Problem p03621 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using pii = pair<int, int>;
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U> void chmin(T &t, const U &u) {
  if (t > u)
    t = u;
}
template <class T, class U> void chmax(T &t, const U &u) {
  if (t < u)
    t = u;
}

template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}

template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
  os << "{";
  rep(i, v.size()) {
    if (i)
      os << ",";
    os << v[i];
  }
  os << "}";
  return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << H;
  debug_out(T...);
}
#define debug(...)                                                             \
  cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

template <unsigned int MOD> struct ModInt {
  using uint = unsigned int;
  using ull = unsigned long long;
  using M = ModInt;

  uint v;

  ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
  M &set_norm(uint _v) { //[0, MOD * 2)->[0, MOD)
    v = (_v < MOD) ? _v : _v - MOD;
    return *this;
  }

  explicit operator bool() const { return v != 0; }
  M operator+(const M &a) const { return M().set_norm(v + a.v); }
  M operator-(const M &a) const { return M().set_norm(v + MOD - a.v); }
  M operator*(const M &a) const { return M().set_norm(ull(v) * a.v % MOD); }
  M operator/(const M &a) const { return *this * a.inv(); }
  M &operator+=(const M &a) { return *this = *this + a; }
  M &operator-=(const M &a) { return *this = *this - a; }
  M &operator*=(const M &a) { return *this = *this * a; }
  M &operator/=(const M &a) { return *this = *this / a; }
  M operator-() const { return M() - *this; }
  M &operator++(int) { return *this = *this + 1; }
  M &operator--(int) { return *this = *this - 1; }

  M pow(ll n) const {
    if (n < 0)
      return inv().pow(-n);
    M x = *this, res = 1;
    while (n) {
      if (n & 1)
        res *= x;
      x *= x;
      n >>= 1;
    }
    return res;
  }

  M inv() const {
    ll a = v, b = MOD, p = 1, q = 0, t;
    while (b != 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(p -= t * q, q);
    }
    return M(p);
  }

  bool operator==(const M &a) const { return v == a.v; }
  bool operator!=(const M &a) const { return v != a.v; }
  friend ostream &operator<<(ostream &os, const M &a) { return os << a.v; }
  static uint get_mod() { return MOD; }
};

using Mint = ModInt<998244353>;

// depend on ModInt, must use NTT friendly mod

template <class D> struct NumberTheoreticTransform {
  D root;
  V<D> roots = {0, 1};
  V<int> rev = {0, 1};
  int base = 1, max_base = -1;

  void init() {
    int mod = D::get_mod();
    int tmp = mod - 1;
    max_base = 0;
    while (tmp % 2 == 0) {
      tmp /= 2;
      max_base++;
    }

    root = 2;

    while (true) {
      if (root.pow(1 << max_base).v == 1) {
        if (root.pow(1 << (max_base - 1)).v != 1) {
          break;
        }
      }
      root++;
    }
  }

  void ensure_base(int nbase) {
    if (max_base == -1)
      init();
    if (nbase <= base)
      return;
    assert(nbase <= max_base);

    rev.resize(1 << nbase);
    for (int i = 0; i < (1 << nbase); ++i) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    roots.resize(1 << nbase);

    while (base < nbase) {
      D z = root.pow(1 << (max_base - 1 - base));
      for (int i = 1 << (base - 1); i < (1 << base); ++i) {
        roots[i << 1] = roots[i];
        roots[(i << 1) + 1] = roots[i] * z;
      }
      ++base;
    }
  }

  void ntt(V<D> &a, bool inv = false) {
    int n = a.size();
    // assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;

    for (int i = 0; i < n; i++) {
      if (i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }

    for (int k = 1; k < n; k <<= 1) {
      for (int i = 0; i < n; i += 2 * k) {
        for (int j = 0; j < k; j++) {
          D x = a[i + j];
          D y = a[i + j + k] * roots[j + k];
          a[i + j] = x + y;
          a[i + j + k] = x - y;
        }
      }
    }

    int v = D(n).inv().v;
    if (inv) {
      reverse(a.begin() + 1, a.end());
      for (int i = 0; i < n; i++) {
        a[i] *= v;
      }
    }
  }

  V<D> mul(V<D> a, V<D> b) {
    int s = a.size() + b.size() - 1;
    int nbase = 1;
    while ((1 << nbase) < s)
      nbase++;
    int sz = 1 << nbase;
    a.resize(sz);
    b.resize(sz);
    ntt(a);
    ntt(b);

    for (int i = 0; i < sz; i++) {
      a[i] *= b[i];
    }
    ntt(a, true);

    a.resize(s);
    return a;
  }
};

