#include <bits/stdc++.h>
using namespace std;
const int mod = (int)1e9 + 9;
long long fp(int n, int k) {
  if (k == 0) return 1;
  long long hf = fp(n, k / 2);
  return k % 2 ? hf * hf % mod * n % mod : hf * hf % mod;
}
int n, a, b, k;
long long invbda, x;
string str;
int main() {
  cin >> n >> a >> b >> k;
  getchar();
  getline(cin, str);
  long long sing = 0;
  invbda = 1LL * b * fp(a, mod - 2) % mod;
  long long now = fp(a, n);
  for (int i = 0; i < k; i++) {
    if (str[i] == '-') now = -now;
    sing = (((sing + now) % mod) + mod) % mod;
    if (str[i] == '-') now = -now;
    now *= invbda;
    now %= mod;
  }
  x = fp((int)invbda, k);
  int d = (n + 1) / k;
  long long res;
  if (x != 1)
    res =
        ((((sing * fp(x, d) % mod - sing) * fp(x - 1, mod - 2)) % mod) + mod) %
        mod;
  else
    res = sing * d % mod;
  cout << res;
}

### 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 int mod = (int)1e9 + 9;
long long fp(int n, int k) {
  if (k == 0) return 1;
  long long hf = fp(n, k / 2);
  return k % 2 ? hf * hf % mod * n % mod : hf * hf % mod;
}
int n, a, b, k;
long long invbda, x;
string str;
int main() {
  cin >> n >> a >> b >> k;
  getchar();
  getline(cin, str);
  long long sing = 0;
  invbda = 1LL * b * fp(a, mod - 2) % mod;
  long long now = fp(a, n);
  for (int i = 0; i < k; i++) {
    if (str[i] == '-') now = -now;
    sing = (((sing + now) % mod) + mod) % mod;
    if (str[i] == '-') now = -now;
    now *= invbda;
    now %= mod;
  }
  x = fp((int)invbda, k);
  int d = (n + 1) / k;
  long long res;
  if (x != 1)
    res =
        ((((sing * fp(x, d) % mod - sing) * fp(x - 1, mod - 2)) % mod) + mod) %
        mod;
  else
    res = sing * d % mod;
  cout << res;
}

```