#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 9;
string w;
int n, a, b, k;
int my_pow(int n, int k) {
  if (k == 0) return 1;
  int g = my_pow(n, k / 2);
  g = 1ll * g * g % mod;
  if (k & 1) g = 1ll * g * n % mod;
  return g;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> a >> b >> k;
  cin >> w;
  int ra = my_pow(a, mod - 2);
  ra = my_pow(ra, k);
  long long ans = 0;
  for (int i = 0; i < k; i++) {
    long long s = 1ll * my_pow(a, n - i) * my_pow(b, i) % mod;
    long long c = 1ll * ra * my_pow(b, k) % mod;
    int t = (n - i) / k + 1;
    if (c != 1)
      s = 1ll * s * (my_pow(c, t) - 1) % mod * my_pow(c - 1, mod - 2) % mod;
    else
      s = 1ll * s * t % mod;
    if (w[i] != '+') s = mod - s;
    ans += s;
    if (ans >= mod) ans -= mod;
  }
  cout << ans << "\n";
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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;
string w;
int n, a, b, k;
int my_pow(int n, int k) {
  if (k == 0) return 1;
  int g = my_pow(n, k / 2);
  g = 1ll * g * g % mod;
  if (k & 1) g = 1ll * g * n % mod;
  return g;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> a >> b >> k;
  cin >> w;
  int ra = my_pow(a, mod - 2);
  ra = my_pow(ra, k);
  long long ans = 0;
  for (int i = 0; i < k; i++) {
    long long s = 1ll * my_pow(a, n - i) * my_pow(b, i) % mod;
    long long c = 1ll * ra * my_pow(b, k) % mod;
    int t = (n - i) / k + 1;
    if (c != 1)
      s = 1ll * s * (my_pow(c, t) - 1) % mod * my_pow(c - 1, mod - 2) % mod;
    else
      s = 1ll * s * t % mod;
    if (w[i] != '+') s = mod - s;
    ans += s;
    if (ans >= mod) ans -= mod;
  }
  cout << ans << "\n";
  return 0;
}

```