// depends on FFT libs
// basically use with ModInt

NumberTheoreticTransform<Mint> ntt;

template <class D> struct Poly : public V<D> {
  template <class... Args> Poly(Args... args) : V<D>(args...) {}
  Poly(initializer_list<D> init) : V<D>(init.begin(), init.end()) {}

  int size() const { return V<D>::size(); }
  D at(int p) const { return (p < this->size() ? (*this)[p] : D(0)); }

  // first len terms
  Poly pref(int len) const {
    return Poly(this->begin(), this->begin() + min(this->size(), len));
  }

  // for polynomial division
  Poly rev() const {
    Poly res = *this;
    reverse(res.begin(), res.end());
    return res;
  }

  Poly operator+(const Poly &r) const {
    auto n = max(size(), r.size());
    V<D> tmp(n);
    for (int i = 0; i < n; ++i) {
      tmp[i] = at(i) + r.at(i);
    }
    return tmp;
  }
  Poly operator-(const Poly &r) const {
    auto n = max(size(), r.size());
    V<D> tmp(n);
    for (int i = 0; i < n; ++i) {
      tmp[i] = at(i) - r.at(i);
    }
    return tmp;
  }

  // scalar
  Poly operator*(const D &k) const {
    int n = size();
    V<D> tmp(n);
    for (int i = 0; i < n; ++i) {
      tmp[i] = at(i) * k;
    }
    return tmp;
  }

  Poly operator*(const Poly &r) const {
    Poly a = *this;
    Poly b = r;
    auto v = ntt.mul(a, b);
    return v;
  }

  // scalar
  Poly operator/(const D &k) const { return *this * k.inv(); }

  Poly operator/(const Poly &r) const {
    if (size() < r.size()) {
      return {{}};
    }
    int d = size() - r.size() + 1;
    return (rev().pref(d) * r.rev().inv(d)).pref(d).rev();
  }

  Poly operator%(const Poly &r) const {
    auto res = *this - *this / r * r;
    while (res.size() && !res.back()) {
      res.pop_back();
    }
    return res;
  }

  Poly diff() const {
    V<D> res(max(0, size() - 1));
    for (int i = 1; i < size(); ++i) {
      res[i - 1] = at(i) * i;
    }
    return res;
  }

  Poly inte() const {
    V<D> res(size() + 1);
    for (int i = 0; i < size(); ++i) {
      res[i + 1] = at(i) / (D)(i + 1);
    }
    return res;
  }

  // f * f.inv(m) === 1 mod (x^m)
  // f_0 ^ -1 must exist
  Poly inv(int m) const {
    Poly res = Poly({D(1) / at(0)});
    for (int i = 1; i < m; i *= 2) {
      res = (res * D(2) - res * res * pref(i * 2)).pref(i * 2);
    }
    return res.pref(m);
  }

  // f_0 = 1 must hold
  Poly log(int n) const {
    auto f = pref(n);
    return (f.diff() * f.inv(n - 1)).pref(n - 1).inte();
  }

  // f_0 = 0 must hold
  Poly exp(int n) const {
    auto h = diff();
    Poly f({1}), g({1});

    for (int m = 1; m < n; m *= 2) {
      g = (g * D(2) - f * g * g).pref(m);
      auto q = h.pref(m - 1);
      auto w = (q + g * (f.diff() - f * q)).pref(m * 2 - 1);
      f = (f + f * (*this - w.inte()).pref(m * 2)).pref(m * 2);
    }

    return f.pref(n);
  }

  // f_0 = 0 must hold?
  //**537
  Poly pow(int n, ll k) const { return (log(n) * (D)k).exp(n); }

  // f_0 = 1 must hold (use it with modular sqrt)
  // CF250E
  Poly sqrt(int n) const {
    Poly f = pref(n);
    Poly g({1});
    for (int i = 1; i < n; i *= 2) {
      g = (g + f.pref(i * 2) * g.inv(i * 2)) * D(2).inv();
    }
    return g.pref(n);
  }

  D eval(D x) const {
    D res = 0, c = 1;
    for (auto a : *this) {
      res += a * c;
      c *= x;
    }
    return res;
  }

