#include <bits/stdc++.h>
using namespace std;
const int Mod = 1e9 + 9;
int Pow(int x, int e) {
  int ret = 1;
  while (e) {
    if (e & 1) ret = 1ll * ret * x % Mod;
    x = 1ll * x * x % Mod;
    e >>= 1;
  }
  return ret;
}
const int N = 1e5 + 10;
char S[N];
int main() {
  int n, a, b, k;
  scanf("%d%d%d%d%s", &n, &a, &b, &k, S);
  int ia = Pow(a, Mod - 2);
  int coe = Pow(a, n), ans = 0;
  for (int i = 0; i <= k - 1; i++) {
    ans = (ans + 1ll * (S[i] == '+' ? 1 : Mod - 1) * coe) % Mod;
    coe = 1ll * coe * ia % Mod * b % Mod;
  }
  int p = 1ll * Pow(ia, k) * Pow(b, k) % Mod;
  if (p == 1)
    ans = 1ll * ans * ((n + 1) / k) % Mod;
  else
    ans =
        1ll * ans * (Pow(p, (n + 1) / k) - 1) % Mod * Pow(p - 1, Mod - 2) % Mod;
  printf("%d\n", ans);
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 = 1e9 + 9;
int Pow(int x, int e) {
  int ret = 1;
  while (e) {
    if (e & 1) ret = 1ll * ret * x % Mod;
    x = 1ll * x * x % Mod;
    e >>= 1;
  }
  return ret;
}
const int N = 1e5 + 10;
char S[N];
int main() {
  int n, a, b, k;
  scanf("%d%d%d%d%s", &n, &a, &b, &k, S);
  int ia = Pow(a, Mod - 2);
  int coe = Pow(a, n), ans = 0;
  for (int i = 0; i <= k - 1; i++) {
    ans = (ans + 1ll * (S[i] == '+' ? 1 : Mod - 1) * coe) % Mod;
    coe = 1ll * coe * ia % Mod * b % Mod;
  }
  int p = 1ll * Pow(ia, k) * Pow(b, k) % Mod;
  if (p == 1)
    ans = 1ll * ans * ((n + 1) / k) % Mod;
  else
    ans =
        1ll * ans * (Pow(p, (n + 1) / k) - 1) % Mod * Pow(p - 1, Mod - 2) % Mod;
  printf("%d\n", ans);
  return 0;
}

```