Problem: You are given two arrays a_0, a_1, …, a_{n - 1} and b_0, b_1, …, b_{m-1}, and an integer c.

Compute the following sum:

$$$∑_{i=0}^{n-1} ∑_{j=0}^{m-1} a_i b_j c^{i^2\,j^3}$$$

Since it's value can be really large, print it modulo 490019.

Input

First line contains three integers n, m and c (1 ≤ n, m ≤ 100 000, 1 ≤ c < 490019).

Next line contains exactly n integers a_i and defines the array a (0 ≤ a_i ≤ 1000).

Last line contains exactly m integers b_i and defines the array b (0 ≤ b_i ≤ 1000).

Output

Print one integer — value of the sum modulo 490019.

Examples

Input

2 2 3
0 1
0 1


Output

3


Input

3 4 1
1 1 1
1 1 1 1


Output

12


Input

2 3 3
1 2
3 4 5


Output

65652

Note

In the first example, the only non-zero summand corresponds to i = 1, j = 1 and is equal to 1 ⋅ 1 ⋅ 3^1 = 3.

In the second example, all summands are equal to 1.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
string to_string(string s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
const int md = 490019;
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }
  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }
  Modular& operator+=(const Modular& other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }
  Modular& operator-=(const Modular& other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }
  template <typename U>
  Modular& operator+=(const U& other) {
    return *this += Modular(other);
  }
  template <typename U>
  Modular& operator-=(const U& other) {
    return *this -= Modular(other);
  }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) *
                                     rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type&
  operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
  Modular inverse() const {
    Type a = value, b = mod(), u = 0, v = 1;
    while (a != 0) {
      Type t = b / a;
      b -= t * a;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    assert(b == 1);
    return Modular(u);
  }
  Modular& operator/=(const Modular& other) { return *this *= other.inverse(); }
  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
  template <typename U>
  friend std::istream& operator>>(std::istream& stream, Modular<U>& number);

