#include <bits/stdc++.h>
using namespace std;
template <typename T, typename S>
ostream &operator<<(ostream &os, const pair<T, S> &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <typename C, typename T = decay<decltype(*begin(declval<C>()))>,
          typename enable_if<!is_same<C, string>::value>::type * = nullptr>
ostream &operator<<(ostream &os, const C &c) {
  bool f = true;
  os << "[";
  for (const auto &x : c) {
    if (!f) os << ", ";
    f = false;
    os << x;
  }
  return os << "]";
}
template <typename T>
void debug(string s, T x) {
  cerr << s << " = " << x << "\n";
}
template <typename T, typename... Args>
void debug(string s, T x, Args... args) {
  for (int i = 0, b = 0; i < (int)s.size(); i++)
    if (s[i] == '(' || s[i] == '{')
      b++;
    else if (s[i] == ')' || s[i] == '}')
      b--;
    else if (s[i] == ',' && b == 0) {
      cerr << s.substr(0, i) << " = " << x << " | ";
      debug(s.substr(s.find_first_not_of(' ', i + 1)), args...);
      break;
    }
}
const int MOD = 1e9 + 9;
template <int MOD>
struct ModInt {
  long long v;
  ModInt(long long _v = 0) {
    v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
    if (v < 0) v += MOD;
  }
  ModInt &operator+=(const ModInt &other) {
    v += other.v;
    if (v >= MOD) v -= MOD;
    return *this;
  }
  ModInt &operator-=(const ModInt &other) {
    v -= other.v;
    if (v < 0) v += MOD;
    return *this;
  }
  ModInt &operator*=(const ModInt &other) {
    v = v * other.v % MOD;
    return *this;
  }
  ModInt &operator/=(const ModInt &other) { return *this *= inverse(other); }
  bool operator==(const ModInt &other) const { return v == other.v; }
  bool operator!=(const ModInt &other) const { return v != other.v; }
  friend ModInt operator+(ModInt a, const ModInt &b) { return a += b; }
  friend ModInt operator-(ModInt a, const ModInt &b) { return a -= b; }
  friend ModInt operator*(ModInt a, const ModInt &b) { return a *= b; }
  friend ModInt operator/(ModInt a, const ModInt &b) { return a /= b; }
  friend ModInt operator-(const ModInt &a) { return 0 - a; }
  friend ModInt power(ModInt a, long long b) {
    ModInt ret(1);
    while (b > 0) {
      if (b & 1) ret *= a;
      a *= a;
      b >>= 1;
    }
    return ret;
  }
  friend ModInt inverse(ModInt a) { return power(a, MOD - 2); }
  friend ostream &operator<<(ostream &os, const ModInt &m) { return os << m.v; }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, a, b, k;
  string s;
  cin >> n >> a >> b >> k >> s;
  auto geo = [&](ModInt<MOD> r, int len) -> ModInt<MOD> {
    return r == 1 ? len : (power(r, len) - 1) / (r - 1);
  };
  ModInt<MOD> first = 0;
  for (int i = 0; i < k; i++)
    first += (s[i] == '+' ? 1 : -1) * power(ModInt<MOD>(a), n - i) *
             power(ModInt<MOD>(b), i);
  cout << first * geo(power(ModInt<MOD>(b) / ModInt<MOD>(a), k), (n + 1) / k)
       << "\n";
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

You are given two integers a and b. Moreover, you are given a sequence s_0, s_1, ..., s_{n}. All values in s are integers 1 or -1. It's known that sequence is k-periodic and k divides n+1. In other words, for each k ≤ i ≤ n it's satisfied that s_{i} = s_{i - k}.

Find out the non-negative remainder of division of ∑ _{i=0}^{n} s_{i} a^{n - i} b^{i} by 10^{9} + 9.

Note that the modulo is unusual!

Input

The first line contains four integers n, a, b and k (1 ≤ n ≤ 10^{9}, 1 ≤ a, b ≤ 10^{9}, 1 ≤ k ≤ 10^{5}).

The second line contains a sequence of length k consisting of characters '+' and '-'. 

If the i-th character (0-indexed) is '+', then s_{i} = 1, otherwise s_{i} = -1.