  Poly &operator+=(const Poly &r) { return *this = *this + r; }
  Poly &operator-=(const Poly &r) { return *this = *this - r; }
  Poly &operator*=(const D &r) { return *this = *this * r; }
  Poly &operator*=(const Poly &r) { return *this = *this * r; }
  Poly &operator/=(const Poly &r) { return *this = *this / r; }
  Poly &operator/=(const D &r) { return *this = *this / r; }
  Poly &operator%=(const Poly &r) { return *this = *this % r; }

  friend ostream &operator<<(ostream &os, const Poly &pl) {
    if (pl.size() == 0)
      return os << "0";
    for (int i = 0; i < pl.size(); ++i) {
      if (pl[i]) {
        os << pl[i] << "x^" << i;
        if (i + 1 != pl.size())
          os << ",";
      }
    }
    return os;
  }
};

const int maxv = 100010;

V<Mint> fact(maxv), ifact(maxv), inv(maxv);

void init() {
  fact[0] = 1;
  for (int i = 1; i < maxv; ++i) {
    fact[i] = fact[i - 1] * i;
  }

  ifact[maxv - 1] = fact[maxv - 1].inv();

  for (int i = maxv - 2; i >= 0; --i) {
    ifact[i] = ifact[i + 1] * (i + 1);
  }

  for (int i = 1; i < maxv; ++i) {
    inv[i] = ifact[i] * fact[i - 1];
  }
}

Mint comb(int n, int r) {
  if (n < 0 || r < 0 || r > n)
    return Mint(0);
  return fact[n] * ifact[r] * ifact[n - r];
}

int main() {
  init();

  string A, B;
  cin >> A >> B;

  V<int> va, vb;
  int n = A.size();

  rep(i, n) {
    va.pb(A[i] - '0');
    vb.pb(B[i] - '0');
  }

  int path = 0, bt = 0;
  rep(i, n) {
    if (va[i] && !vb[i]) {
      path++;
    }
    if (va[i] && vb[i]) {
      bt++;
    }
  }

  ntt.init();
  Poly<Mint> pl(n + 1);
  for (int i = 0; i <= n; ++i) {
    pl[i] = ifact[i + 1];
  }
  pl = pl.pow(n, path);

  Mint ans;
  for (int i = 0; i <= bt; ++i) {
    ans += pl[i];
  }
  ans *= fact[path + bt] * fact[path] * fact[bt];
  cout << ans << endl;
  return 0;
}

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

using ll = long long;
using pii = pair<int, int>;
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U> void chmin(T &t, const U &u) {
  if (t > u)
    t = u;
}
template <class T, class U> void chmax(T &t, const U &u) {
  if (t < u)
    t = u;
}

template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}

template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
  os << "{";
  rep(i, v.size()) {
    if (i)
      os << ",";
    os << v[i];
  }
  os << "}";
  return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << H;
  debug_out(T...);
}
#define debug(...)                                                             \
  cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

template <unsigned int MOD> struct ModInt {
  using uint = unsigned int;
  using ull = unsigned long long;
  using M = ModInt;

  uint v;

  ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
  M &set_norm(uint _v) { //[0, MOD * 2)->[0, MOD)
    v = (_v < MOD) ? _v : _v - MOD;
    return *this;
  }

  explicit operator bool() const { return v != 0; }
  M operator+(const M &a) const { return M().set_norm(v + a.v); }
  M operator-(const M &a) const { return M().set_norm(v + MOD - a.v); }
  M operator*(const M &a) const { return M().set_norm(ull(v) * a.v % MOD); }
  M operator/(const M &a) const { return *this * a.inv(); }
  M &operator+=(const M &a) { return *this = *this + a; }
  M &operator-=(const M &a) { return *this = *this - a; }
  M &operator*=(const M &a) { return *this = *this * a; }
  M &operator/=(const M &a) { return *this = *this / a; }
  M operator-() const { return M() - *this; }
  M &operator++(int) { return *this = *this + 1; }
  M &operator--(int) { return *this = *this - 1; }

  M pow(ll n) const {
    if (n < 0)
      return inv().pow(-n);
    M x = *this, res = 1;
    while (n) {
      if (n & 1)
        res *= x;
      x *= x;
      n >>= 1;
    }
    return res;
  }

  M inv() const {
    ll a = v, b = MOD, p = 1, q = 0, t;
    while (b != 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(p -= t * q, q);
    }
    return M(p);
  }

  bool operator==(const M &a) const { return v == a.v; }
  bool operator!=(const M &a) const { return v != a.v; }
  friend ostream &operator<<(ostream &os, const M &a) { return os << a.v; }
  static uint get_mod() { return MOD; }
};

using Mint = ModInt<998244353>;