 private:
  Type value;
};
template <typename T>
bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T>& lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) == rhs;
}
template <typename T>
bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T>& lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T>
Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T>
Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T>
Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T>
Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T>& lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T>& rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}
template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
  return stream << number();
}
template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
  stream >> number.value;
  number.value = Modular<T>::normalize(number.value);
  return stream;
}
struct VarMod {
  static int value;
};
int VarMod::value;
using Mint = Modular<std::integral_constant<int, md>>;
namespace fft {
struct num {
  double x, y;
  num() { x = y = 0; }
  num(double x_, double y_) : x(x_), y(y_) {}
};
inline num operator+(num a, num b) { return num(a.x + b.x, a.y + b.y); }
inline num operator-(num a, num b) { return num(a.x - b.x, a.y - b.y); }
inline num operator*(num a, num b) {
  return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
}
inline num conj(num a) { return num(a.x, -a.y); }
int base = 1;
vector<num> roots = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
const double PI = static_cast<double>(acosl(-1.0));
void ensure_base(int nbase) {
  if (nbase <= base) {
    return;
  }
  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) {
    double angle = 2 * PI / (1 << (base + 1));
    for (int i = 1 << (base - 1); i < (1 << base); i++) {
      roots[i << 1] = roots[i];
      double angle_i = angle * (2 * i + 1 - (1 << base));
      roots[(i << 1) + 1] = num(cos(angle_i), sin(angle_i));
    }
    base++;
  }
}
void fft(vector<num>& a, int n = -1) {
  if (n == -1) {
    n = (int)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++) {
        num z = a[i + j + k] * roots[j + k];
        a[i + j + k] = a[i + j] - z;
        a[i + j] = a[i + j] + z;
      }
    }
  }
}
vector<num> fa, fb;
vector<int64_t> square(const vector<int>& a) {
  if (a.empty()) {
    return {};
  }
  int need = (int)a.size() + (int)a.size() - 1;
  int nbase = 1;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if ((sz >> 1) > (int)fa.size()) {
    fa.resize(sz >> 1);
  }
  for (int i = 0; i < (sz >> 1); i++) {
    int x = (2 * i < (int)a.size() ? a[2 * i] : 0);
    int y = (2 * i + 1 < (int)a.size() ? a[2 * i + 1] : 0);
    fa[i] = num(x, y);
  }
  fft(fa, sz >> 1);
  num r(1.0 / (sz >> 1), 0.0);
  for (int i = 0; i <= (sz >> 2); i++) {
    int j = ((sz >> 1) - i) & ((sz >> 1) - 1);
    num fe = (fa[i] + conj(fa[j])) * num(0.5, 0);
    num fo = (fa[i] - conj(fa[j])) * num(0, -0.5);
    num aux = fe * fe + fo * fo * roots[(sz >> 1) + i] * roots[(sz >> 1) + i];
    num tmp = fe * fo;
    fa[i] = r * (conj(aux) + num(0, 2) * conj(tmp));
    fa[j] = r * (aux + num(0, 2) * tmp);
  }
  fft(fa, sz >> 1);
  vector<int64_t> res(need);
  for (int i = 0; i < need; i++) {
    res[i] = llround(i % 2 == 0 ? fa[i >> 1].x : fa[i >> 1].y);
  }
  return res;
}
vector<int64_t> multiply(const vector<int>& a, const vector<int>& b) {
  if (a.empty() || b.empty()) {
    return {};
  }
  if (a.size() == b.size() && a == b) {
    return square(a);
  }
  int need = (int)a.size() + (int)b.size() - 1;
  int nbase = 1;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) {
    fa.resize(sz);
  }
  for (int i = 0; i < sz; i++) {
    int x = (i < (int)a.size() ? a[i] : 0);
    int y = (i < (int)b.size() ? b[i] : 0);
    fa[i] = num(x, y);
  }
  fft(fa, sz);
  num r(0, -0.25 / (sz >> 1));
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num z = (fa[j] * fa[j] - conj(fa[i] * fa[i])) * r;
    fa[j] = (fa[i] * fa[i] - conj(fa[j] * fa[j])) * r;
    fa[i] = z;
  }
  for (int i = 0; i < (sz >> 1); i++) {
    num A0 = (fa[i] + fa[i + (sz >> 1)]) * num(0.5, 0);
    num A1 = (fa[i] - fa[i + (sz >> 1)]) * num(0.5, 0) * roots[(sz >> 1) + i];
    fa[i] = A0 + A1 * num(0, 1);
  }
  fft(fa, sz >> 1);
  vector<int64_t> res(need);
  for (int i = 0; i < need; i++) {
    res[i] = llround(i % 2 == 0 ? fa[i >> 1].x : fa[i >> 1].y);
  }
  return res;
}
vector<int> multiply_mod(const vector<int>& a, const vector<int>& b, int m) {
  if (a.empty() || b.empty()) {
    return {};
  }
  int eq = (a.size() == b.size() && a == b);
  int need = (int)a.size() + (int)b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) {
    fa.resize(sz);
  }
  for (int i = 0; i < (int)a.size(); i++) {
    int x = (a[i] % m + m) % m;
    fa[i] = num(x & ((1 << 15) - 1), x >> 15);
  }
  fill(fa.begin() + a.size(), fa.begin() + sz, num{0, 0});
  fft(fa, sz);
  if (sz > (int)fb.size()) {
    fb.resize(sz);
  }
  if (eq) {
    copy(fa.begin(), fa.begin() + sz, fb.begin());
  } else {
    for (int i = 0; i < (int)b.size(); i++) {
      int x = (b[i] % m + m) % m;
      fb[i] = num(x & ((1 << 15) - 1), x >> 15);
    }
    fill(fb.begin() + b.size(), fb.begin() + sz, num{0, 0});
    fft(fb, sz);
  }
  double ratio = 0.25 / sz;
  num r2(0, -1);
  num r3(ratio, 0);
  num r4(0, -ratio);
