#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 9;
long long power(long long a, long long n) {
  long long res = 1;
  for (; n; n >>= 1, a = a * a % mod)
    if (n & 1) res = res * a % mod;
  return res;
}
int main() {
  long long n, a, b, k, t = 0;
  char x;
  cin >> n >> a >> b >> k;
  for (long long i = 0; i < k; i++) {
    cin >> x;
    if (x == '+')
      t += power(a, n - i) * power(b, i) % mod;
    else
      t -= power(a, n - i) * power(b, i) % mod;
    t = (t + mod) % mod;
  }
  n = (n + 1) / k;
  b = power(b, k);
  a = power(a, k);
  long long tt = b * power(a, mod - 2) % mod;
  if (tt != 1)
    t = t * (power(tt, n) + mod - 1) % mod *
        power((tt + mod - 1) % mod, mod - 2) % mod;
  else
    t = n * t % mod;
  cout << t;
  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 long long mod = 1e9 + 9;
long long power(long long a, long long n) {
  long long res = 1;
  for (; n; n >>= 1, a = a * a % mod)
    if (n & 1) res = res * a % mod;
  return res;
}
int main() {
  long long n, a, b, k, t = 0;
  char x;
  cin >> n >> a >> b >> k;
  for (long long i = 0; i < k; i++) {
    cin >> x;
    if (x == '+')
      t += power(a, n - i) * power(b, i) % mod;
    else
      t -= power(a, n - i) * power(b, i) % mod;
    t = (t + mod) % mod;
  }
  n = (n + 1) / k;
  b = power(b, k);
  a = power(a, k);
  long long tt = b * power(a, mod - 2) % mod;
  if (tt != 1)
    t = t * (power(tt, n) + mod - 1) % mod *
        power((tt + mod - 1) % mod, mod - 2) % mod;
  else
    t = n * t % mod;
  cout << t;
  return 0;
}

```