// depend on ModInt, must use NTT friendly mod

template <class D> struct NumberTheoreticTransform {
  D root;
  V<D> roots = {0, 1};
  V<int> rev = {0, 1};
  int base = 1, max_base = -1;

  void init() {
    int mod = D::get_mod();
    int tmp = mod - 1;
    max_base = 0;
    while (tmp % 2 == 0) {
      tmp /= 2;
      max_base++;
    }

    root = 2;

    while (true) {
      if (root.pow(1 << max_base).v == 1) {
        if (root.pow(1 << (max_base - 1)).v != 1) {
          break;
        }
      }
      root++;
    }
  }

  void ensure_base(int nbase) {
    if (max_base == -1)
      init();
    if (nbase <= base)
      return;
    assert(nbase <= max_base);

    rev.resize(1 << nbase);
    for (int i = 0; i < (1 << nbase); ++i) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    roots.resize(1 << nbase);

    while (base < nbase) {
      D z = root.pow(1 << (max_base - 1 - base));
      for (int i = 1 << (base - 1); i < (1 << base); ++i) {
        roots[i << 1] = roots[i];
        roots[(i << 1) + 1] = roots[i] * z;
      }
      ++base;
    }
  }

  void ntt(V<D> &a, bool inv = false) {
    int n = a.size();
    // assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;

    for (int i = 0; i < n; i++) {
      if (i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }

    for (int k = 1; k < n; k <<= 1) {
      for (int i = 0; i < n; i += 2 * k) {
        for (int j = 0; j < k; j++) {
          D x = a[i + j];
          D y = a[i + j + k] * roots[j + k];
          a[i + j] = x + y;
          a[i + j + k] = x - y;
        }
      }
    }

    int v = D(n).inv().v;
    if (inv) {
      reverse(a.begin() + 1, a.end());
      for (int i = 0; i < n; i++) {
        a[i] *= v;
      }
    }
  }

  V<D> mul(V<D> a, V<D> b) {
    int s = a.size() + b.size() - 1;
    int nbase = 1;
    while ((1 << nbase) < s)
      nbase++;
    int sz = 1 << nbase;
    a.resize(sz);
    b.resize(sz);
    ntt(a);
    ntt(b);

    for (int i = 0; i < sz; i++) {
      a[i] *= b[i];
    }
    ntt(a, true);

    a.resize(s);
    return a;
  }
};

// depends on FFT libs
// basically use with ModInt

NumberTheoreticTransform<Mint> ntt;

template <class D> struct Poly : public V<D> {
  template <class... Args> Poly(Args... args) : V<D>(args...) {}
  Poly(initializer_list<D> init) : V<D>(init.begin(), init.end()) {}

  int size() const { return V<D>::size(); }
  D at(int p) const { return (p < this->size() ? (*this)[p] : D(0)); }

  // first len terms
  Poly pref(int len) const {
    return Poly(this->begin(), this->begin() + min(this->size(), len));
  }

  // for polynomial division
  Poly rev() const {
    Poly res = *this;
    reverse(res.begin(), res.end());
    return res;
  }

  Poly operator+(const Poly &r) const {
    auto n = max(size(), r.size());
    V<D> tmp(n);
    for (int i = 0; i < n; ++i) {
      tmp[i] = at(i) + r.at(i);
    }
    return tmp;
  }
  Poly operator-(const Poly &r) const {
    auto n = max(size(), r.size());
    V<D> tmp(n);
    for (int i = 0; i < n; ++i) {
      tmp[i] = at(i) - r.at(i);
    }
    return tmp;
  }

  // scalar
  Poly operator*(const D &k) const {
    int n = size();
    V<D> tmp(n);
    for (int i = 0; i < n; ++i) {
      tmp[i] = at(i) * k;
    }
    return tmp;
  }

  Poly operator*(const Poly &r) const {
    Poly a = *this;
    Poly b = r;
    auto v = ntt.mul(a, b);
    return v;
  }

  // scalar
  Poly operator/(const D &k) const { return *this * k.inv(); }

  Poly operator/(const Poly &r) const {
    if (size() < r.size()) {
      return {{}};
    }
    int d = size() - r.size() + 1;
    return (rev().pref(d) * r.rev().inv(d)).pref(d).rev();
  }

  Poly operator%(const Poly &r) const {
    auto res = *this - *this / r * r;
    while (res.size() && !res.back()) {
      res.pop_back();
    }
    return res;
  }

