#include <bits/stdc++.h>
using namespace std;
long long n, a, b, k, sum, cnt, m;
char s[100007];
const long long mod = 1e9 + 9;
long long po(long long x, long long y) {
  if (y == 0) return 1;
  long long temp;
  temp = po(x, y / 2);
  if (y % 2 == 0)
    return (temp * temp) % mod;
  else
    return (((temp * temp) % mod) * x) % mod;
}
int main() {
  cin >> n >> a >> b >> k;
  for (int i = 0; i < k; i++) cin >> s[i];
  m = (n + 1) / k;
  cnt = 0;
  for (int i = 0; i < k; i++) {
    if (s[i] == '+')
      cnt = (cnt + po(a, n - i) * po(b, i) % mod) % mod;
    else
      cnt = (cnt - po(a, n - i) * po(b, i) % mod + mod) % mod;
  }
  {
    sum = (po(b, k) * po(po(a, mod - 2) % mod, k)) % mod;
    if (sum == 1)
      sum = m;
    else
      sum = (po(sum, m) - 1 + mod) * po(sum - 1, mod - 2) % mod;
    sum %= mod;
  }
  sum = sum * cnt;
  sum += mod;
  sum %= mod;
  cout << sum;
}

### Prompt

Generate 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;
long long n, a, b, k, sum, cnt, m;
char s[100007];
const long long mod = 1e9 + 9;
long long po(long long x, long long y) {
  if (y == 0) return 1;
  long long temp;
  temp = po(x, y / 2);
  if (y % 2 == 0)
    return (temp * temp) % mod;
  else
    return (((temp * temp) % mod) * x) % mod;
}
int main() {
  cin >> n >> a >> b >> k;
  for (int i = 0; i < k; i++) cin >> s[i];
  m = (n + 1) / k;
  cnt = 0;
  for (int i = 0; i < k; i++) {
    if (s[i] == '+')
      cnt = (cnt + po(a, n - i) * po(b, i) % mod) % mod;
    else
      cnt = (cnt - po(a, n - i) * po(b, i) % mod + mod) % mod;
  }
  {
    sum = (po(b, k) * po(po(a, mod - 2) % mod, k)) % mod;
    if (sum == 1)
      sum = m;
    else
      sum = (po(sum, m) - 1 + mod) * po(sum - 1, mod - 2) % mod;
    sum %= mod;
  }
  sum = sum * cnt;
  sum += mod;
  sum %= mod;
  cout << sum;
}

```