#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000009;
const long long INF = mod * mod;
const long double eps = 1e-12;
const long double pi = acos(-1.0);
long long mod_pow(long long a, long long n, long long m = mod) {
  long long res = 1;
  while (n) {
    if (n & 1) res = res * a % m;
    a = a * a % m;
    n >>= 1;
  }
  return res;
}
struct modint {
  long long n;
  modint() : n(0) { ; }
  modint(long long m) : n(m) {
    if (n >= mod)
      n %= mod;
    else if (n < 0)
      n = (n % mod + mod) % mod;
  }
  operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint &a, modint b) {
  a.n += b.n;
  if (a.n >= mod) a.n -= mod;
  return a;
}
modint operator-=(modint &a, modint b) {
  a.n -= b.n;
  if (a.n < 0) a.n += mod;
  return a;
}
modint operator*=(modint &a, modint b) {
  a.n = ((long long)a.n * b.n) % mod;
  return a;
}
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
  if (n == 0) return modint(1);
  modint res = (a * a) ^ (n / 2);
  if (n % 2) res = res * a;
  return res;
}
long long inv(long long a, long long p) {
  return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
const int max_n = 10000;
modint fact[max_n], factinv[max_n];
void init_f() {
  fact[0] = modint(1);
  for (int i = 0; i < max_n - 1; i++) {
    fact[i + 1] = fact[i] * modint(i + 1);
  }
  factinv[max_n - 1] = modint(1) / fact[max_n - 1];
  for (int i = max_n - 2; i >= 0; i--) {
    factinv[i] = factinv[i + 1] * modint(i + 1);
  }
}
modint comb(int a, int b) {
  if (a < 0 || b < 0 || a < b) return 0;
  return fact[a] * factinv[b] * factinv[a - b];
}
int dx[4] = {0, 1, 0, -1};
int dy[4] = {1, 0, -1, 0};
void solve() {
  int n, a, b, k;
  cin >> n >> a >> b >> k;
  string str;
  cin >> str;
  modint c = ((modint)b ^ k) / ((modint)a ^ k);
  if (c == (modint)1) {
    modint ans = 0;
    for (int i = 0; i < min(n + 1, k); i++) {
      int dif = n - i;
      int t = 1 + dif / k;
      modint s = mod_pow(a, n - i) * mod_pow(b, i);
      modint csum = (modint)t * s;
      if (str[i] == '+')
        ans += csum;
      else
        ans -= csum;
    }
    cout << ans << "\n";
    return;
  }
  modint bb = (modint)1 / ((modint)1 - c);
  modint ans = 0;
  for (int i = 0; i < min(n + 1, k); i++) {
    int dif = n - i;
    int t = 1 + dif / k;
    modint s = mod_pow(a, n - i) * mod_pow(b, i);
    modint csum = bb * s * ((modint)1 - (modint)mod_pow(c, t));
    if (str[i] == '+')
      ans += csum;
    else
      ans -= csum;
  }
  cout << ans << "\n";
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  solve();
  char nyaa;
  cin >> nyaa;
  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;
const long long mod = 1000000009;
const long long INF = mod * mod;
const long double eps = 1e-12;
const long double pi = acos(-1.0);
long long mod_pow(long long a, long long n, long long m = mod) {
  long long res = 1;
  while (n) {
    if (n & 1) res = res * a % m;
    a = a * a % m;
    n >>= 1;
  }
  return res;
}
struct modint {
  long long n;
  modint() : n(0) { ; }
  modint(long long m) : n(m) {
    if (n >= mod)
      n %= mod;
    else if (n < 0)
      n = (n % mod + mod) % mod;
  }
  operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint &a, modint b) {
  a.n += b.n;
  if (a.n >= mod) a.n -= mod;
  return a;
}
modint operator-=(modint &a, modint b) {
  a.n -= b.n;
  if (a.n < 0) a.n += mod;
  return a;
}
modint operator*=(modint &a, modint b) {
  a.n = ((long long)a.n * b.n) % mod;
  return a;
}
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
  if (n == 0) return modint(1);
  modint res = (a * a) ^ (n / 2);
  if (n % 2) res = res * a;
  return res;
}
long long inv(long long a, long long p) {
  return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
const int max_n = 10000;
modint fact[max_n], factinv[max_n];
void init_f() {
  fact[0] = modint(1);
  for (int i = 0; i < max_n - 1; i++) {
    fact[i + 1] = fact[i] * modint(i + 1);
  }
  factinv[max_n - 1] = modint(1) / fact[max_n - 1];
  for (int i = max_n - 2; i >= 0; i--) {
    factinv[i] = factinv[i + 1] * modint(i + 1);
  }
}
modint comb(int a, int b) {
  if (a < 0 || b < 0 || a < b) return 0;
  return fact[a] * factinv[b] * factinv[a - b];
}
int dx[4] = {0, 1, 0, -1};
int dy[4] = {1, 0, -1, 0};
void solve() {
  int n, a, b, k;
  cin >> n >> a >> b >> k;
  string str;
  cin >> str;
  modint c = ((modint)b ^ k) / ((modint)a ^ k);
  if (c == (modint)1) {
    modint ans = 0;
    for (int i = 0; i < min(n + 1, k); i++) {
      int dif = n - i;
      int t = 1 + dif / k;
      modint s = mod_pow(a, n - i) * mod_pow(b, i);
      modint csum = (modint)t * s;
      if (str[i] == '+')
        ans += csum;
      else
        ans -= csum;
    }
    cout << ans << "\n";
    return;
  }
  modint bb = (modint)1 / ((modint)1 - c);
  modint ans = 0;
  for (int i = 0; i < min(n + 1, k); i++) {
    int dif = n - i;
    int t = 1 + dif / k;
    modint s = mod_pow(a, n - i) * mod_pow(b, i);
    modint csum = bb * s * ((modint)1 - (modint)mod_pow(c, t));
    if (str[i] == '+')
      ans += csum;
    else
      ans -= csum;
  }
  cout << ans << "\n";
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  solve();
  char nyaa;
  cin >> nyaa;
  return 0;
}

```