#include <bits/stdc++.h>
using namespace std;
const int p = 1e9 + 9;
long long powmod(long long a, long long b) {
  long long r = 1;
  while (b) {
    if (b & 1) r = r * a % p;
    a = a * a % p;
    b >>= 1;
  }
  return r;
}
int main() {
  long long n, a, b, k;
  string s;
  cin >> n >> a >> b >> k >> s;
  long long res = 0;
  long long q = powmod(powmod(a, k), p - 2) * powmod(b, k) % p;
  long long mul;
  if (q != 1)
    mul = (1 - powmod(q, (n + 1) / k) + p) % p *
          powmod((1 - q + p) % p, p - 2) % p;
  else
    mul = (n + 1) / k;
  long long A = powmod(a, n), B = 1;
  a = powmod(a, p - 2);
  for (int i = 0; i < k; i++) {
    long long base = A * B % p;
    if (s[i] == '+')
      res = (res + base * mul % p) % p;
    else
      res = (res + p - base * mul % p) % p;
    A = A * a % p;
    B = B * b % p;
  }
  cout << res << endl;
  return 0;
}

### Prompt

Please provide a Cpp coded solution 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 p = 1e9 + 9;
long long powmod(long long a, long long b) {
  long long r = 1;
  while (b) {
    if (b & 1) r = r * a % p;
    a = a * a % p;
    b >>= 1;
  }
  return r;
}
int main() {
  long long n, a, b, k;
  string s;
  cin >> n >> a >> b >> k >> s;
  long long res = 0;
  long long q = powmod(powmod(a, k), p - 2) * powmod(b, k) % p;
  long long mul;
  if (q != 1)
    mul = (1 - powmod(q, (n + 1) / k) + p) % p *
          powmod((1 - q + p) % p, p - 2) % p;
  else
    mul = (n + 1) / k;
  long long A = powmod(a, n), B = 1;
  a = powmod(a, p - 2);
  for (int i = 0; i < k; i++) {
    long long base = A * B % p;
    if (s[i] == '+')
      res = (res + base * mul % p) % p;
    else
      res = (res + p - base * mul % p) % p;
    A = A * a % p;
    B = B * b % p;
  }
  cout << res << endl;
  return 0;
}

```