  num r5(0, 1);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num a1 = (fa[i] + conj(fa[j]));
    num a2 = (fa[i] - conj(fa[j])) * r2;
    num b1 = (fb[i] + conj(fb[j])) * r3;
    num b2 = (fb[i] - conj(fb[j])) * r4;
    if (i != j) {
      num c1 = (fa[j] + conj(fa[i]));
      num c2 = (fa[j] - conj(fa[i])) * r2;
      num d1 = (fb[j] + conj(fb[i])) * r3;
      num d2 = (fb[j] - conj(fb[i])) * r4;
      fa[i] = c1 * d1 + c2 * d2 * r5;
      fb[i] = c1 * d2 + c2 * d1;
    }
    fa[j] = a1 * b1 + a2 * b2 * r5;
    fb[j] = a1 * b2 + a2 * b1;
  }
  fft(fa, sz);
  fft(fb, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) {
    int64_t aa = llround(fa[i].x);
    int64_t bb = llround(fb[i].x);
    int64_t cc = llround(fa[i].y);
    res[i] = static_cast<int>((aa + ((bb % m) << 15) + ((cc % m) << 30)) % m);
  }
  return res;
}
}  // namespace fft
template <typename T>
typename enable_if<is_same<typename Modular<T>::Type, int>::value,
                   vector<Modular<T>>>::type
operator*(const vector<Modular<T>>& a, const vector<Modular<T>>& b) {
  if (a.empty() || b.empty()) {
    return {};
  }
  if (min(a.size(), b.size()) < 150) {
    vector<Modular<T>> c(a.size() + b.size() - 1, 0);
    for (int i = 0; i < (int)a.size(); i++) {
      for (int j = 0; j < (int)b.size(); j++) {
        c[i + j] += a[i] * b[j];
      }
    }
    return c;
  }
  vector<int> A(a.size());
  for (int i = 0; i < (int)A.size(); i++) {
    A[i] = static_cast<int>(a[i]);
  }
  vector<int> B(b.size());
  for (int i = 0; i < (int)B.size(); i++) {
    B[i] = static_cast<int>(b[i]);
  }
  vector<int> C = fft::multiply_mod(A, B, T::value);
  vector<Modular<T>> c(C.size());
  for (int i = 0; i < (int)C.size(); i++) {
    c[i] = C[i];
  }
  return c;
}
template <typename T>
typename enable_if<is_same<typename Modular<T>::Type, int>::value,
                   vector<Modular<T>>>::type&
operator*=(vector<Modular<T>>& a, const vector<Modular<T>>& b) {
  return a = a * b;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  Mint c;
  cin >> n >> m >> c;
  vector<Mint> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  vector<Mint> b(m);
  for (int i = 0; i < m; i++) {
    cin >> b[i];
  }
  vector<Mint> cpw(md - 1);
  cpw[0] = 1;
  for (int i = 1; i < (int)cpw.size(); i++) {
    cpw[i] = cpw[i - 1] * c;
  }
  vector<int> t2(n);
  for (int i = 0; i < n; i++) {
    t2[i] = (int)((int64_t)i * i % (md - 1));
  }
  vector<int> t3(m);
  for (int i = 0; i < m; i++) {
    t3[i] = (int)((int64_t)i * i * i % (md - 1));
  }
  vector<int> primes = {2, 491, 499};
  vector<int> gens = {1, 2, 7};
  Mint ans = 0;
  vector<vector<int>> pw(primes.size());
  vector<vector<int>> invpw(primes.size());
  for (int i = 0; i < (int)primes.size(); i++) {
    pw[i].resize(primes[i] - 1);
    pw[i][0] = 1;
    for (int j = 1; j < primes[i] - 1; j++) {
      pw[i][j] = pw[i][j - 1] * gens[i] % primes[i];
    }
    invpw[i].resize(primes[i]);
    invpw[i][0] = 0;
    for (int j = 0; j < primes[i] - 1; j++) {
      invpw[i][pw[i][j]] = j;
    }
  }
  vector<vector<vector<int>>> crt(
      primes[0], vector<vector<int>>(primes[1], vector<int>(primes[2], -1)));
  for (int i = 0; i < primes[0] * primes[1] * primes[2]; i++) {
    crt[i % primes[0]][i % primes[1]][i % primes[2]] = i;
  }
  vector<int> eq(3), neq(3);
  for (eq[0] = 0; eq[0] < 2; eq[0]++) {
    for (eq[1] = 0; eq[1] < 2; eq[1]++) {
      for (eq[2] = 0; eq[2] < 2; eq[2]++) {
        int sz = max(1, (eq[1] ? 1024 : 1) * (eq[2] ? 1024 : 1) / 2);
        vector<Mint> p(sz);
        for (int i = 0; i < n; i++) {
          if ((i % primes[0] > 0 || eq[0] == 0) &&
              (i % primes[1] > 0 || eq[1] == 0) &&
              (i % primes[2] > 0 || eq[2] == 0)) {
            p[(eq[1] == 0 ? 0
                          : invpw[1][t2[i] % primes[1]] << (eq[2] ? 10 : 0)) +
              (eq[2] == 0 ? 0 : invpw[2][t2[i] % primes[2]])] += a[i];
          }
        }
        vector<Mint> q(sz);
        for (int j = 0; j < m; j++) {
          if ((j % primes[0] > 0 || eq[0] == 0) &&
              (j % primes[1] > 0 || eq[1] == 0) &&
              (j % primes[2] > 0 || eq[2] == 0)) {
            q[(eq[1] == 0 ? 0
                          : invpw[1][t3[j] % primes[1]] << (eq[2] ? 10 : 0)) +
              (eq[2] == 0 ? 0 : invpw[2][t3[j] % primes[2]])] += b[j];
          }
        }
        vector<Mint> pq = p * q;
        for (int i = 0; i < (int)pq.size(); i++) {
          if (pq[i] != 0) {
            for (neq[0] = 0; neq[0] <= eq[0]; neq[0]++)
              for (neq[1] = 0; neq[1] <= eq[1]; neq[1]++)
                for (neq[2] = 0; neq[2] <= eq[2]; neq[2]++) {
                  int r0 = (neq[0] ? 1 : 0);
                  int r1 =
                      (neq[1] ? pw[1][(i >> (eq[2] ? 10 : 0)) % (primes[1] - 1)]
                              : 0);
                  int r2 = (neq[2] ? pw[2][(i & 1023) % (primes[2] - 1)] : 0);
                  int r = crt[r0][r1][r2];
                  42;
                  ans +=
                      pq[i] * cpw[r] *
                      ((neq[0] + neq[1] + neq[2] - eq[0] - eq[1] - eq[2]) % 2 ==
                               0
                           ? 1
                           : -1);
                }
          }
        }
      }
    }
  }
  cout << ans << '\n';
  return 0;
}