  Poly diff() const {
    V<D> res(max(0, size() - 1));
    for (int i = 1; i < size(); ++i) {
      res[i - 1] = at(i) * i;
    }
    return res;
  }

  Poly inte() const {
    V<D> res(size() + 1);
    for (int i = 0; i < size(); ++i) {
      res[i + 1] = at(i) / (D)(i + 1);
    }
    return res;
  }

  // f * f.inv(m) === 1 mod (x^m)
  // f_0 ^ -1 must exist
  Poly inv(int m) const {
    Poly res = Poly({D(1) / at(0)});
    for (int i = 1; i < m; i *= 2) {
      res = (res * D(2) - res * res * pref(i * 2)).pref(i * 2);
    }
    return res.pref(m);
  }

  // f_0 = 1 must hold
  Poly log(int n) const {
    auto f = pref(n);
    return (f.diff() * f.inv(n - 1)).pref(n - 1).inte();
  }

  // f_0 = 0 must hold
  Poly exp(int n) const {
    auto h = diff();
    Poly f({1}), g({1});

    for (int m = 1; m < n; m *= 2) {
      g = (g * D(2) - f * g * g).pref(m);
      auto q = h.pref(m - 1);
      auto w = (q + g * (f.diff() - f * q)).pref(m * 2 - 1);
      f = (f + f * (*this - w.inte()).pref(m * 2)).pref(m * 2);
    }

    return f.pref(n);
  }

  // f_0 = 0 must hold?
  //**537
  Poly pow(int n, ll k) const { return (log(n) * (D)k).exp(n); }

  // f_0 = 1 must hold (use it with modular sqrt)
  // CF250E
  Poly sqrt(int n) const {
    Poly f = pref(n);
    Poly g({1});
    for (int i = 1; i < n; i *= 2) {
      g = (g + f.pref(i * 2) * g.inv(i * 2)) * D(2).inv();
    }
    return g.pref(n);
  }

  D eval(D x) const {
    D res = 0, c = 1;
    for (auto a : *this) {
      res += a * c;
      c *= x;
    }
    return res;
  }

  Poly &operator+=(const Poly &r) { return *this = *this + r; }
  Poly &operator-=(const Poly &r) { return *this = *this - r; }
  Poly &operator*=(const D &r) { return *this = *this * r; }
  Poly &operator*=(const Poly &r) { return *this = *this * r; }
  Poly &operator/=(const Poly &r) { return *this = *this / r; }
  Poly &operator/=(const D &r) { return *this = *this / r; }
  Poly &operator%=(const Poly &r) { return *this = *this % r; }

  friend ostream &operator<<(ostream &os, const Poly &pl) {
    if (pl.size() == 0)
      return os << "0";
    for (int i = 0; i < pl.size(); ++i) {
      if (pl[i]) {
        os << pl[i] << "x^" << i;
        if (i + 1 != pl.size())
          os << ",";
      }
    }
    return os;
  }
};

const int maxv = 100010;

V<Mint> fact(maxv), ifact(maxv), inv(maxv);

void init() {
  fact[0] = 1;
  for (int i = 1; i < maxv; ++i) {
    fact[i] = fact[i - 1] * i;
  }

  ifact[maxv - 1] = fact[maxv - 1].inv();

  for (int i = maxv - 2; i >= 0; --i) {
    ifact[i] = ifact[i + 1] * (i + 1);
  }

  for (int i = 1; i < maxv; ++i) {
    inv[i] = ifact[i] * fact[i - 1];
  }
}

Mint comb(int n, int r) {
  if (n < 0 || r < 0 || r > n)
    return Mint(0);
  return fact[n] * ifact[r] * ifact[n - r];
}

int main() {
  init();

  string A, B;
  cin >> A >> B;

  V<int> va, vb;
  int n = A.size();

  rep(i, n) {
    va.pb(A[i] - '0');
    vb.pb(B[i] - '0');
  }

  int path = 0, bt = 0;
  rep(i, n) {
    if (va[i] && !vb[i]) {
      path++;
    }
    if (va[i] && vb[i]) {
      bt++;
    }
  }

  ntt.init();
  Poly<Mint> pl(n + 1);

  if (path > 0) {
    for (int i = 0; i <= n; ++i) {
      pl[i] = ifact[i + 1];
    }
    pl = pl.pow(n, path);
  } else {
    pl[0] = 1;
  }

  Mint ans;
  for (int i = 0; i <= bt; ++i) {
    ans += pl[i];
  }
  ans *= fact[path + bt] * fact[path] * fact[bt];
  cout << ans << endl;
  return 0;
}