'001'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
#define inf infty<ll>

using pi = pair<ll, ll>;
using vi = vector<ll>;
using vvi = vector<vector<ll>>;
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 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__))))

#define rep1(a) for (ll _ = 0; _ < (ll)(a); ++_)
#define rep2(i, a) for (ll i = 0; i < (ll)(a); ++i)
#define rep3(i, a, b) for (ll i = a; i < (ll)(b); ++i)
#define rep4(i, a, b, c) for (ll i = a; i < (ll)(b); i += (c))
#define rrep1(a) for (ll i = (a)-1; i >= (ll)(0); --i)
#define rrep2(i, a) for (ll i = (a)-1; i >= (ll)(0); --i)
#define rrep3(i, a, b) for (ll i = (b)-1; i >= (ll)(a); --i)
#define rrep4(i, a, b, c) for (ll i = (b)-1; i >= (ll)(a); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)

#define all(x) (x).begin(),(x).end()
#define len(x) (ll)(x.size())
#define elif else if
#define bit(x, i) (((x)>>(i))&1)

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

#define stoi stoll
#define abs llabs

#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()), x.shrink_to_fit()

ll popcnt(ll x) { return __builtin_popcountll(x); }
ll popcnt(u64 x) { return __builtin_popcountll(x); }
ll popcnt_mod_2(ll x) { return __builtin_parityll(x); }
ll popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
ll topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
ll topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
ll lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
ll lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

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

template <typename T>
T POP(queue<T> &que) {
  T a = que.front();
  que.pop();
  return a;
}
template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
f128 binary_search_real(F check, f128 ok, f128 ng, ll iter = 100) {
  rep(iter) {
    f128 x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  rep(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

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

// stable sort
template <typename T>
vi argsort(const vector<T> &A) {
  vi ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](ll i, ll j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vi &I) {
  vc<T> B(len(I));
  rep(i, len(I)) B[i] = A[I[i]];
  return B;
}

template<typename T> inline bool chmax(T &a, T b) {return ((a<b)?(a=b,true):(false));}
template<typename T> inline bool chmin(T &a, T b) {return ((a>b)?(a=b,true):(false));}

inline void wt(const char c) { cout << c; }
inline void wt(const string s) { cout << s; }
inline void wt(const char *s) { cout << s; }

template <typename T>
void wt_integer(T x) {
  cout << (x);
}
template <typename T>
void wt_real(T x) {
  cout << fixed << setprecision(15) << (long double)(x);
}
template <typename T>
void wt_integer128(T x) {
  char buf[64];
  char *d = end(buf);
  d--; *d = '\0';
  __uint128_t tmp = ((x < 0)? -x : x);
  do {
    d--; *d = char(tmp%10 + '0'); tmp /= 10;
  } while (tmp);
  if (x < 0) {
    d--; *d = '-';
  }
  cout << d;
}

inline void wt(int x) { wt_integer(x); }
inline void wt(ll x) { wt_integer(x); }
inline void wt(i128 x) { wt_integer128(x); }
inline void wt(u32 x) { wt_integer(x); }
inline void wt(u64 x) { wt_integer(x); }
inline void wt(u128 x) { wt_integer128(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 <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first); wt(' '); wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

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

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); }
void onez(bool t = 1) { print(t ? 1 : 0); }
#define endl '\n'
#define dump(x) {cerr << #x " = " << x << '\n';}
#line 2 "/opt/library/mod/modint_common.hpp"

struct has_mod_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};

template <typename mint>
mint inv(ll n) {
  static const ll mod = mint::get_mod();
  static vector<mint> dat = {0, 1};
  assert(0 <= n);
  if (n >= mod) n %= mod;
  while (len(dat) <= n) {
    ll k = len(dat);
    ll q = (mod + k - 1) / k;
    dat.eb(dat[k * q - mod] * mint::raw(q));
  }
  return dat[n];
}

template <typename mint>
mint fact(ll n) {
  static const ll mod = mint::get_mod();
  assert(0 <= n && n < mod);
  static vector<mint> dat = {1, 1};
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
  return dat[n];
}

template <typename mint>
mint fact_inv(ll n) {
  static vector<mint> dat = {1, 1};
  if (n < 0) return mint(0);
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
  return dat[n];
}