Note that only the first k members of the sequence are given, the rest can be obtained using the periodicity property.

Output

Output a single integer — value of given expression modulo 10^{9} + 9.

Examples

Input

2 2 3 3
+-+


Output

7


Input

4 1 5 1
-


Output

999999228

Note

In the first example:

(∑ _{i=0}^{n} s_{i} a^{n - i} b^{i}) = 2^{2} 3^{0} - 2^{1} 3^{1} + 2^{0} 3^{2} = 7

In the second example:

(∑ _{i=0}^{n} s_{i} a^{n - i} b^{i}) = -1^{4} 5^{0} - 1^{3} 5^{1} - 1^{2} 5^{2} - 1^{1} 5^{3} - 1^{0} 5^{4} = -781 ≡ 999999228 \pmod{10^{9} + 9}.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T, typename S>
ostream &operator<<(ostream &os, const pair<T, S> &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <typename C, typename T = decay<decltype(*begin(declval<C>()))>,
          typename enable_if<!is_same<C, string>::value>::type * = nullptr>
ostream &operator<<(ostream &os, const C &c) {
  bool f = true;
  os << "[";
  for (const auto &x : c) {
    if (!f) os << ", ";
    f = false;
    os << x;
  }
  return os << "]";
}
template <typename T>
void debug(string s, T x) {
  cerr << s << " = " << x << "\n";
}
template <typename T, typename... Args>
void debug(string s, T x, Args... args) {
  for (int i = 0, b = 0; i < (int)s.size(); i++)
    if (s[i] == '(' || s[i] == '{')
      b++;
    else if (s[i] == ')' || s[i] == '}')
      b--;
    else if (s[i] == ',' && b == 0) {
      cerr << s.substr(0, i) << " = " << x << " | ";
      debug(s.substr(s.find_first_not_of(' ', i + 1)), args...);
      break;
    }
}
const int MOD = 1e9 + 9;
template <int MOD>
struct ModInt {
  long long v;
  ModInt(long long _v = 0) {
    v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
    if (v < 0) v += MOD;
  }
  ModInt &operator+=(const ModInt &other) {
    v += other.v;
    if (v >= MOD) v -= MOD;
    return *this;
  }
  ModInt &operator-=(const ModInt &other) {
    v -= other.v;
    if (v < 0) v += MOD;
    return *this;
  }
  ModInt &operator*=(const ModInt &other) {
    v = v * other.v % MOD;
    return *this;
  }
  ModInt &operator/=(const ModInt &other) { return *this *= inverse(other); }
  bool operator==(const ModInt &other) const { return v == other.v; }
  bool operator!=(const ModInt &other) const { return v != other.v; }
  friend ModInt operator+(ModInt a, const ModInt &b) { return a += b; }
  friend ModInt operator-(ModInt a, const ModInt &b) { return a -= b; }
  friend ModInt operator*(ModInt a, const ModInt &b) { return a *= b; }
  friend ModInt operator/(ModInt a, const ModInt &b) { return a /= b; }
  friend ModInt operator-(const ModInt &a) { return 0 - a; }
  friend ModInt power(ModInt a, long long b) {
    ModInt ret(1);
    while (b > 0) {
      if (b & 1) ret *= a;
      a *= a;
      b >>= 1;
    }
    return ret;
  }
  friend ModInt inverse(ModInt a) { return power(a, MOD - 2); }
  friend ostream &operator<<(ostream &os, const ModInt &m) { return os << m.v; }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, a, b, k;
  string s;
  cin >> n >> a >> b >> k >> s;
  auto geo = [&](ModInt<MOD> r, int len) -> ModInt<MOD> {
    return r == 1 ? len : (power(r, len) - 1) / (r - 1);
  };
  ModInt<MOD> first = 0;
  for (int i = 0; i < k; i++)
    first += (s[i] == '+' ? 1 : -1) * power(ModInt<MOD>(a), n - i) *
             power(ModInt<MOD>(b), i);
  cout << first * geo(power(ModInt<MOD>(b) / ModInt<MOD>(a), k), (n + 1) / k)
       << "\n";
  return 0;
}

```