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

template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
  return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}

template <typename mint>
mint C_dense(ll n, ll k) {
  static vvc<mint> C;
  static ll H = 0, W = 0;
  auto calc = [&](ll i, ll 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) {
    rep(i, H) {
      C[i].resize(k + 1);
      rep(j, W, k + 1) { C[i][j] = calc(i, j); }
    }
    W = k + 1;
  }
  if (H <= n) {
    C.resize(n + 1);
    rep(i, H, n + 1) {
      C[i].resize(W);
      rep(j, W) { C[i][j] = calc(i, j); }
    }
    H = n + 1;
  }
  return C[n][k];
}

template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
  assert(n >= 0);
  if (k < 0 || n < k) return 0;
  if constexpr (dense) return C_dense<mint>(n, k);
  if constexpr (!large) return multinomial<mint>(n, k, n - k);
  k = min(k, n - k);
  mint x(1);
  rep(i, k) x *= mint(n - i);
  return x * fact_inv<mint>(k);
}

template <typename mint, bool large = false, bool dense = false>
mint H(ll n, ll k) {
  return C<mint, large, dense>(n+k-1, k);
}

template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
  assert(n >= 0);
  assert(0 <= k && k <= n);
  if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
  return mint(1) / C<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 C<mint, large, dense>(n + d - 1, d);
}
#line 3 "/opt/library/mod/modint.hpp"

template <ll mod>
struct modint {
  static constexpr u32 umod = u32(mod);
  static_assert(umod < u32(1) << 31);
  u32 val;

  static modint raw(u32 v) {
    modint x;
    x.val = v;
    return x;
  }
  constexpr modint() : val(0) {}
  constexpr modint(u32 x) : val(x % umod) {}
  constexpr modint(u64 x) : val(x % umod) {}
  constexpr modint(u128 x) : val(x % umod) {}
  constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
  bool operator<(const modint &other) const { return val < other.val; }
  modint &operator+=(const modint &p) {
    if ((val += p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator-=(const modint &p) {
    if ((val += umod - p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator*=(const modint &p) {
    val = u64(val) * p.val % umod;
    return *this;
  }
  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }
  modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
  modint operator+(const modint &p) const { return modint(*this) += p; }
  modint operator-(const modint &p) const { return modint(*this) -= p; }
  modint operator*(const modint &p) const { return modint(*this) *= p; }
  modint operator/(const modint &p) const { return modint(*this) /= p; }
  bool operator==(const modint &p) const { return val == p.val; }
  bool operator!=(const modint &p) const { return val != p.val; }
  modint inverse() const {
    ll a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint(u);
  }
  modint pow(ll n) const {
    assert(n >= 0);
    modint ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  static constexpr ll get_mod() { return mod; }
  // (n, r), r は 1 の 2^n 乗根
  static constexpr pair<ll, ll> ntt_info() {
    if (mod == 120586241) return {20, 74066978};
    if (mod == 167772161) return {25, 17};
    if (mod == 469762049) return {26, 30};
    if (mod == 754974721) return {24, 362};
    if (mod == 880803841) return {23, 211};
    if (mod == 943718401) return {22, 663003469};
    if (mod == 998244353) return {23, 31};
    if (mod == 1045430273) return {20, 363};
    if (mod == 1051721729) return {20, 330};
    if (mod == 1053818881) return {20, 2789};
    return {-1, -1};
  }
  static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};

template <ll mod>
void wt(modint<mod> x) {
  wt(x.val);
}

using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 1 "/opt/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};

ll factorial107(ll n) {
  constexpr ll mod = 1000000007;
  if (n >= mod) return 0;
  auto [q, r] = divmod<ll>(n, 1 << 20);
  ll x = factorial107table[q];
  ll s = q << 20;
  rep(i, r) x = x * (s + i + 1) % mod;
  return x;
}
#line 4 "main.cpp"
using mint = modint107;

int solve();
int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll T = 1;
  while (!solve()) if (--T == 0) break;
  return 0;
}

int solve() {
  ll N;
  cin >> N;
  vi c(10);
  rep(i, 1, 10) cin >> c[i];
  mint ans = 0;
  vc<mint> pow10(N);
  pow10[0] = 1;
  rep(i, 1, N) pow10[i] = pow10[i-1] * 10;
  mint fn = factorial107(N-1);
  vi f(10);
  rep(i, 1, 10) f[i] = factorial107(c[i]);
  rep(i, 1, 10) {
    if (c[i] == 0) continue;
    mint comb = fn;
    rep(j, 1, 10) comb /= (i == j) ? factorial107(c[j]-1) : f[j];
    rep(j, N) {
      ans += pow10[j] * i * comb;
    }
  }
  print(ans);
  return 0;
}